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MSL
Mul$-RobotSystemsLab
DepartmentofMechanicalEngineering
BostonUniversity
CDC2015,Osaka,Japan
Dec.15,2015
Mul'-RobotManipula'onwithnoCommunica'onUsingOnlyLocalMeasurements
ZijianWangandMacSchwager
MSL1001RobotsMovingaPiano
2
MSLMo$va$on
3
Mul$-RobotManipula$onandTransport
• Transportlargeobjects• Construc$on,manufacturing,disasterrelief
MinimalistApproach• Simpleindividualrobots
• Noexplicitcommunica$on
• Nogloballocaliza$oninforma$on
• Localmeasurements
MSLOurApproach:Overview
4
v
,cx
ixcir
iR
,M J
iF( ), ( )
Q
CoordinatedForces
Uncoordinatedforces
Objectitself“communicates”necessaryinforma$on
MSLRelatedWork
5
Fink,Michael,Kumar
ICRA08
Becker,Habibi,Werfel,
Rubenstein,McLurkin
ICRA13
Caging/ForceClosure EnsembleControl
MSLProblemFormula$on
6
Rigid-bodyDynamics(Planar)
Transla$onal
Rota$onal
Goal
DecentralizedcontrollawforbeingcontrolledFi
J �̇ =N�
i=1
ri � Fi + T1 �µ�
MJ�
v
,cx
ixcir
iR
,M J
iF( ), ( )
Q
MSLControlStrategy
7
• Manyfollowerrobots,oneleader(robotorhuman)
• Followers’forceswilltrackleader’sforceusinglocal
measurementsoftheobject’smo$on
• Leaderusesfeedbackcontrollertosteerthesumforce,and
thennavigatetheobjectthroughthedesiredtrajectory
MSLForceCoordina$onviaConsensus
8
• Linearconsensusalgorithm
• Leader-following(steering)Fixonerobot
x1(t) = x1(0)
Olfa$-Saber,Murray,TAC2004
Jadbabaie,Lin,Morse,TAC2003
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
MSLLocalMeasurements
10
Ø Measurementat
LocalAgachmentPointsvs.CenterofMass
(thispaper)(priorwork)
Newforcecoordina$onlaw:
HeterogenousLocalMeasurements
MSLMatrixRepresenta$on
11
CentrosymmetricAssump$on
ForceConsensus?
Time-varying
MSLConsensusAnalysis2
12
Ø Consensuswithoutaleader
Proof:useLyapunovTheorem&Barbalat’sLemma
MSLConsensusAnalysis1
13
Ø Time-independentCharacteriza$on
Lemma 3: Time-invariant equilibria
Lemma
Lemma
MSLConsensusAnalysis2
14
Ø Consensuswithoutaleader
Proof:useLyapunovTheorem&Barbalat’sLemma
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
MSLConsensusAnalysis3
16
Ø Groupforcecontrolvialeaderfollowing
Canshow:equilibrium,eigenvalue(longproof)
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
MSLCentrosymmetry
18
Centrosymmetric Non-Centrosymmetric
MSLRelaxingTheCentrosymmetric
Assump$on
19
• Probleminduced
Changeofequilibrium,eigenvalue.
Introducecentrifugalforce
• Modeltheasymmetryasaperturba$on
MSLSimula$onsinOpenDynamic
Engine(ODE)
20
12Robots,1Leader
1kgRectangularPlank
0.6mx0.2mx0.1m
1001Robots,1Leader
290kgYamahaC1GrandPiano
1.6mx1.5mx1.0m
MSLSummary
21
• Adecentralized,scalablemul$-robotmanipula$onapproach
• Noexplicitcommunica$on
• Nogloballocaliza$oninforma$onforfollowers
• Guaranteefollowers‘forcecoordina$on
• Useonlylocalmeasurements
• Leadersteersthegroup
MSLFutureWork
22
• Rigorousanalysisontheasymmetriccase
• Physicalexperiment[SubmigedtoICRA2016]
• Human-swarminterac$on[SubmigedtoICRA2016]
• Adap$vecontrol
MSL
Q&A
Thankyou!
Mul'-RobotManipula'onwithnoCommunica'onUsingOnlyLocalMeasurements
ZijianWangandMacSchwager
Mul$-RobotSystemsLab
BostonUniversity
hgp://sites.bu.edu/msl