cooperative motion and task planning under …introduction nominal scenario recon guration...

Introduction Nominal Scenario Reconfiguration Multi-agent Summary

Cooperative Motion and Task PlanningUnder Temporal Tasks

Meng Guo

Automatic Control Lab EESRoyal Institute of Technology KTH Sweden

Licentiate Seminar

Meng Guo Licentiate Seminar 1


IntroductionMotivationBackground

Nominal ScenarioProblem FormulationNominal Solution

Reconfiguration

Motion and ActionPotentially Infeasible TaskPartially-known Workspace

Multi-agentDependent Local TasksIndependent Local Tasks

SummarySummary



MotivationIndustrial and domestic robots1 boosted by

I Development of digital processing unitsbull more powerful in speed and capacity

bull more affordable

I Wireless communication technologybull potentially connects the robots

bull integrates with other ldquosmartrdquo devices

1Gostai Roomba Romo Amigo service robotsMeng Guo Licentiate Seminar 3









Motivation

I Imagine several care robots in your house

bull ldquoAmigo go to the kitchen find anapple and bring it to merdquo

bull ldquoGostai keep an eye on the kids inthe living room and bedroomrdquo

bull ldquoAmigo put all the toys in thebasketrdquo

bull middot middot middot



Motivation








Motivation








Motivation








Challenges

Challenges for system engineers (us)

I Provide the non-expert end-users

bull a formal but flexible way to specify daily tasks

bull task execution status as feedback

I Design algorithms for robots that

bull synthesize and execute a plan to satisfy the task

bull without or with minimal human intervention

bull accommodate changes in the workspace

bull initiate communication with other devices

bull handle collaborative tasks



Challenges


I Provide the non-expert end-usersbull a formal but flexible way to specify daily tasks










Challenges




I Design algorithms for robots thatbull synthesize and execute a plan to satisfy the task







Challenges











Background

I Motion and task planning

bull motion plan of dynamic systems2

bull task plan for discrete-event systems3

I Model checkingbull for verification4

bull for plan synthesis

2S M LaValle Planning algorithms 20063M Ghallab et al Automated planning theory amp practice 20044C Baier J-P Katoen Principles of model checking 2008



Background

I Motion and task planningbull motion plan of dynamic systems2







Background








Background




bull for plan synthesis2S M LaValle Planning algorithms 20063M Ghallab et al Automated planning theory amp practice 20044C Baier J-P Katoen Principles of model checking 2008



Multi-agent System

I Multi-agent system to solve a global task

bull decompose into sub-tasks

bull top-down tightly-coupled

I Multi-agent system with local tasks

bull favour individual interests

bull bottom-up loosely-coupled



Main Contributions

I Reconfiguration for single- and multi-agent systemsbull M Guo K H Johansson and D V Dimarogonas Motion and Action

Planning under LTL Specification using Navigation Functions andAction Description Language IROS Japan 2013

bull M Guo and D V Dimarogonas Reconfiguration in Motion Planningof Single- and Multi-agent Systems under Infeasible Local LTLSpecifications CDC Italy 2013

I Real-time adaptation for single- and multi-agent systemsbull M Guo K H Johansson and D V Dimarogonas Revising Motion

Planning under Linear Temporal Logic Specifications in PartiallyKnown Workspaces ICRA Germany 2013

bull M Guo and D V Dimarogonas Distributed Plan Reconfiguration viaKnowledge Transfer in Multi-agent Systems under Local LTLSpecifications ICRA Hongkong 2014

bull M Guo and D V Dimarogonas Multi-agent Plan Reconfigurationunder Local LTL Specifications IJRR Submitted





Reconfiguration



SummarySummary



Motion Abstraction

I Abstracted as the weighted finite transition system (FTS)

Tc = (Π minusrarrc Π0 AP Lc Wc)

where the finite regions Π = π1 π2 middot middot middot πW

bull properties of interest AP = APr capAPpbull Π0 initial states

bull minusrarrcsube ΠtimesΠ control-driven transition

bull Lc Π rarr 2AP labelling function

bull Wc ΠtimesΠ rarr R+ weight function

I Examples

1

2 3

4



Motion Abstraction



where the finite regions Π = π1 π2 middot middot middot πW bull properties of interest AP = APr capAPpbull Π0 initial states




I Examples

1

2 3

4



Abstraction Outcome



Temporal Task Specification

How to formally specify the task

I Language Linear-time Temporal Logic (LTL) formula

I Syntax

ϕ = True | a | ϕ1 or ϕ2 | notϕ | copy ϕ | ϕ1 Uϕ2

I Semantics5

I Specified over AP

I To specify control tasks

bull Safety notϕ1 Order diams(ϕ1 and diams(ϕ2 and diamsϕ3))

bull Response ϕ1 rArr ϕ2 Liveness diamsϕ1

5C Baier J-P Katoen Principles of model checking 2008Meng Guo Licentiate Seminar 12





I Syntax


I Semantics5

I Specified over AP






Task Interpretation

I ldquogo to the kitchen find anapple and bring it to merdquo

I ldquokeep an eye on the kids inthe living room andbedroomrdquo

I ldquoput all the toys in thebasketrdquo

I middot middot middot

I ϕ =diams((Kitand PickApp)anddiams(Liv)

)

I ϕ = diamsLiv anddiamsBed

I ϕ = diams

(PickToyrarr(

notPickToy U (Bas and

DropToy)))




Task Interpretation






)I ϕ = diamsLiv anddiamsBed

I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation

Given the FTS Tc and the LTL task ϕ

I Synthesize a discrete plan that satisfies ϕ

I Construct the hybrid control strategy to execute thederived plan

r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Nominal Solution Outline

I Automata-based model-checking algorithm6

I Hybrid controller synthesis7

6C Baier J-P Katoen Principles of model checking 20087G E Fainekos et al Temporal logic motion planning for dynamic

robots Automatica 2009Meng Guo Licentiate Seminar 15


Step 1 Translation

I Translate ϕ into the Nondeterministic Buchi automaton(NBA) Aϕ over 2AP

Aϕ = (Q 2AP δ Q0 F)

q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4

nota4a1 amp a2 amp a3 amp nota4

a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp a3 amp nota4

q0

bull Q is a finite set of states

bull 2AP are alphabets

bull δ sube Qtimes 2AP timesQ

bull Q0 F are initial accepting states

bull χ(qm qn) = l isin 2AP | (qm l qn) isin δ

I Automated

I Fast translation algorithm8

8D Oddoux P Gastin LTL2BA software 2009Meng Guo Licentiate Seminar 16


Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 2 Product Automaton

I Construct the weighted product automaton Ap = Tc otimesAϕ

Ap = (Qprime δprime Qprime0 F prime Wp)

where Qprime = ΠtimesQ Qprime0 = Π0 timesQ0 F prime = ΠtimesFbull δprime sube QtimesQ where (〈πi qm〉〈πj qn〉) isin δprime iff (πi πj) isinminusrarrc

and (qm Lc(πi) qn) isin δ

bull Wp δprime rarr R+ Wp((〈πi qm〉〈πj qn〉)) = Wc(πi πj)

I Algorithms

bull static construction

bull on-the-fly construction









I Algorithms





Plan Structure and Cost

I Accepting run R of Ap with the prefix-suffix structure

R = Rpre (Rsuf)ω = qprime0 q

prime1 middot middot middot qprimefminus1

[qprimef q

primef+1 middot middot middot qprimen

]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0

Wp(qprimei qprimei+1) + γ

nminus1sumi=f

Wp(qprimei qprimei+1)



Step 3 Graph Search

I Algorithm based on Nested-Dijkstra shortest path

bull shortest path from every qprime0 isin Qprime0 to every qprimef isin F prime

bull shortest cycle from qprimef and backP_FFP_IF

I The derived accepting run Ropt with minimal cost

I Corresponding plan τ = Ropt|Π

I Complexity O(|δprime| middot log2 |Qprime| middot (|Qprime0|+ |F prime|))



Step 3 Graph Search









Step 4 Hybrid Control Strategy

To execute τ = Ropt|Π using U(x(t) πi πj)

I generate an infinite execution with finite representation

I monitor the execution status

I record past motions

r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω



Shortcomings of Nominal Solution

I Reconfiguration

bull plan as sequence of motion (no actions)

bull feasible task

I Real-time adaptation

bull fully-known workspace

bull plan synthesized once off-line

bull executed regardless of the real observation


bull independent or dependent tasks

bull communication

bull collaborative tasks




I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary



Motion and Action Planning

Motion Planning

Geometric Constrains

Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic

I Why is it necessarybull to automate the choice of actions

bull plan as sequence of motion and actions

I Why plan motion and action togetherbull the purpose of ldquogoing somewhererdquo is to ldquodo somethingrdquo

I Why model motion and action separatelybull robotrsquos mobility depend on the workspace structure

bull robotrsquos capable actions relatively fixed



Model of Mobility and Action

I Mobility abstraction is given by (similarly as Tc)

M = (ΠM actM minusrarrM ΠM0 ΨM LM WM)

I Capable action set ActB = actB0 actB1 middot middot middot actBKI Precondition function

Cond ActB times 2Ψp times 2Ψs minusrarr TrueFalse

I Effect function

Eff ActB times (2Ψs timesΨb) minusrarr (2Ψs timesΨb)

I Mimic action description language (ADL)



Model of Complete Functionalities

hellip

|||

M

Bhellip

R

I Complete functionalities by composing M and B

R = (ΠR ActR minusrarrR ΠR0 ΨR LR WR)

I Automated algorithm



Results

I Much richer task specifications

I Given ϕ over robot motion action and internal states

I Accepting run with prefix-suffix structure with similardefinition for cost

I Plan as a sequence of motion and action minimal cost

I Construct the hybrid controller accordingly

r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG

c3 c2 r2Drop c2 r5PickR

c2 r2Drop c2 c1(r1)ω



Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Potentially Infeasible Task

I Def 26 ϕ is infeasible for Tc if no accepting run of Ap canbe found

I Closely related to partially-known workspace

I Examplebull ldquogo to the kitchen find an apple and bring it to merdquo

rArr infeasible if no apple

bull ldquokeep an eye on the kids in the living room and bedroomrdquorArr infeasible if not known where the bedroom is

I Nominal solution fails

I Our goal

bull synthesize the plan satisfying the task partially

bull user-defined balance on satisfiability and cost of the plan










I Our goal












I Our goalbull synthesize the plan satisfying the task partially




Solution

I Relaxed product automaton Ar = TctimesAϕ

Ar = (Qprime 2AP δprime Qprime0 F prime Wr)

where Qprime = ΠtimesQ Qprime0 = Π0 timesQ0 F prime = ΠtimesF

bull δprime sube Qprime timesQprime (〈πi qm〉〈πj qn〉) isin δprime iff (πi πj) isinminusrarrc andexist l isin 2AP such that (qm l qn) isin δ

bull Wr δprime rarr R+ is the weight function

Wr(〈πi qm〉〈πj qn〉)= Wc(πi πj) + α middot Dist(L(πi) χ(qm qn))

I α ge 0 user-defined balance



Solution










Balanced Cost

I Accepting run R with prefix-suffix structure

R = qprime0 qprime1 middot middot middot [ qprimef qprimef+1 middot middot middot qprimen ]ω

= 〈π0 q0〉〈π1 q1〉 middot middot middot [ 〈πf qf 〉 middot middot middot 〈πn qn〉 ]ω

I The balanced cost of an accepting run

Cost(R Ar) =

fminus1sumi=0

Wr(qprimei qprimei+1) + γ

nminus1sumi=f

Wr(qprimei qprimei+1)

= costτ + α middot distϕ

I costτ implementation cost distϕ distance to ϕ

I distϕ = 0rArr R|Π |= ϕ



Results

I The balanced accepting run

Rbal = minR

Cost(R Ar)

I The balanced plan τbal = Rbal|Π

I Proposed algorithms

bull synthesize Rbal given γ and α

bull computes the associated costτ and distϕ for τbal

I Theorem 31 If ϕ is feasible over Tc the balanced plan τbal

satisfies ϕ if α gt α



Results


Rbal = minR

Cost(R Ar)

I The balanced plan τbal = Rbal|ΠI Proposed algorithms







Feedback by Tuning αI α tunable balance between costτ and distϕ

bull α uarr rArr distϕ darr rArr satisfy ϕ more

bull α darr rArr costτ darr rArr cheaper

I Example ϕ = diamsa1 andnot(a2 and a3)

π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1

not a2 amp not a3 not a2 amp not a3

q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110

120Cost of the Optimal Accepting Path

To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n

Potential Motion Plans

Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)



Soft and Hard Specification

I Specification with two distinctive parts

ϕ = ϕhard and ϕsoft

I ϕhard for safety or securitybull ldquodo not go to the balconyrdquo ldquoalways alarm if see firerdquo

I ϕsoft for additional achievement (maybe infeasible)bull ldquocollect the toys in all roomsrdquo


I Our goal

bull synthesize the plan satisfies ϕhard completely and ϕsoft

partially










I Our goal


partially










I Our goalbull synthesize the plan satisfies ϕhard completely and ϕsoft

partially




SolutionI Relaxed intersection of Asoft and Ahard as Aϕ by Alg 9


I Safety-ensured and relaxed product automaton

Ar = TctimesAϕ = (Qprime δprime Qprime0 F prime Wr)


bull δprime Qprime rarr 2Qprime 〈πj qn〉 isin δprime(〈πi qm〉) iff (πi πj) isinminusrarrc and

qn isin δ(qm Lc(πi))


Wr(〈πi qm〉〈πj qn〉)=Wc(πi πj) + α middot Dist(Lc(πi) χsoft(q2 q2))














Results

I Theorem 33 Assume R is an accepting run of Arτ = R|Π is safe for Tc and ϕ

I Balanced cost of accepting runs

Cost(R Ar) = costτ + α middot distϕsoft

I The safe accepting run

Rsafe = minR

Cost(R Ar)

I The safe plan τsafe = Rsafe|ΠI Similar algorithms to synthesize Rsafe

I Lemma 32 distϕsoft = 0rArr τsafe |= ϕ



Results





Rsafe = minR

Cost(R Ar)





On-line Planning

Why put planner on-line

I To handle partially-knownworkspace

I Plan may not be executedas expected

I Plan could be improved

I Feed real-time observationback to planner



Problem Formulation

I The agentrsquos FTS at time t ge 0

T tc = (Π minusrarrtc Π0 AP L

tc W

tc )

I Task specification

ϕ = ϕsoft and ϕhard

I Our goal

bull model the robotrsquos sensing

bull update the system model

bull guarantee the plan is always valid and safe



Solution Framework



Initial Synthesis and System Update

I Step 1 initial synthesis at t = 0

bull τ0 obtained for feasible or infeasible task

bull starts executing τ0

I Step 2 knowledge update at t ge 0

bull sensing information obtained

Senset = ((π S Snot) E Enot)

I Step 2 update T tc based on Senset























Plan Verification and Revision

I Step 3 validate the current planbull validity lArrrArr invalid transitions

bull safety lArrrArr unsafe transitions

I Step 4 local revision instead of full synthesis

I Low complexity suitable for real-time applications

I Theorem 35 validity and safety of the revised planguaranteed



















Simulation Example

I Nonholonomic ground vehicle

I Potential filed-based navigation controller9

I Surveillance over regions 2 3 4

I Detect walls and obstacles in real-time

1

23

5

6

7

9

10

11

12

8

4

1

2 3

4

9S R Lindemann I I Hussein S M LaValle Real time feedbackcontrol for nonholonomic mobile robots with obstacles CDC 2006





Reconfiguration



SummarySummary



Dependent Local Tasks

I System of N agents i = 1 middot middot middot N

Ti = (Πi minusrarri Πi0 APi Li Wi)

I Locally-assigned LTL specification by ϕi

I ϕi may contain requirements on other agents j 6= i

bull constraints eg ldquodo not be in the same room with agent 1rdquo

bull collaborations eg ldquomove the desk together with agent 1rdquo

I Difficultiesbull the joined execution may not be mutually feasible even

though the individual one is

bull the priority of each agent plays an important role















Dependency Cluster

I Dependency Agents i and j are called dependent if

Θ3

Θ2

Θ1

Θ4

(1) agent i depends on agent j ifAPϕi

andAPj 6= empty or

(2) agent j depends on agent i ifAPϕj

andAPi 6= empty

I Dependency graph Gd = (V E) V = 1 2 middot middot middot N andE sube V times V is the dependency relation

I Dependency cluster Θ sube V foralli j isin Θ there is a path fromi to j in Gd



Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible

Within one cluster Θ = 1 2 middot middot middot MI The composed FTS TΘ = T1 times middot middot middot TM is

TΘ = (ΠΘ minusrarrΘ ΠΘ0 APΘ LΘ WΘ)

I The mutual specification is

ϕΘ = ϕ1 and ϕ2 middot middot middot and ϕM

I Mutually infeasible if ϕΘ is infeasible over TΘ

I The relaxed intersection of Aϕi of ϕi i isin Θ

AϕΘ = (Q 2APϕΘ δ Q0 F)



Mutual Infeasible










Solution

I The relaxed product automaton

ArΘ = TΘ times AϕΘ = (Qprime δprime Qprime0 F prime Wr)

where Qprime = ΠΘ timesQ Qprime0 = ΠΘ0 timesQ0 F prime = ΠΘ timesF

bull δprime sube Qprime timesQprime (〈πΘ qa〉〈πprimeΘ qb〉) isin δprime iff (πΘ π

primeΘ) isinminusrarrΘ

and (qa qb) isin δ


Wr(〈πΘ q1 middot middot middot qM t〉〈πprimeΘ q

prime1 middot middot middot qprimeM tprime〉)

= WΘ(πΘ πprimeΘ) + α

Msumi=1

βi Dist(LΘ(πΘ) χi(qi qprimei))

I α penalty on violating ϕΘ

I βi priority of agent irsquo task



Solution



where Qprime = ΠΘ timesQ Qprime0 = ΠΘ0 timesQ0 F prime = ΠΘ timesFbull δprime sube Qprime timesQprime (〈πΘ qa〉〈πprime

Θ qb〉) isin δprime iff (πΘ πprimeΘ) isinminusrarrΘ

and (qa qb) isin δ





Msumi=1






Results

I Synthesize the balanced accepting run of ArΘI Projection onto Ti as the individual plan i isin Θ

I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)

Unique Optimal Accepting Paths

0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Independent Local Tasks

I System of N agents coexisting within a partially-knownworkspace

T ti = (Πi minusrarrti Πi0 APi L

ti W

ti )

I Locally-assigned task specification and independent

ϕi = ϕsofti and ϕhard

i

I Motivation

bull agents located at various locations within the workspace

bull observe up-to-date information

bull beneficial to communicate






ti W

ti )



i

I Motivation






Knowledge Update and Transfer

I Knowledge update bybull own sensing ability Sensetk = (π S Snot) E Enotbull communication with others

I Communication network Nk isin N (static or dynamic)

I Transfer knowledge

bull request once Requesttkg = (k ϕk|APk)

bull event-based reply Replythk = (π Sprime Sprimenot) where

Sprime = S cap (ϕh|APh) and Sprime

not = Snot cap (ϕh|APh)

I Update T tk based on Sensetk and Replytgk

I Validate and revise the current plan















Results

I Full synthesis or local revision

I Event-based trigger to re-synthesize the plan

0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]

Ar_1Ar_2Ar_3Ar_4Ar_5

0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s


Gw_1Gw_2Gw_3Gw_4Gw_5

Gf_1Gf_2Gf_3Gf_4Gf_5



Software ImplementationI Robot operating system(ROS)-based

I ROS core + ROS nodes

I ROS node for planning



Experiments

I NAO humanoid

I MAS Lab CVAP

I NEXUS ground vehicle

I Smart Mobility Lab ACL





Reconfiguration



SummarySummary



Summary

I Motion and task planningbull Discrete motion and task plan with minimal costbull Hybrid control strategy

I Reconfiguration and real-time adaptationbull Potentially infeasible taskbull Soft and hard specificationsbull Partially-known workspacebull Motion and action planning

I Multi-agent systems with local tasksbull Dependent tasksbull Independent tasksbull Software implementation



Summary






Summary






Future Work

I Automated abstraction

I Natural language to LTL graphic interface

I Trade-off between computational complexity andoptimality

I Robustness and fault tolerance (both motion and action)

I Continuous constraints coupled dynamics



Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action


Partially-known Workspace

Multi-agent



Summary

Summary




Reconfiguration



SummarySummary

















Motivation








Motivation








Motivation








Motivation








Challenges













Challenges












Challenges











Challenges











Background









Background








Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary
















Motivation








Motivation








Motivation








Motivation








Challenges













Challenges












Challenges











Challenges











Background









Background








Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Motivation








Motivation








Motivation








Challenges













Challenges












Challenges











Challenges











Background









Background








Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Motivation








Motivation








Challenges













Challenges












Challenges











Challenges











Background









Background








Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Motivation








Challenges













Challenges












Challenges











Challenges











Background









Background








Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Challenges













Challenges












Challenges











Challenges











Background









Background








Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Challenges












Challenges











Challenges











Background









Background








Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Challenges











Challenges











Background









Background








Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Challenges











Background









Background








Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Background









Background








Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Background








Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Background








Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Background







Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Multi-agent System









Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Main Contributions












Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary




Reconfiguration



SummarySummary



Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Motion Abstraction








I Examples

1

2 3

4



Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Motion Abstraction







I Examples

1

2 3

4



Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Abstraction Outcome






I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary





I Syntax


I Semantics5

I Specified over AP









I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary





I Syntax


I Semantics5

I Specified over AP






Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Task Interpretation






)


I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Task Interpretation







I ϕ = diams

(PickToyrarr(


DropToy)))




Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000



Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Problem Formulation




r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

0 500 1000 1500 20000

500

1000

1500

2000









Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary








Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated




Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Step 1 Translation



q1

q2

q3

q1q1 nota4

a1 amp nota4

nota4

a2 amp nota4

nota4

a1 amp nota4

a2 amp a3 amp nota4


a3 amp nota4

a1 amp a2 amp nota4

a1 amp a2 amp nota4


q0






I Automated










I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary








I Algorithms











I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary








I Algorithms









[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary






[qprimef q


]ω

I The total cost

Cost(R Ap) =

fminus1sumi=0


nminus1sumi=f




Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Step 3 Graph Search









Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Step 3 Graph Search














r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary







r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω




I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary



I Reconfiguration


bull feasible task







bull communication





I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary



I Reconfiguration


bull feasible task







bull communication






Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary




Reconfiguration



SummarySummary




Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary



Motion Planning


Workspace Model

Model-checking

TaskAction Planning

Discrete Planning

PropositionalLogic













I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary







I Effect function






hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary



hellip

|||

M

Bhellip

R






Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG





Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Results






r1 c1 c2 c3 r3

c3 c2 r2 c2 r5

c2 r2 c2 c1(r1)ω

r1 c1 c2 c3 r3PickG












I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary









I Our goal












I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary









I Our goal
















Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary













Solution










Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Solution










Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Balanced Cost





Cost(R Ar) =

fminus1sumi=0


nminus1sumi=f







Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Results


Rbal = minR

Cost(R Ar)









Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Results


Rbal = minR

Cost(R Ar)












π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary






π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)







π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary






π1

π2

π3

a2a3

a1

a2

30

40 20

10Φ

π0 a1qq1

a1


q05 5

0 5 10 15 20 25 3030

40

50

60

70

80

90

100

110


To

tal C

ost

by

(7)

30 40 50 60 70 80 900

1

2

3

4

5

6

7

8

Implementation Cost

Dis

tan

ce t

o S

pec

ific

atio

n


Plan1 (0)

Plan2 0

1(

3)

Plan3 0

2(

3)









I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary








I Our goal


partially










I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary








I Our goal


partially











partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary









partially


























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary
























Results





Rsafe = minR

Cost(R Ar)





Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Results





Rsafe = minR

Cost(R Ar)





On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


On-line Planning








Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Problem Formulation



tc W

tc )



I Our goal






Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Solution Framework

























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary
























































Simulation Example





1

23

5

6

7

9

10

11

12

8

4

1

2 3

4






Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary




Reconfiguration



SummarySummary



























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


























Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Dependency Cluster


Θ3

Θ2

Θ1

Θ4


andAPj 6= empty or


andAPi 6= empty





Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Mutual Infeasible










Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Mutual Infeasible










Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Solution






and (qa qb) isin δ





Msumi=1






Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Solution





and (qa qb) isin δ





Msumi=1






Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2



Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Results


I Change α and β

I Example

0 1 2 3 4 5 6 7 8 9 100

2

4

6

8

10

12

14

16

18

20

2 (

1=1)


0 05 1 15 2 25 3 35 4 45 50

05

1

15

2

25

3

35

4

6

Distance to 1


10

2028

24

36

Dis

tan

ce t

o

2






ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary





ti W

ti )



i

I Motivation









ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary





ti W

ti )



i

I Motivation






























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


























Results



0 20 40 60 80 100Time (s)

0

1000

2000

3000

4000

5000

6000

Tota

l Cos

t

[5522]

[3319]

[3132]

[139]

[139]

[5522]

[3319]

[1134]

[341]

[241]

[139]

[7512]

[0318]

[3130]

[139]

[6520]

[0227]

[0135]

[139]

[8520]

[2133]

[240]

[139]


0 10 20 30 40 50 60Time

0

2

4

6

8

10

12

14

o

f Mes

sage

s











Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary







Experiments

I NAO humanoid

I MAS Lab CVAP







Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary




Reconfiguration



SummarySummary



Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Summary






Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Summary






Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Summary






Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Future Work








Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary


Thank you


Introduction

Motivation

Background

Nominal Scenario

Problem Formulation

Nominal Solution

Reconfiguration

Motion and Action



Multi-agent



Summary

Summary

cooperative motion and task planning under …introduction nominal scenario recon guration...

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