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