ON MULTI-ROBOT TASK ALLOCATION by Brian Paul Gerkey

126 Pages·2003·1.16 MB·English

CRES Technical Report CRES-03-012
Center for Robotics and Embedded Systems, University of Southern California, Los Angeles
ONMULTI-ROBOTTASKALLOCATION
by
BrianPaulGerkey
ADissertationPresentedtothe
FACULTYOFTHEGRADUATESCHOOL
UNIVERSITYOFSOUTHERNCALIFORNIA
InPartialFulfillmentofthe
RequirementsfortheDegree
DOCTOROFPHILOSOPHY
(COMPUTERSCIENCE)
August2003
Copyright 2003 BrianPaulGerkey
Contents
ListOfTables v
ListOfFigures vi
Abstract viii
1 Introduction 1
1.1 Multi-RobotTaskAllocation(MRTA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Towardformalanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Relatedwork 8
2.1 Robotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Multi-agentsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Theproblem 13
3.1 TheOptimalAssignmentProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1.1 Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.1.2 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Operationsresearchandlinearprogramming . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.1 MRTAasanintegrallinearprogram . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.2 ThesimplexandHungarianmethods . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.3 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Economicsandgametheory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.1 MRTAasaneconomicgame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.2 Auctionalgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4 Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4.1 MRTAasaschedulingproblem . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4.2 Preemption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.5 Networkflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.5.1 MRTAasanetworkflowproblem . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.6 Combinatorialoptimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.6.1 MRTAasacombinatorialoptimizationproblem. . . . . . . . . . . . . . . . . . . 31
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
ii
4 Aneconomicsolution 33
4.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.1 Anonymouscommunication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.2 Hierarchicaltaskstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.1.3 Auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2 Murdoch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2.1 Publish/subscribemessaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.2.1.2 Subjectnamespace. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.2 Auctionprotocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.2.1 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Experimentalvalidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.1 Platform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3.2 Experimentaldesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3.2.1 Loosely-coupledtaskallocation . . . . . . . . . . . . . . . . . . . . . . 42
4.3.2.2 Box-pushing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4.1 Loosely-coupledtaskallocation . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4.2 Box-pushing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.5 RelatedWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5.1 Unembodiedtaskallocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5.2 Embodiedtaskallocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.5.3 Box-pushing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5 Ataxonomy 61
5.1 AxesofMRTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2 ST-SR-IA:Single-taskrobots,single-robottasks,instantaneousassignment . . . . . . . . 63
5.2.1 Variant: iteratedassignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2.2 Variant: onlineassignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2.3 Analysisofsomeexistingapproaches . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2.3.1 Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2.3.2 Results&discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.3 ST-SR-TE:Single-taskrobots,single-robottasks,time-extendedassignment . . . . . . . . 72
5.3.1 Variant: ALLIANCEEfficiencyProblem . . . . . . . . . . . . . . . . . . . . . . 73
5.4 ST-MR-IA:Single-taskrobots,multi-robottasks,instantaneousassignment . . . . . . . . 74
5.5 ST-MR-TE:Single-taskrobots,multi-robottasks,time-extendedassignment . . . . . . . . 76
5.6 MT-SR-IA&MT-SR-TE:Multi-taskrobots,single-robottasks . . . . . . . . . . . . . . . 76
5.7 MT-MR-IA:Multi-taskrobots,multi-robottasks,instantaneousassignment . . . . . . . . 77
5.8 MT-MR-TE:Multi-taskrobots,multi-robottasks,time-extendedassignment . . . . . . . . 78
5.9 Otherproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.9.1 Interrelatedutilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.9.2 Taskconstraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6 Enablinginfrastructure 82
6.1 Player&Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.1.1 Thesoftware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.1.2 Playergoalsanddesign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.1.2.1 Clientinterface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.1.2.2 Stagegoalsanddesign. . . . . . . . . . . . . . . . . . . . . . . . . . . 86
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6.1.3 Opportunitiesforresearch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.1.3.1 Embeddedsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.1.3.2 Sophisticateddevices . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.1.3.3 Commondeviceinterfaces . . . . . . . . . . . . . . . . . . . . . . . . 90
6.1.3.4 Novelcontrolsystems . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.1.3.5 Comparingcontrollersandperformancemetrics . . . . . . . . . . . . . 91
6.1.3.6 Fantasticsensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.1.3.7 Challengesinscalingsensor-basedsimulation . . . . . . . . . . . . . . 92
6.1.4 Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.1.5 Relatedwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.1.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.2 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7 Conclusion 98
7.1 Addingdomaininformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
ReferenceList 105
iv
List Of Tables
(cid:0)
4.1 Mean ( ) and standard deviation ((cid:1) ) of the elapsed time (in seconds) for the successful
pushingtrialsineachofthefourbox-pushingExperimentSets. . . . . . . . . . . . . . . . 54
5.1 Summary of selected iterated assignment architectures for MRTA. Shown here for each
architecture are the computational and communication requirements, as well as solution
quality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 SummaryofselectedonlineassignmentarchitecturesforMRTA.Shownhereforeachar-
chitecture are the computational and communication requirements, as well as solution
quality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
v
List Of Figures
4.1 Overheadsnapshotofthelong-termloosely-coupledscenario. Therobotinthecenterof
theimageisperformingthecleanuptaskwhiletherobottoitsimmediateleftisperforming
theobject-trackingtask. Intheupperrightcorneristhechargingstation. . . . . . . . . . 43
4.2 Theexperimentalbox-pushingsetup. Thetaskisforthepusherstomovetheboxtothe
goalwiththehelpofthewatcher. (Image1of3takenfromanexperimentaltrial; see
Figures4.4&4.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.3 Themodelusedtoderivethepushingvelocitiesformovingtheboxalongthedesired
trajectory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.4 Fault-toleranceinaction: afterasinglerobotfailurewasinduced,theremainingrobotis
lefttopushonitsown. (Image2of3takenfromanexperimentaltrial;seeFigures4.2&4.5) 49
4.5 Afterthefailedrobotwas“revived”,itwasreintegratedintotheteam,andallcompleted
thetasktogether. (Image3of3takenfromanexperimentaltrial;seeFigures4.2&4.4) . . 50
4.6 ThesetupforExperimentSet5.Thegoalisapproximately(cid:2)(cid:4)(cid:3)(cid:6)(cid:5) offthecenterline,requiring
therobotstopushtheboxalongacurvedtrajectory.. . . . . . . . . . . . . . . . . . . . . 51
4.7 An example plot of task execution during the long-term experiment. Shown here is the
activity, over the first half of the experiment, of the robot equipped with a camera, laser
range-finder,andbumpers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.8 Thecommunicationoverheadincurredby MURDOCH. Shownhereisthetotalamountof
datatransferredamongtherobotsduringthefirst15minutesofthelong-termexperiment.
Eachspikecorrespondstoanauction,whichcausesabriefflurryofactivity. . . . . . . . . 53
4.9 Path of the box in an example trial from Experiment Set 3 (units are meters). The right
pusherfails,leavingtheotherpushertopusheitherendoftheboxinturn. . . . . . . 54
4.10 PathoftheboxintrialsfromExperimentSet5(unitsaremeters).Shownhereisthetrajec-
toryofthecenteroftheboxforfoursuccessfultrialsineitherdirection. Forcomparison,
thedashedlinesrepresentthe“ideal”paths. . . . . . . . . . . . . . . . . . . . . . . . . . 54
vi
5.1 Comparisonofthecomputationaloverheadofassignmentalgorithms. Thesolidlineand
dashedlineshowtheamountoftimerequiredbytheHungarianmethodandAuctionalgo-
rithm,respectively,tosolverandomlygeneratedsymmetric((cid:7)(cid:9)(cid:8)(cid:10)(cid:7) )instancesoftheOptimal
AssignmentProblem(OAP)ona700MhzPentiumIIIrunningLinux. Forcomparison,the
dotted line is (cid:11)(cid:13)(cid:12)(cid:15)(cid:14)(cid:10)(cid:16)(cid:18)(cid:17)(cid:19)(cid:7)(cid:10)(cid:20)(cid:4)(cid:21)(cid:22)(cid:24)(cid:23) ; the Hungarian method is known to exhibit a running time of
(cid:25)(cid:27)(cid:26)
(cid:7)(cid:10)(cid:20)(cid:29)(cid:28) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2 Comparisonofthecommunicationoverheadofassignmentalgorithms. Thesolidlineand
dashed line show the number of messages sent by the Hungarian method and Auction
algorithm,respectively,whensolvingrandomlygeneratedsymmetric((cid:7)(cid:30)(cid:8)(cid:31)(cid:7) )instancesof
theOptimalAssignmentProblem(OAP). . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.1 Stagescreenshotshowingtworobots(solidrectangles)withvisualizationofthetoprobot’s
laserrangescanner,sonarandcolorblob-finderdata.Stage’smodulararchitectureallows
multipleGUIs;thisisGNOME2.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2 AtypicalPioneer2-DXrobot.Visibleinthisimagearethetwodrivewheels,frontsonar
ring,compass(smallcube),Ethernetmodem(antennaeprotrudingvertically),andlaser
range-finder(lookslikeacoffee-maker).Attherearoftherobotisanotherringofsonars.. 96
vii
Abstract
Despite more than a decade of experimental work in multi-robot systems, important theoretical aspects
ofmulti-robotcoordinationmechanismshave,todate,beenlargelyignored. Toaddresspartofthisneg-
ligence, this dissertation focuses on the problem of multi-robot task allocation (MRTA). Most work on
MRTA has been ad hoc and empirical, with many coordination architectures having been proposed and
validatedinaproof-of-conceptfashion,butinfrequentlyanalyzed.
Withthegoalofbringingsomeobjectivegroundingtothisimportantareaofresearch,thisdissertation
presentsaformalstudyofMRTAproblems.Adomain-independenttaxonomyofMRTAproblemsisgiven,
anditisshownhowmanysuchproblemscanbeviewedasinstancesofother,well-studied,optimization
problems. BycastingMRTAproblemsinthewell-understoodframeworkofoptimization,ahalf-century
of work in operations research, game theory, economics, and network flows can be adapted for use in
robotic domains. This dissertation demonstrates how such theory can be used for analysis and greater
understandingofexistingapproachestotaskallocation,andsuggestshowthesametheorycanbeusedin
thesynthesisofnewapproaches.
Although vital for the advancement of the field, analysis is only one component of a comprehensive
researchagenda. Sensor-actuatorsystemssuchasrobotspresentarich,complexproblemdomainthatcan
exhibitsignificantlevelsofnoiseanduncertainty. Onemustimplementandempiricallyvalidateproposed
MRTA algorithms. Thus this dissertation also presents experimental work with an auction-based task
allocationsystem,implementedonphysicalrobots. Optimizationtheoryisusedtoexplainhowandwhy
thisapproachissuccessful.
viii
Thiskindofempiricalworkisanaturalcomplementtoformalanalysis,andcanservethecrucialrole
of suggesting modifications to the formal model that is analyzed. Such experiments require substantial
supportingsoftwareinfrastructure. Thisdissertationdescribestheunderlyingsoftwarefacilitiesthatwere
developedforexperimentaluseinthestudyofMRTA,aswellasformoregeneraluse. Specificallydis-
cussedisthePlayer/Stageproject,whichproduceshigh-qualityOpenSourcesoftwaretosupportrobotics
research,withthegoalofprovidingastandardplatformformobilerobotexperimentationandsimulation.
ix
Chapter 1
Introduction
Overthepastdecade,asignificantshiftoffocushasoccurredinthefieldofmobileroboticsasresearchers
have begun to investigate problems involving multiple, rather than single, robots. From early work on
simpleloosely-coupledtaskssuchasforaging(e.g.,Mataric´(1992),Arkin,Balch&Nitz(1993))torecent
work on sophisticated team coordination for robot soccer (e.g., Stone & Veloso (1999), Asada, Kitano,
Noda & Veloso (1999)), the complexity of the multi-robot systems being studied has increased. This
complexity has two primary sources: larger team sizes and greater heterogeneity of robots and tasks.
As significant achievements have been made along these axes, the bar has been raised; it is no longer
a sufficient demonstration of multi-robot coordination to show, for example, only two robots observing
targets(Parker1999b),oralargegroupofrobotsonlyflocking(Mataric´1995).Rathertodaywereasonably
expecttoseelargerandlargerrobotteamsengagedinconcurrentanddiversetasksoverextendedperiods
oftime.
1.1 Multi-Robot Task Allocation (MRTA)
Asaresultofthefocusonmulti-robotsystems,multi-robotcoordinationhasreceivedsignificantattention.
In particular, multi-robot task allocation (MRTA) has recently risen to prominence. Originally a side-
show to other problems, MRTA has now become a key research issue in its own right. As researchers
1