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Map Building with Mobile Robots in Populated Environments Dirk H ahnel Dirk Schulz Wolfram Burgard University of Freiburg Department of Computer Science Germany University of Bonn Department of Compu
Map Building with Mobile Robots in Populated Environments Dirk H ahnel Dirk Schulz Wolfram Burgard University of Freiburg Department of Computer Science Germany University of Bonn Department of Compu

Map Building with Mobile Robots in Populated Environments Dirk H ahnel Dirk Schulz Wolfram Burgard University of Freiburg Department of Computer Science Germany University of Bonn Department of Compu - PDF document

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Map Building with Mobile Robots in Populated Environments Dirk H ahnel Dirk Schulz Wolfram Burgard University of Freiburg Department of Computer Science Germany University of Bonn Department of Compu - Description

How ever most of the approaches assume that the environment is static during the dataacquisition phase In this paper we consider the problem of creating maps with mobile robots in populated environments Our approach uses a probabilistic method to tr ID: 22389 Download Pdf

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Presentation on theme: "Map Building with Mobile Robots in Populated Environments Dirk H ahnel Dirk Schulz Wolfram Burgard University of Freiburg Department of Computer Science Germany University of Bonn Department of Compu"— Presentation transcript

thereareKpersonsandletXt=fxt1;:::;xtKgbethestatesofthesepersonsattimet.Notethateachxtiisarandomvariablerangingoverthestatespaceofasingleperson.Furthermore,letZ(t)=fz1(t);:::;zmt(t)gde-noteafeaturesetobservedattimet,wherezj(t)isonefeatureofsuchaset.Ztisthesequenceofallfeaturesetsuptotimet.Thekeyquestionwhentrackingmulti-plepersonsishowtoassigntheobservedfeaturestotheindividualobjects.IntheJPDAFframework,ajointassociationeventisasetofpairs(j;i)2f0;:::;mtgf1;:::;Kg.Eachuniquelydetermineswhichfeatureisassignedtowhichobject.Pleasenote,thatintheJPDAFframework,thefeaturez0(t)isusedtomodelsituationsinwhichanob-jecthasnotbeendetected,i.e.nofeaturehasbeenfoundforobjecti.Letjidenotethesetofallvalidjointasso-ciationeventswhichassignfeaturejtotheobjecti.Attimet,theJPDAFconsiderstheposteriorprobabilitythatfeaturejiscausedbyobjecti: ji=X2jiP(jZt):(1)Accordingto[11],wecancomputethe jias ji=X2ji (mt�jj)Y(j;i)2p(zj(t)jxti):(2)Itremainstodescribe,howthebeliefsp(xti)aboutthestatesoftheindividualobjectsarerepresentedandup-dated.Inourapproach[11],weusesample-basedrepre-sentationsoftheindividualbeliefs.Thekeyideaunderly-ingallparticleltersistorepresentthedensityp(xtijZt)byasetStiofNweighted,randomsamplesorparticlessti;n(n=1:::N).Asamplesetconstitutesadiscreteapproximationofaprobabilitydistribution.Eachsampleisatuple(xti;n;wti;n)consistingofstatexti;nandanim-portancefactorwti;n.Thepredictionstepisrealizedbydrawingsamplesfromthesetcomputedinthepreviousiterationandbyupdatingtheirstateaccordingtothepre-dictionmodelp(xtijxt�1i;t).Inthecorrectionstep,afeaturesetZ(t)isintegratedintothesamplesobtainedinthepredictionstep.Therebyweconsidertheassign-mentprobabilities ji.Inthesample-basedvariant,thesequantitiesareobtainedbyintegratingoverallsamples:p(zj(t)jxti)=1 NNXn=1p(zj(t)jxti;n):(3)Giventheassignmentprobabilitieswenowcancomputetheweightsofthesampleswti;n= mtXj=0 jip(zj(t)jxti;n);(4)where isanormalizerensuringthattheweightssumuptooneoverallsamples.Finally,weobtainNnewsam-plesfromthecurrentsamplesbybootstrapresampling. Figure1:Typicallaserrangenderscan.Twoofthelocalminimaarecausedbypeoplewalkingbytherobot(leftimage).Featuresextractedfromthescan,thegrey-levelrepresentstheprobabilitythataperson'slegsareattheposition(center).Occlusiongrid,thegrey-levelrepresentstheprobabilitythatthepositionisoccluded(rightimage). Figure2:Fromlefttoright,top-down:theoccupancymapforthecurrentscan,theoccupancymapforthepre-viousscan,theresultingdifferencemap,andthefusionofthedifferencemapwiththefeaturemapsforthescandepictedinFigure1Forthispurposeweselecteverysamplexti;nwithproba-bilitywti;n.InoursystemweapplytheSJPDAFtoestimatethetra-jectoriesofpersonsinrangescans.Sincethelaserrangescannersmountedonourplatformsareataheightofapprox.40cm,thebeamsarereectedbythelegsofthepeoplewhichtypicallyappearaslocalminimainthescans.TheselocalminimaareusedasthefeaturesoftheSJPDAF.SeeleftandmiddlepartofFigure1.Unfor-tunately,thereareotherobjectswhichproducepatternssimilartopeople.Todistinguishthesestaticobjectsfrommovingpeopleoursystemadditionallyconsidersthedif-ferencesbetweenoccupancyprobabilitygridsbuiltfromconsecutivescans.Staticfeaturesarelteredout.ThisisillustratedinFigure2.Finally,wehavetodealwithpossibleocclusions.Wethereforecomputeaso-called“occlusionmap”contain-ingforeachpositioninthevicinityoftherobottheprob-abilitythatthecorrespondingpositionisnotvisiblegiventhecurrentrangescan.SeerightpartofFigure1.3ComputingConsistentMapsOurcurrentsystemisabletolearn2dand3dmapsus-ingrangescansrecordedwithamobilerobot.Inbothcases,theapproachisincremental.Mathematically,wecalculateasequenceofposes^l1;^l2;:::andcorrespond-ingmapsbymaximizingthemarginallikelihoodofthe t-thposeandmaprelativetothe(t�1)-thposeandmap:^lt=argmaxltfp(stjlt;^m(^lt�1;st�1))p(ltjut�1;^lt�1)g(5)Inthisequationthetermp(stjlt;^m(^lt�1;st�1))istheprobabilityofthemostrecentmeasurementstgiventheposeltandthemap^m(^lt�1;st�1)constructedsofar.Thetermp(ltjut�1;^lt�1)representstheprobabilitythattherobotisatlocationltgiventherobotwaspreviouslyatposition^lt�1andhascarriedout(ormeasured)themo-tionut�1.Theresultingpose^ltisthenusedtogenerateanewmap^mviathestandardincrementalmap-updatingfunctionpresentedin[9]:^m(^lt;st)=argmaxmp(mj^lt;st)(6)Onedisadvantageoftheapproachdescribedaboveliesinthefact,thatthecomplexityofasinglemaximizationstepisinO(t),sinceeverymeasurementiscomparedwithallpreviousmeasurements.Inoursystem,wethereforeuseamap^m(^lt�1;t;st�1;t)=^m(^lt�1;:::;^lt�t;st�1;:::;st�t)(7)thatisconstructedbasedofthetmostrecentmea-surementsonly.Thisismotivatedbytwoobservations.First,proximitysensorshaveonlyalimitedrangesothatthesystemgenerallycannotcoverthewholeenvironmentwithasinglescan.Additionally,objectsintheenviron-mentleadtoocclusionssothatmanyaspectsofagivenareaareinvisiblefromotherpositions.Therefore,mea-surementsobtainedatdistantplacesoftenprovidenoin-formationtomaximize(5).Theoverallapproachcanbesummarizedasfollows:Atanypointt�1intimetherobotisgivenanestimateofitspose^lt�1andamap^m(^lt�1;t;st�1;t).Aftertherobotmovedfurtheronandaftertakinganewmeasure-mentst,therobotdeterminesthemostlikelynewpose^lt.Itdoesthisbytradingofftheconsistencyofthemeasure-mentwiththemap(rsttermontheright-handsidein(5))andtheconsistencyofthenewposewiththecontrolactionandthepreviouspose(secondtermontheright-handsidein(5)).Themapisthenextendedbythenewmeasurementst,usingthepose^ltastheposeatwhichthismeasurementwastaken.ItremainstodescribehowweactuallymaximizeEqua-tion(5).Oursystemappliestwodifferentapproachesde-pendingonwhethertheunderlyingscansare2dor3dscans.3.1Two-dimensionalScanAlignmentOuralgorithmto2dscanmatchingisanextensionoftheapproachpresentedin[14].Toalignascanrelativetothe Figure3:Two-dimensionalscanalignment.Mapcreatedoutofthetmostrecentscans(leftimage),measurementstobtainedattimet(centerimage)andresultingalign-ment(rightimage).tmostrecentscans,werstconstructalocalgridmap^m(^lt�1;t;st�1;t)outofthetmostrecentscans.Ad-ditionallyto[14]weintegrateoversmallGaussianerrorsintherobotposewhencomputingthemaps.Thisavoidsthatmanycellsremainunknownespeciallyiftissmall,increasesthesmoothnessofthelikelihoodfunctiontobeoptimizedandthusresultsinbetteralignments.TheleftimageofFigure3showsatypicalmapconstructedoutof100scans.Thedarkeralocation,themorelikelyitisthatthecorrespondingplaceintheenvironmentiscoveredbyanobstacle.Pleasenotethatthemapappearsslightlyblurredaccordingtotheintegrationoversmallposeer-rors.Tomaximizethelikelihoodofascanwithrespecttothismap,weapplyahillclimbingstrategy.Atypi-calscanisshowninthecenterofFigure3.TheoptimalalignmentofthisscanwithrespecttothemapisshownintherightimageofFigure3.Ascanbeseenfromthegure,thealignmentisquiteaccurate.3.2AligningThree-dimensionalRangeScansUnfortunately,athree-dimensionalvariantofthemapsusedforthe2dscanalignmentwouldconsumetoomuchmemoryinthecaseofthreedimensions.Thereforethisapproachisnotapplicableto3dscanalignment.Instead,werepresentthe3dmapsastrianglemeshesconstructedfromtheindividualscans.Wecreateatriangleforthreeneighboringscanpoints,ifthemaximumlengthofanedgedoesnotexceedacertainthresholdwhichdependsonthelengthofthebeams.Tocomputethemostlikelypositionofanew3dscanwithrespecttothecurrent3dmodel,weapplyanap-proximativephysicalmodeloftherangescanningpro-cess.Obviously,anidealsensorwouldalwaysmeasurethecorrectdistancetotheclosestobstacleinthesensingdirection.However,sensorsandmodelsgeneratedoutofrangescannersarenoisy.Therefore,oursystemsin-corporatesmeasurementnoiseandrandomnoisetodealwitherrorstypicallyfoundin3drangescans.First,wegenerallyhavenormallydistributedmeasurementerrorsaroundthedistance“expected”accordingtothecurrentpositionofthescannerandthegivenmodeloftheenvi-ronment.Additionally,weobserverandomlydistributedmeasurementsbecauseoferrorsinthemodelandbecauseofdeviationsintheanglesbetweencorrespondingbeams Figure9:Three-dimensionalmapofabuilding(left)andpeopleltered(right).niedviewofthecorrespondingportionofthemap.Ifweintegratetheinformationobtainedfromthepeopletracker,however,thesespuriousobjectsarecompletelyremoved(seerightimageofFigure9).Thenumberoftrianglesinthesemodelsare416.800withoutlteringand412.500withltering.Pleasenote,thatthisexper-imentalsoillustratestheadvantageofusingatrackingsystemoverapurefeature-basedapproach.Duetothedisplacementofthescanners,peoplearenotalwaysvisi-bleinbothscanners.Accordingly,apurelyfeature-basedapproachlike[15]willaddobjectstothe3dmodelwhen-evertheyarenotdetectedbytherstscanner.Oursys-tem,however,canpredictpositionsofpersonsinthecaseofocclusionsandthuscanlteroutthecorrespondingreadingsevenifthefeaturesaremissing.6ConclusionsInthispaperwepresentedaprobabilisticapproachtomappinginpopulatedenvironments.Thekeyideaofthistechniqueistouseajointprobabilisticdataassociationltertotrackpeopleinthedataobtainedwiththesensorsoftherobot.Theresultsofthepeopletrackingareinte-gratedintothescanalignmentprocessandintothemapgenerationprocess.Thisleadstotwodifferentimprove-ments.First,theresultingposeestimatesarebetterandsecond,theresultingmapscontainlessspuriousobjectsthanthemapscreatedwithoutlteringpeople.Ourtechniquehasbeenimplementedandtestedondiffer-entroboticplatformsandforgenerating2dand3dmaps.Theexperimentsdemonstratethatourapproachcanse-riouslyreducethenumberofbeamscorruptedbypeoplewalkingthroughtheenvironment.Additionally,exten-sivesimulationexperimentsillustratethattheposeesti-matesaresignicantlybetteriftheresultsofthetrackingsystemareincorporatedduringtheposeestimation.AcknowledgementsThisworkhaspartlybeensupportedbytheECundercontractnumberIST-2000-29456.References[1]P.BeslandN.McKay.Amethodforregistrationof3dshapes.Trans.Patt.Anal.Mach.Intell.14(2),pages239–256,1992.[2]J.A.Castellanos,J.M.M.Montiel,J.Neira,andJ.D.Tard´os.TheSPmap:Aprobabilisticframeworkforsimultaneouslocalizationandmapbuilding.IEEETransactionsonRoboticsandAutomation,15(5):948–953,1999.[3]I.J.Cox.Areviewofstatisticaldataassociationtechniquesformotioncorrespondence.InternationalJournalofComputerVision,10(1):53–66,1993.[4]G.Dissanayake,H.Durrant-Whyte,andT.Bailey.Acomputa-tionallyefcientsolutiontothesimultaneouslocalizationandmapbuilding(SLAM)problem.InICRA'2000WorkshoponMobileRobotNavigationandMapping,2000.[5]M.A.GreenspanandG.Godin.AnearestneighbormethodforefcientICP.InProc.ofthe3rdInt.Conf.on3-DDigitalImagingandModeling(3DIM01),2001.[6]J.-S.GutmannandK.Konolige.Incrementalmappingoflargecyclicenvironments.InProc.oftheIEEEInt.Symp.onComputa-tionalIntelligenceinRoboticsandAutomation(CIRA),1999.[7]J.J.LeonardandH.J.S.Feder.Acomputationallyefcientmethodforlarge-scaleconcurrentmappingandlocalization.InProc.oftheNinthInt.Symp.onRoboticsResearch(ISRR),1999.[8]F.LuandE.Milios.Globallyconsistentrangescanalignmentforenvironmentmapping.AutonomousRobots,4:333–349,1997.[9]H.P.Moravec.Sensorfusionincertaintygridsformobilerobots.AIMagazine,pages61–74,Summer1988.[10]H.Samet.ApplicationsofSpatialDataStructures.Addison-WesleyPublishingCompany,1990.[11]D.Schulz,W.Burgard,D.Fox,andA.B.Cremers.Trackingmulti-plemovingobjectswithamobilerobot.InProc.oftheIEEECom-puterSocietyConferenceonComputerVisionandPatternRecog-nition(CVPR),2001.[12]H.Shatkay.LearningModelsforRobotNavigation.PhDthesis,ComputerScienceDepartment,BrownUniversity,Providence,RI,1998.[13]S.Thrun.Aprobabilisticonlinemappingalgorithmforteamsofmobilerobots.InternationalJournalofRoboticsResearch,20(5):335–363,2001.[14]S.Thrun,W.Burgard,andD.Fox.Areal-timealgorithmformo-bilerobotmappingwithapplicationstomulti-robotand3Dmap-ping.InProc.oftheIEEEInternationalConferenceonRobotics&Automation(ICRA),2000.[15]C.-C.WangandC.Thorpe.Simultaneouslocalizationandmap-pingwithdetectionandtrackingofmovingobjects.InProc.oftheIEEEInternationalConferenceonRobotics&Automation(ICRA),2002.