coordination control of multiple mobile robots -...

Coordination Controlof Multiple Mobile Robots

Filippo Arrichiello

webuser.unicas.it/arrichiello

Universita degli Studi di Cassino

PHILOSOPHIAE DOCTOR in

Electrical and Information Engineering

November 2006

Filippo Arrichiello PhD Thesis: Coordination Control of Multiple Mobile Robots – p. 1/31

http://webuser.unicas.it/arrichiello

Outline

→ Introduction on Multi-Robot Systems

→ The Null-Space-based Behavioral control (NSB)

→ NSB for the control of a team of grounded mobile robots

→ NSB for the control of a fleet of marine surface vessels

→ NSB for the control of a team of mobile antennas

→ Conclusions


Motivations

→ Increasing the mission efficiency

→ Performing tasks not executable by a single robot

→ Tolerance to possible vehicles’ faults

→ Increasing the flexibility of tasks’ execution

→ Advantages of distributed sensing and actuation


Applications

→ Explorations

→ Box-pushing

→ Localization and Mapping

→ Rescue Operations

→ Military Tasks

→ Entertainment (e.g., Robocup)


Vehicles’ typologies

→ Grounded Mobile Robots

→ Marine robots

→ Aerial Vehicles


Approcci comportamentali

→ Biological Inspiration

→ Making the robots

behave like animals


Behavioral approaches

Composition of the behaviors:




Competitive approaches selective activation of the behaviors





Cooperative approaches the behaviors are combined with proper weights






Null-Space-Based approach Following the task priority inverse kinematics, a

hierarchy-based technique is adopted based on null-space projection






Null-Space-Based approach Following the task priority inverse kinematics, a

hierarchy-based technique is adopted based on null-space projection The

NSB behavioral control differs from the other behavioral approaches in

the way it combines multiple behaviors


NSB control

→ The mission is decomposed in elementary behaviors or tasks


NSB control


→ For each elementary behavior a task function is properly defined

σ = f(p1, . . . ,pn)

σ =n∑

i=1

∂f(p)

∂pi

vi = J(p)v


NSB control


→ For each elementary behavior a task function is properly defined

σ = f(p1, . . . ,pn)

σ =n∑

i=1

∂f(p)

∂pi

vi = J(p)v

and a motion reference command to each vehicle is elaborated

vd = J†(σd + Λσ

)σ = σd−σ


NSB: Merging different tasks

→ To simultaneously handle different, eventually conflicting, tasks the NSB

adopts a singularity-robust task priority inverse kinematics technique

vd = J†p

(σp,d + Λpσp

)

︸︷︷︸+

(I − J†

pJp

)

︸︷︷︸J†

s

(σs,d + Λsσs

)

︸︷︷︸primary null-Space secondary


NSB: Merging different tasks

→ To simultaneously handle different, eventually conflicting, tasks the NSB

adopts a singularity-robust task priority inverse kinematics technique

vd = J†p

(σp,d + Λpσp

)

︸︷︷︸+

(I − J†

pJp

)

︸︷︷︸J†

s

(σs,d + Λsσs

)

︸︷︷︸primary null-Space secondary

→ Three-task example:

vi = J†i

(σi,d + Λiσi

)(i = 1, 2, 3)

vd = v1 +(I − J

†1J1

) [v2 +

(I − J

†2J2

)v3

]


Implementation aspectsNSB

NSB + Vehicles’ Control


Multi-robot: elementary behaviors

Definition of the task functions: “Barycenter”

σb = f b (p1, . . . , pn) =1

n

n∑

i=1

pi

σb =n∑

i=1

∂f b (p)

∂pi

vi = J b (p) v

J b =1

n

1 0

0 1. . .

1 0

0 1

J

†b = nJT

b

vb = J†b

(σb,d + Λbσb

)



Definition of the task functions: “Rigid Formation”

σf =

p1 − pb

...

pn − pb

vf = JfΛf σf

Jf =

A O

O A

A =

1− 1

n− 1

n. . . − 1

n

− 1

n1− 1

n. . . − 1

n

......

. . ....

− 1

n− 1

n. . . 1− 1

n

J†f = Jf



Definition of the task functions: “Obstacle Avoidance”

The obstacle avoidance task function is built individually to each vehicle, i.e., it

is not an aggregate task function

σo = ‖p − po‖ σo,d = d Jo = rT J†o = r

po: obstacle position

d: safe distance

r=p−p

o

‖p−po‖ : unit vector

of the obstacle-to-vehicle direction

vo = J†oλoσo = λo

(d − ‖p−po‖

)r

N (Jo) = I − rrT


Team of wheeled mobile robots

→ Platoon of 7 Khepera II

→ Differential-drive mobile robots

→ Each robot has a Bluetooth turret


Experimental set-up


ExperimentsMission 1: Obstacle-Barycenter-Linear Formation

Movie 1


ExperimentsMission 1: Mission steps

0 50 100 150−50

0

50

100

150

t = 27.58

0 50 100 150−50

0

50

100

150

t = 28.72

0 50 100 150−50

0

50

100

150

t = 29.93

0 50 100 150−50

0

50

100

150

t = 31.06

0 50 100 150−50

0

50

100

150

t = 32.29

0 50 100 150−50

0

50

100

150

t = 33.43

0 50 100 150−50

0

50

100

150

t = 34.53

0 50 100 150−50

0

50

100

150

t = 36.1

Movie 1


ExperimentsMission 1: Barycenter and rigid formation task function errors

0 10 20 300

20

40

60

80

100

[s]

[cm

]

0 10 20 300

20

40

60

80

100

[s]

[cm

]Movie 1


ExperimentsMission 2: Obstacle-Barycenter-Circular Formation

Movie 2


ExperimentsMission 2: Mission steps

t = 0 t = 5.9 t = 12.17 t = 18.49

t = 24.99 t = 31.19 t = 37.56 t = 43.46

t = 49.58 t = 55.69 t = 61.83 t = 67.84

Movie 2


ExperimentsMission 2: Paths of the robots

0 50 100 150−50

0

50

100

150

X[cm]

Y[c

m]

Movie 2


ExperimentsMission 2: Barycenter and Rigid Formation task function errors

0 20 40 600

20

40

60

80

100

[s]

[cm

]

0 20 40 600

50

100

150

[s]

[cm

]Movie 2


ExperimentsMission 3: Escorting/Entrapment mission

Movie 3


Feet of marine vessels

→ Navigation in formation

→ Autonomous navigation systems

→ Harbor operations


Guidance system

→ Supervisor: Null-Space-based Behavioral control

→ Maneuvering control


Single-vessel modelling

Kinematics

n

e

U

ψ

u

v

χ

β{B}

ν = (u v r )T linear and

angular velocity in surge-sway-

yaw BODY components

η = (n e ψ )T position and

orientation in the NE-plane

η=R(ψ) ν



Dynamics

Mν + N (ν)ν = τ + RT(ψ) w

Inertial Parameters

Hydrodynamic Effects

Environmental Disturbances:

- Wind

- Waves

- Current



Actuation System

→ Two main thrusters

→ One tunnel thruster (for low-speed maneuvers)



Actuation System

Main Propellers

Tunnel thrusters

F1

F2

F3

{BODY }

0 1 2 30

1

2

3

4

x 104 b

u

τ2,m

ax

Fully-Actuated Under-Actuated

τ =

F1 + F2

F3

τ3(F1, F2, F3)

τ =

F1 + F2

0

τ3(F1, F2)


Maneuvering control

τ = Mα + Nα − RT w − hk1z1 − K2z2


Maneuvering control

τ = Mα + Nα − RT w − hk1z1 − K2z2

α =

UNSB cos(βNSB)

α2

ψNSB−z1

βNSB = χNSB − ψ

α2 =

{UNSB sin(βNSB) [FA]

tale che τ2 =0 [UA]


Maneuvering control

τ = Mα + Nα − RT w − hk1z1 − K2z2

α =

UNSB cos(βNSB)

α2

ψNSB−z1

βNSB = χNSB − ψ

α2 =

{UNSB sin(βNSB) [FA]

tale che τ2 =0 [UA]

z1 = ψ−ψNSB k1 > 0

z2 = ν−α K2 > 0

˙w = ΓR z2 Γ =Γ T > 0

h =

0

0

1


Case studies

Mission 1

−200 0 200 400 600 800 1000−500

−400

−300

−200

−100

0

100

200

300

400

500

e[m]

n[m

]

−200 0 200 400 600 800 1000−500

−400

−300

−200

−100

0

100

200

300

400

500

e[m]

n[m

]

−200 0 200 400 600 800 1000−500

−400

−300

−200

−100

0

100

200

300

400

500

e[m]

n[m

]

−200 0 200 400 600 800 1000−500

−400

−300

−200

−100

0

100

200

300

400

500

e[m]

n[m

]

Simulation 1


Case studies

Mission 1

0 200 400 600 800 1000−150

−100

−50

0

50

100

150

σ f

t[s]

d

0 500 1000 1500 2000−10

0

10

20

30

40

σ b

t[s]

c

0 200 400 600 800 1000−5

0

5

10

15

20

25

30

σ o

t[s]

b

0 500 1000−500

0

500

e[m]

n[m

]

a

Simulation 1


Case studies

Mission 1

0 500 1000 1500 2000 2500−3

−2

−1

0

1

2

3x 10

4

t[s]

τ [N

]

a)

0 500 1000 1500 2000 2500−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5

t[s]

θ [r

ad

]

b)

Simulation 1


Case studies

Mission 2

−200 0 200 400 600 800 1000−500

−400

−300

−200

−100

0

100

200

300

400

500

e[m]

n[m

]

−200 0 200 400 600 800 1000−500

−400

−300

−200

−100

0

100

200

300

400

500

e[m]

n[m

]

−200 0 200 400 600 800 1000−500

−400

−300

−200

−100

0

100

200

300

400

500

e[m]

n[m

]

−200 0 200 400 600 800 1000−500

−400

−300

−200

−100

0

100

200

300

400

500

e[m]

n[m

]

Simulation 2


Case studies

Mission 2

0 200 400 600 800 1000−60

−40

−20

0

20

40

60

σ f

t[s]

d

0 500 1000 1500 2000−20

−15

−10

−5

0

5

10

15

σ b

t[s]

c

0 200 400 600 800 10000

5

10

15

20

25

30

σ o

t[s]

b

0 500 1000−500

0

500

e[m]

n[m

]

a

Simulation 2


Case studies

Mission 2

0 500 1000 1500 2000 2500−3

−2

−1

0

1

2

3

4

5x 10

4

t[s]

τ [N

]

a)

0 500 1000 1500 2000 2500−3

−2

−1

0

1

2

t[s]

θ [r

ad

]

b)

Simulation 2


Team of mobile antennas

base station

mobile antennas

agent

→ Mobile Ad-hoc NETworks (MANET)

→ To guarantee coverage of an autonomous vehicle

→ Platoon of robots carrying repeater antennas


MANET

antennadmin

dmax

rmax

→ Each antenna has a maximum communication range equal to rmax

→ Each antenna needs to be in a range [dmin, dmax] from the other

antennas


MANETThe task function aimed at ensuring connection of the chain is:

σc =n∑

i=1

σc,i

σc,i =

‖r‖ if ‖r‖≤dmin

0 if dmin <‖r‖<dmax with r = pi−pi−1

‖r‖ if ‖r‖≥dmax

J c,i =

{0 if σc,i =0

rT otherwise .

σd,i =

dmin if ‖r‖≤dmin

0 if dmin <‖r‖<dmax

dmax if ‖r‖≥dmax .


MANET

The tasks are organized in priorities :

1. avoid the obstacles;

2. keep the next antenna in the coverage area;

3. keep the previous antenna in the coverage area.

A supervisor is in charge of detecting when the moving robot is going outside

the maximum MANET coverage and, eventually, modifying the tasks’ priorities

or adding/removing tasks

The virtual chain is organized at each sampling time

Simulations: Obstacles building


Conclusions

→ Introduction to multi-robot systems

→ Description of the Null-Space-based Behavioral (NSB) control for the

control of a generic multi-robot system

→ Implementation of the NSB to control a team wheeled mobile robots

performing several formation control missions with collision avoidance

→ The NSB has been test in simulative case studies while controlling a fleet

of marine surface vessels with a particular actuation system and a team

of mobile antennas


Conclusioni

→ The experimental and simulative results prove the effectiveness and

flexibility of the approach

→ The NSB is well suitable to control several typologies of vehicles

performing different missions

→ The NSB results robust to sensor noise, external disturbances and

non-static environment

→ The NSB results dynamically scalable to the adding or removing a vehicle

from the team during the mission


Publications

Journal Papers:

1. G. Antonelli, F. Arrichiello, S. Chiaverini, The Null-Space-Based Behavioral Control for Autonomous

Robotic Systems, Journal of Intelligent Service Robotics,in press 2007

2. G. Antonelli, F. Arrichiello, S. Chiaverini and R. Setola, Coordinated control of mobile antennas for

ad-hoc networks, International Journal of Modelling, Identification and Control, Special/Inaugural

issue on Intelligent Robot Systems, Vol. 1, No. 1, pp.63-71, 2006

Book Chapters

1. F. Arrichiello, S. Chiaverini and T.I. Fossen, Formation Control of Marine Surface Vessels using the

Null-Space-Based Behavioral Control, In Group Coordination and Cooperative Control

(K.Y.Pettersen, T.Gravdahl, and H.Nijmeijer, Eds.). Lecture Notes in Control and Information

Systems series, Springer-Verlag, pp.1-19, 2006


Publications

International Conference Papers (with review):

11. G. Antonelli, F. Arrichiello, S. Chakraborty and S. Chiaverini, Experiences of formation control of

multi-robot systems with the Null-Space-based Behavioral Control, Proceedings 2007 IEEE

International Conference on Robotics and Automation, Rome, I, 2007.

10. F. Arrichiello, S. Chiaverini and T.I. Fossen, Formation Control of Underactuated Surface Vessels using

the Null-Space-Based Behavioral Control, Proceedings 2006 IEEE/RSJ International Conference on

Intelligent Robots and Systems, Beijing, China, 2006

9. G. Antonelli, F. Arrichiello, S. Chiaverini and K.J. Rao, Preliminary Experiments of Formation Control

using the Null-Space-Based Behavioral Control, 8th IFAC Symposium on Robot Control, Bologna, I,

2006

8. G. Antonelli, F. Arrichiello, S. Chiaverini, Experiments of Formation Control with Collisions Avoidance

using the Null-Space-Based Behavioral Control, 14th Mediterranean Conference on Control and

Automation, Ancona, I, 2006

7. F. Arrichiello, S. Chiaverini, A simulation package for coordinated motion control of a fleet of

under-actuated surface vessels, 5th MATHMOD Conference, Vienna, Austria, 2006


Publications

6. G. Antonelli, F. Arrichiello, S. Chiaverini and R. Setola, Coordinated control of mobile antennas for

ad-hoc networks in cluttered environments, 9th International Conference on Intelligent Autonomous

Systems, Tokyo, J,2006

5. G. Antonelli, F. Arrichiello, S. Chiaverini and R. Setola, A Self-Configuring MANET for Coverage Area

Adaptation through Kinematic Control of a Platoon of Mobile Robots, IEEE/RSJ International

Conference on Intelligent Robots and Systems, Edmonton, CA, pp.1332-1337, 2005

4. G. Antonelli, F. Arrichiello and S. Chiaverini, The Null-Space-Based Behavioral Control for

Soccer-Playing Mobile Robots, 2005 IEEE/ASME International Conference on Advanced Intelligent

Mechatronics, Monterey, CA, pp.1257-1262, 2005

3. G. Antonelli, F. Arrichiello and S. Chiaverini, Experimental kinematic comparison of behavioral

approaches for mobile robots, 16th IFAC World Congress, Praha, CZ, 2005

2. G. Antonelli, F. Arrichiello and S. Chiaverini, The Null-Space-Based behavioral control for mobile robots,

IEEE International Symposium on Computational Intelligence in Robotics and Automation, Espoo,

Finland, pp.15-20, 2005

1. F. Arrichiello, S. Gerbino, How to investigate constraints and motions in assemblies by screw theory,

Proc. of 4th CIRP ICME’04 Int. Conf., Sorrento, I, 2004


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