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
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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],wecancomputethejiasji=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-mentprobabilitiesji.Inthesample-basedvariant,thesequantitiesareobtainedbyintegratingoverallsamples:p(zj(t)jxti)=1 NNXn=1p(zj(t)jxti;n):(3)Giventheassignmentprobabilitieswenowcancomputetheweightsofthesampleswti;n= mtXj=0jip(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.