mul'-robot manipula'on with no communica'on using only...
TRANSCRIPT
![Page 1: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/1.jpg)
MSL
Mul$-RobotSystemsLab
DepartmentofMechanicalEngineering
BostonUniversity
CDC2015,Osaka,Japan
Dec.15,2015
Mul'-RobotManipula'onwithnoCommunica'onUsingOnlyLocalMeasurements
ZijianWangandMacSchwager
![Page 2: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/2.jpg)
MSL1001RobotsMovingaPiano
2
![Page 3: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/3.jpg)
MSLMo$va$on
3
Mul$-RobotManipula$onandTransport
• Transportlargeobjects• Construc$on,manufacturing,disasterrelief
MinimalistApproach• Simpleindividualrobots
• Noexplicitcommunica$on
• Nogloballocaliza$oninforma$on
• Localmeasurements
![Page 4: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/4.jpg)
MSLOurApproach:Overview
4
v
,cx
ixcir
iR
,M J
iF( ), ( )
Q
CoordinatedForces
Uncoordinatedforces
Objectitself“communicates”necessaryinforma$on
![Page 5: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/5.jpg)
MSLRelatedWork
5
Fink,Michael,Kumar
ICRA08
Becker,Habibi,Werfel,
Rubenstein,McLurkin
ICRA13
Caging/ForceClosure EnsembleControl
![Page 6: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/6.jpg)
MSLProblemFormula$on
6
Rigid-bodyDynamics(Planar)
Transla$onal
Rota$onal
Goal
DecentralizedcontrollawforbeingcontrolledFi
J �̇ =N�
i=1
ri � Fi + T1 �µ�
MJ�
v
,cx
ixcir
iR
,M J
iF( ), ( )
Q
![Page 7: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/7.jpg)
MSLControlStrategy
7
• Manyfollowerrobots,oneleader(robotorhuman)
• Followers’forceswilltrackleader’sforceusinglocal
measurementsoftheobject’smo$on
• Leaderusesfeedbackcontrollertosteerthesumforce,and
thennavigatetheobjectthroughthedesiredtrajectory
![Page 8: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/8.jpg)
MSLForceCoordina$onviaConsensus
8
• Linearconsensusalgorithm
• Leader-following(steering)Fixonerobot
x1(t) = x1(0)
Olfa$-Saber,Murray,TAC2004
Jadbabaie,Lin,Morse,TAC2003
![Page 9: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/9.jpg)
MSLPriorWork:
FollowerControlLaw
9
ForceCoordina$onwithoutCommunica$on
Linearconsensuslaw
Sumofforces Newton’sLaw
Z. Wang and M. Schwager, Distributed Autonomous Robotic Systems (DARS), 2014
Requires
measurements
attheC.O.M.of
theobject
![Page 10: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/10.jpg)
MSLLocalMeasurements
10
Ø Measurementat
LocalAgachmentPointsvs.CenterofMass
(thispaper)(priorwork)
Newforcecoordina$onlaw:
HeterogenousLocalMeasurements
![Page 11: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/11.jpg)
MSLMatrixRepresenta$on
11
CentrosymmetricAssump$on
ForceConsensus?
Time-varying
![Page 12: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/12.jpg)
MSLConsensusAnalysis2
12
Ø Consensuswithoutaleader
Proof:useLyapunovTheorem&Barbalat’sLemma
![Page 13: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/13.jpg)
MSLConsensusAnalysis1
13
Ø Time-independentCharacteriza$on
Lemma 3: Time-invariant equilibria
Lemma
Lemma
![Page 14: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/14.jpg)
MSLConsensusAnalysis2
14
Ø Consensuswithoutaleader
Proof:useLyapunovTheorem&Barbalat’sLemma
![Page 15: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/15.jpg)
MSLConsensusAnalysis2
15
Ø Consensuswithoutaleader
−2
−1
0
1
2fx
Average
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−2
−1
0
1
2
Time / s
fy
Average
![Page 16: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/16.jpg)
MSLConsensusAnalysis3
16
Ø Groupforcecontrolvialeaderfollowing
Canshow:equilibrium,eigenvalue(longproof)
![Page 17: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/17.jpg)
MSLConsensusAnalysis3
17
Ø Groupforcecontrolvialeaderfollowing
−2
−1
0
1
2fx
Leader
0 2 4 6 8 10 12 14 16 18 20−2
−1
0
1
2
Time / s
fy
Leader
![Page 18: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/18.jpg)
MSLCentrosymmetry
18
Centrosymmetric Non-Centrosymmetric
![Page 19: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/19.jpg)
MSLRelaxingTheCentrosymmetric
Assump$on
19
• Probleminduced
Changeofequilibrium,eigenvalue.
Introducecentrifugalforce
• Modeltheasymmetryasaperturba$on
![Page 20: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/20.jpg)
MSLSimula$onsinOpenDynamic
Engine(ODE)
20
12Robots,1Leader
1kgRectangularPlank
0.6mx0.2mx0.1m
1001Robots,1Leader
290kgYamahaC1GrandPiano
1.6mx1.5mx1.0m
![Page 21: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/21.jpg)
MSLSummary
21
• Adecentralized,scalablemul$-robotmanipula$onapproach
• Noexplicitcommunica$on
• Nogloballocaliza$oninforma$onforfollowers
• Guaranteefollowers‘forcecoordina$on
• Useonlylocalmeasurements
• Leadersteersthegroup
![Page 22: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/22.jpg)
MSLFutureWork
22
• Rigorousanalysisontheasymmetriccase
• Physicalexperiment[SubmigedtoICRA2016]
• Human-swarminterac$on[SubmigedtoICRA2016]
• Adap$vecontrol
![Page 23: Mul'-Robot Manipula'on with no Communica'on Using Only ...web.stanford.edu/~zjwang/docs/WangSchwager_CDC15_Slides.pdf · Proof: use Lyapunov Theorem & Barbalat’s Lemma ... Proof:](https://reader034.vdocument.in/reader034/viewer/2022051800/5ad3733b7f8b9abd6c8df466/html5/thumbnails/23.jpg)
MSL
Q&A
Thankyou!
Mul'-RobotManipula'onwithnoCommunica'onUsingOnlyLocalMeasurements
ZijianWangandMacSchwager
Mul$-RobotSystemsLab
BostonUniversity
hgp://sites.bu.edu/msl