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IEEETRANSACTIONSONROBOTICS,VOL25,NO4,AUGUST2009851VISIONBASED,DISTRIBUTEDCONTROLLAWSFORMOTIONCOORDINATIONOFNONHOLONOMICROBOTSNIMAMOSHTAGH,MEMBER,IEEE,NATHANMICHAEL,MEMBER,IEEE,ALIJADBABAIE,SENIORMEMBER,IEEE,ANDKOSTASDANIILIDIS,SENIORMEMBER,IEEEABSTRACTINTHISPAPER,WESTUDYTHEPROBLEMOFDISTRIBUTEDMOTIONCOORDINATIONAMONGAGROUPOFNONHOLONOMICGROUNDROBOTSWEDEVELOPVISIONBASEDCONTROLLAWSFORPARALLELANDBALANCEDCIRCULARFORMATIONSUSINGACONSENSUSAPPROACHTHEPROPOSEDCONTROLLAWSAREDISTRIBUTEDINTHESENSETHATTHEYREQUIREINFORMATIONONLYFROMNEIGHBORINGROBOTSFURTHERMORE,THECONTROLLAWSARECOORDINATEFREEANDDONOTRELYONMEASUREMENTORCOMMUNICATIONOFHEADINGINFORMATIONAMONGNEIGHBORSBUTINSTEADREQUIREMEASUREMENTSOFBEARING,OPTICALFLOW,ANDTIMETOCOLLISION,ALLOFWHICHCANBEMEASUREDUSINGVISUALSENSORSCOLLISIONAVOIDANCECAPABILITIESAREADDEDTOTHETEAMMEMBERS,ANDTHEEFFECTIVENESSOFTHECONTROLLAWSAREDEMONSTRATEDONAGROUPOFMOBILEROBOTSINDEXTERMSCOOPERATIVECONTROL,DISTRIBUTEDCOORDINATION,VISIONBASEDCONTROLIINTRODUCTIONCOOPERATIVECONTROLOFMULTIPLEAUTONOMOUSAGENTSHASBECOMEAVIBRANTPARTOFROBOTICSANDCONTROLTHEORYRESEARCHTHEMAINUNDERLYINGTHEMEOFTHISLINEOFRESEARCHISTOANALYZEAND/ORSYNTHESIZESPATIALLYDISTRIBUTEDCONTROLARCHITECTURESTHATCANBEUSEDFORMOTIONCOORDINATIONOFLARGEGROUPSOFAUTONOMOUSVEHICLESSOMEOFTHISRESEARCHFOCUSSESONFLOCKINGANDFORMATIONCONTROL9,14,16,22,31,ANDSYNCHRONIZATION2,39,WHILEOTHERSFOCUSONRENDEZVOUS,DISTRIBUTEDCOVERAGE,ANDDEPLOYMENT1,5AKEYASSUMPTIONIMPLIEDINALLOFTHEPREVIOUSREFERENCESISTHATEACHVEHICLEORROBOTHEREAFTERCALLEDANAGENTCOMMUNICATESITSPOSITIONAND/ORVELOCITYINFORMATIONTOITSNEIGHBORSINSPIREDBYTHESOCIALAGGREGATIONPHENOMENAINBIRDSANDFISH6,30,RESEARCHERSINROBOTICSANDCONTROLTHEORYHAVEMANUSCRIPTRECEIVEDFEBRUARY23,2008;REVISEDJANUARY31,2009FIRSTPUBLISHEDJUNE10,2009;CURRENTVERSIONPUBLISHEDJULY31,2009THISPAPERWASRECOMMENDEDFORPUBLICATIONBYASSOCIATEEDITORZWLUOANDEDITORJPLAUMONDUPONEVALUATIONOFTHEREVIEWERS’COMMENTSTHEWORKOFAJADBABAIEWASSUPPORTEDINPARTBYTHEARMYRESEARCHOFFICE–MULTIDISCIPLINARYUNIVERSITYRESEARCHINITIATIVEARO/MURIUNDERGRANTW911NF0510381,INPARTBYTHEOFFICEOFNAVALRESEARCHONR/YOUNGINVESTIGATORPROGRAM542371,INPARTBYONRN000140610436,ANDINPARTUNDERCONTRACTNSFECS0347285THEWORKOFKDANIILIDISWASSUPPORTEDINPARTUNDERCONTRACTNSFIIS0083209,INPARTUNDERCONTRACTNSFIIS0121293,INPARTUNDERCONTRACTNSFEIA0324977,ANDINPARTUNDERCONTRACTARO/MURIDAAD190210383NMOSHTAGHWASWITHTHEGENERALROBOTICS,AUTOMATION,SENSING,ANDPERCEPTIONLABORATORY,UNIVERSITYOFPENNSYLVANIA,PHILADELPHIA,PA19104USAHEISNOWWITHSCIENTIFICSYSTEMSCOMPANY,INC,WOBURN,MA01801USAEMAILNMOSHTAGHSSCICOMNMICHAEL,AJADBABAIE,ANDKDANIILIDISAREWITHTHEGENERALROBOTICS,AUTOMATION,SENSING,ANDPERCEPTIONLABORATORY,UNIVERSITYOFPENNSYLVANIA,PHILADELPHIA,PA19104USAEMAILNMICHAELGRASPUPENNEDU;JADBABAIGRASPUPENNEDU;KOSTASGRASPUPENNEDUCOLORVERSIONSOFONEORMOREOFTHEFIGURESINTHISPAPERAREAVAILABLEONLINEATHTTP//IEEEXPLOREIEEEORGDIGITALOBJECTIDENTIFIER101109/TRO20092022439DEVELOPEDTOOLS,METHODS,ANDALGORITHMSFORDISTRIBUTEDMOTIONCOORDINATIONOFMULTIVEHICLESYSTEMSTWOMAINCOLLECTIVEMOTIONSTHATAREOBSERVEDINNATUREAREPARALLELMOTIONANDCIRCULARMOTION21ONECANINTERPRETSTABILIZINGTHECIRCULARFORMATIONASANEXAMPLEOFACTIVITYCONSENSUS,IE,INDIVIDUALSARE“MOVINGAROUND”TOGETHERSTABILIZINGTHEPARALLELFORMATIONISANOTHERFORMOFACTIVITYCONSENSUSINWHICHINDIVIDUALS“MOVEOFF”TOGETHER33CIRCULARFORMATIONSAREOBSERVEDINFISHSCHOOLING,WHICHISAWELLSTUDIEDTOPICINECOLOGYANDEVOLUTIONARYBIOLOGY6INTHISPAPER,WEPRESENTASETOFCONTROLLAWSFORCOORDINATEDMOTIONS,SUCHASPARALLELANDCIRCULARFORMATIONS,FORAGROUPOFPLANARAGENTSUSINGPURELYLOCALINTERACTIONSTHECONTROLLAWSAREINTERMSOFSHAPEVARIABLES,SUCHASTHERELATIVEDISTANCESANDRELATIVEHEADINGSAMONGTHEAGENTSHOWEVER,THESEPARAMETERSARENOTREADILYMEASURABLEUSINGSIMPLEANDBASICSENSINGCAPABILITIESTHISMOTIVATESTHEREWRITINGOFTHEDERIVEDCONTROLLAWSINTERMSOFBIOLOGICALLYMEASURABLEPARAMETERSEACHAGENTISASSUMEDTOHAVEONLYMONOCULARVISIONANDISALSOCAPABLEOFMEASURINGBASICVISUALQUANTITIES,SUCHASBEARINGANGLE,OPTICALFLOWBEARINGDERIVATIVE,ANDTIMETOCOLLISIONREWRITINGTHECONTROLINPUTSINTERMSOFQUANTITIESTHATARELOCALLYMEASURABLEISEQUIVALENTTOEXPRESSINGTHEINPUTSINTHELOCALBODYFRAMESUCHACHANGEOFCOORDINATESYSTEMFROMAGLOBALFRAMETOALOCALFRAMEPROVIDESUSWITHABETTERINTUITIONONHOWSIMILARBEHAVIORSARECARRIEDOUTINNATUREVERIFICATIONOFTHETHEORYTHROUGHMULTIROBOTEXPERIMENTSDEMONSTRATEDTHEEFFECTIVENESSOFTHEVISIONBASEDCONTROLLAWSTOACHIEVETHEDESIREDFORMATIONSOFCOURSE,INREALITY,ANYFORMATIONCONTROLREQUIRESCOLLISIONAVOIDANCE,ANDINDEED,COLLISIONAVOIDANCECANNOTBEDONEWITHOUTRANGEINORDERTOIMPROVETHEEXPERIMENTALRESULTS,WEPROVIDEDINTERAGENTCOLLISIONAVOIDANCEPROPERTIESTOTHETEAMMEMBERSINTHISPAPER,WESHOWTHATTHETWOTASKSOFFORMATIONKEEPINGANDCOLLISIONAVOIDANCECANBEDONEWITHDECOUPLEDADDITIVETERMSINTHECONTROLLAW,WHERETHETERMSFORKEEPINGPARALLELANDCIRCULARFORMATIONSDEPENDONLYONVISUALPARAMETERSTHISPAPERISORGANIZEDASFOLLOWSINSECTIONII,WEREVIEWANUMBEROFIMPORTANTRELATEDWORKSSOMEBACKGROUNDINFORMATIONONGRAPHTHEORYANDOTHERMATHEMATICALTOOLSUSEDINTHISPAPERAREPROVIDEDINSECTIONIIITHEPROBLEMSTATEMENTISGIVENINSECTIONIVINSECTIONSVANDVI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