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外文翻译---基准分布式控制规律的运动协调非完整的机器人 英文版.pdf

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外文翻译---基准分布式控制规律的运动协调非完整的机器人 英文版.pdf

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,WEPRESENTTHECONTROLLERSTHATSTABILIZEAGROUPOFMOBILEAGENTSINTOPARALLELANDBALANCEDCIRCULARFORMATIONS,RESPECTIVELYINSECTIONVII,WEDERIVETHEVISIONBASEDCONTROLLERSTHATAREINTERMSOFTHEVISUALMEASUREMENTSOFTHENEIGHBORINGAGENTSINSECTIONVIII,COLLISIONAVOIDANCECAPABILITIESAREADDEDTOTHECONTROLLAWS,ANDTHEIREFFECTIVENESSISTESTEDONREALROBOTS15523098/26002009IEEEAUTHORIZEDLICENSEDUSELIMITEDTONANCHANGUNIVERSITYDOWNLOADEDONJANUARY12,2010AT2002FROMIEEEXPLORERESTRICTIONSAPPLY852IEEETRANSACTIONSONROBOTICS,VOL25,NO4,AUGUST2009IIRELATEDWORKANDCONTRIBUTIONSTHEPRIMARYCONTRIBUTIONOFTHISPAPERISTHEPRESENTATIONOFSIMPLECONTROLLAWSTOACHIEVEPARALLELANDCIRCULARFORMATIONSTHATREQUIREONLYVISUALSENSING,IE,THEINPUTSAREINTERMSOFQUANTITIESTHATDONOTREQUIRECOMMUNICATIONAMONGNEARESTNEIGHBORSINCONTRASTWITHTHEWORKOFJUSTHANDKRISHNAPRASAD17,MOSHTAGHANDJADBABAIE27,PALEYETAL32,33,ANDSEPULCHREETAL35,WHEREITISASSUMEDTHATEACHAGENTHASACCESSTOTHEVALUESOFITSNEIGHBORS’POSITIONSANDVELOCITIES,WEDESIGNDISTRIBUTEDCONTROLLAWSTHATUSEONLYVISUALCLUESFROMNEARESTNEIGHBORSTOACHIEVEMOTIONCOORDINATIONOURAPPROACHONDERIVINGTHEVISIONBASEDCONTROLLAWSCANBECLASSIFIEDASANIMAGEBASEDVISUALSEROVING41INIMAGEBASEDVISUALSERVOING,FEATURESAREEXTRACTEDFROMIMAGES,ANDTHENTHECONTROLINPUTISCOMPUTEDASAFUNCTIONOFTHEIMAGEFEATURESIN8,12,AND38,AUTHORSUSEOMNIDIRECTIONALCAMERASASTHEONLYSENSORFORROBOTSIN8AND38,INPUT–OUTPUTFEEDBACKLINEARIZATIONISUSEDTODESIGNCONTROLLAWSFORLEADERFOLLOWINGANDOBSTACLEAVOIDANCEHOWEVER,THEYASSUMETHATASPECIFICVERTICALPOSEOFANOMNIDIRECTIONALCAMERAALLOWSTHECOMPUTATIONOFBOTHBEARINGANDDISTANCEINTHEWORKOFPRATTICHIZZOETAL12,THEDISTANCEMEASUREMENTISNOTUSED;HOWEVER,THELEADERUSESEXTENDEDKALMANFILTERINGTOLOCALIZEITSFOLLOWERS,ANDCOMPUTESTHECONTROLINPUTSANDGUIDESTHEFORMATIONINACENTRALIZEDFASHIONINOURPAPER,THECONTROLARCHITECTUREISDISTRIBUTED,ANDWEDESIGNTHEFORMATIONCONTROLLERSBASEDONTHELOCALINTERACTIONAMONGTHEAGENTSSIMILARTOTHATOF14AND22FURTHERMORE,FOROURVISIONBASEDCONTROLLERS,NODISTANCEMEASUREMENTISREQUIREDIN25AND34,CIRCULARFORMATIONSOFAMULTIVEHICLESYSTEMUNDERCYCLICPURSUITISSTUDIEDTHEIRPROPOSEDSTRATEGYISDISTRIBUTEDANDSIMPLEBECAUSEEACHAGENTNEEDSTOMEASURETHERELATIVEINFORMATIONFROMONLYONEOTHERAGENTITISALSOSHOWNTHATTHEFORMATIONEQUILIBRIAOFTHEMULTIAGENTSYSTEMAREGENERALIZEDPOLYGONSINCONTRASTTO25,OURCONTROLLAWISANONLINEARFUNCTIONOFTHEBEARINGANGLES,ANDASARESULT,OURSYSTEMCONVERGESTOADIFFERENTSETOFSTABLEEQUILIBRIAIIIBACKGROUNDINTHISSECTION,WEBRIEFLYREVIEWANUMBEROFIMPORTANTCONCEPTSREGARDINGGRAPHTHEORYANDREGULARPOLYGONSTHATWEUSETHROUGHOUTTHISPAPERAGRAPHTHEORYANUNDIRECTEDGRAPHGCONSISTSOFAVERTEXSETVANDANEDGESETE,WHEREANEDGEISANUNORDEREDPAIROFDISTINCTVERTICESINGIFX,Y∈VANDX,Y∈E,THENXANDYARESAIDTOBEADJACENT,ORNEIGHBORS,ANDWEDENOTETHISBYWRITINGX∼YTHENUMBEROFNEIGHBORSOFEACHVERTEXISITSDEGREEAPATHOFLENGTHRFROMVERTEXXTOVERTEXYISASEQUENCEOFR1DISTINCTVERTICESTHATSTARTWITHXANDENDWITHYSUCHTHATCONSECUTIVEVERTICESAREADJACENTIFTHEREISAPATHBETWEENANYTWOVERTICESOFAGRAPHG,THENGISSAIDTOBECONNECTEDTHEADJACENCYMATRIXAGAIJOFANUNDIRECTEDGRAPHGISASYMMETRICMATRIXWITHROWSANDCOLUMNSINDEXEDBYTHEVERTICESOFG,SUCHTHATAIJ1IFVERTEXIANDVERTEXJARENEIGHBORS,ANDAIJ0OTHERWISEWEALSOASSUMETHATAII0FORALLITHEDEGREEMATRIXDGOFAGRAPHGISADIAGONALMATRIXWITHROWSANDCOLUMNSINDEXEDBYV,INWHICHTHEI,IENTRYISTHEDEGREEOFVERTEXITHESYMMETRICSINGULARMATRIXDEFINEDASLGDG−AGISCALLEDTHELAPLACIANOFGTHELAPLACIANMATRIXCAPTURESMANYTOPOLOGICALPROPERTIESOFTHEGRAPHTHELAPLACIANLISAPOSITIVESEMIDEFINITEMATRIX,ANDTHEALGEBRAICMULTIPLICITYOFITSZEROEIGENVALUEIE,THEDIMENSIONOFITSKERNELISEQUALTOTHENUMBEROFCONNECTEDCOMPONENTSINTHEGRAPHTHENDIMENSIONALEIGENVECTORASSOCIATEDWITHTHEZEROEIGENVALUEISTHEVECTOROFONES,1N1,,1TFORMOREINFORMATIONONGRAPHTHEORY,SEE13BREGULARPOLYGONSLETDNBEAPOSITIVEINTEGER,ANDDEFINEPN/DLETY1BEAPOINTONTHEUNITCIRCLELETRΑBECLOCKWISEROTATIONBYTHEANGLEΑ2Π/PTHEGENERALIZEDREGULARPOLYGON{P}ISGIVENBYTHEPOINTSYI1RΑYIANDEDGESBETWEENPOINTSIANDI1WHEND1,THEPOLYGON{P}ISCALLEDANORDINARYREGULARPOLYGON,ANDITSEDGESDONOTINTERSECTIFD1ANDNANDDARECOPRIME,THENTHEEDGESINTERSECT,ANDTHEPOLYGONISASTARIFNANDDHAVEACOMMONFACTORL1,THENTHEPOLYGONCONSISTSOFLTRAVERSALSOFTHESAMEPOLYGONWITH{N/L}VERTICESANDEDGESIFDN,THEPOLYGON{N/N}CORRESPONDSTOALLPOINTSATTHESAMELOCATIONIFDN/2WITHNEVEN,THENTHEPOLYGONCONSISTSOFTWOENDPOINTSANDALINEBETWEENTHEM,WITHPOINTSHAVINGANEVENINDEXONONEENDANDPOINTSHAVINGANODDINDEXONTHEOTHERFORMOREINFORMATIONONREGULARGRAPHS,SEE7IVPROBLEMSTATEMENTCONSIDERAGROUPOFNUNITSPEEDPLANARAGENTSEACHAGENTISCAPABLEOFSENSINGINFORMATIONFROMITSNEIGHBORSTHENEIGHBORHOODSETOFAGENTI,THATIS,NI,ISTHESETOFAGENTSTHATCANBE“SEEN”BYAGENTITHEPRECISEMEANINGOF“SEEING”WILLBECLARIFIEDLATERTHESIZEOFTHENEIGHBORHOODDEPENDSONTHECHARACTERISTICSOFTHESENSORSTHENEIGHBORINGRELATIONSHIPBETWEENAGENTSCANBECONVENIENTLYDESCRIBEDBYACONNECTIVITYGRAPHGV,E,WDEFINITION1CONNECTIVITYGRAPHTHECONNECTIVITYGRAPHGV,E,WISAGRAPHCONSISTINGOF1ASETOFVERTICESVINDEXEDBYTHESETOFMOBILEAGENTS;2ASETOFEDGESE{I,J|I,J∈V,ANDI∼J};3ASETOFPOSITIVEEDGEWEIGHTSFOREACHEDGEI,JTHENEIGHBORHOODOFAGENTIISDEFINEDBYNI{J|I∼J}⊆V\{I}LETRIREPRESENTTHEPOSITIONOFAGENTI,ANDLETVI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