Most of the approaches however 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 tra ID: 31455
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landmarksoutofthedataandmatchtheselandmarkstolocalizetherobotinthemapbeinglearned.Theothersetofapproachessuchas[22,13,30]userawsensordataandperformadensematchingofthescans.Althoughallapproachespossesstheabilitytocopewithacertainamountofnoiseinthesensordata,theyassumethattheenvironmentisalmoststaticduringthemappingprocess.Especiallyinpopulatedenvironments,additionalnoiseisintroducedtothesensordatawhichincreasestheriskoflocalizationerrors.Additionally,peopleinthevicinityoftherobotappearasobjectsintheresultingmapsandthereforemakethemapsnotusableforpathplanningetc.RecentlyWangandThorpe[33]presentedaheuristicandfeature-basedapproachtoidentifydynamicobjectsinrangescans.Thecorrespondingmeasurementsarethenlteredoutduring2dscanregistration.Ourapproachinsteadusesatrackingtechniqueandthereforeisabletopredictthepositionsofthepersonseveninsituationsinwhichthecorrespondingfeaturesaretemporarilymissing.Additionally,therehasbeenworkonupdatingmapsorimprovinglocalizationinpopulatedenvironments.Forexample,Burgardetal.[6]updateagivenstaticmapusingthemostrecentsensoryinputtodealwithpeopleintheenvironmentduringpathplanning.Montemerloetal.[23]presentanapproachtosimultaneouslocalizationandpeopletracking.Arrasetal.[1]presentateamoftour-guiderobotsthatoperatesinapopulatedexhibition.Theirsystemuseslinefeaturesforlocalizationandhasbeenreportedtosuccessfullylterrange-measurementsreectedbypersons.Foxetal.[11]presentaprobabilistictechniquetoidentifyrangemeasurementsthatdonotcorrespondtothegivenmodeloftheenvironment.Theseapproaches,however,requireagivenandxedmapwhichisusedforlocalizationandfortheextractionofthefeaturescorrespondingtothepeople.Ourtechnique,incontrast,doesnotrequireagivenmap.Ratheritlearnsthemapfromscratchusingthedataacquiredwiththerobot'ssensors.Furthermore,therehasbeendevelopedavarietyoftechniquesfortrackingpersons,forpredictingfutureposesofpersons,orforadoptingthebehavioroftherobotaccordingtotheinformationobtainedaboutthepersonsinitsvicinity[29,19,34,20,5,17,18,16,32,4,2,28].Alltheseapproaches,however,donotlterthemeasurementscorrespondingtopersonsinordertoimprovethemodeloftheenvironment.Inthispaperwepresentaprobabilisticapproachtolteringpeopleoutofsensordataandtoincorporatetheresultsofthelteringintothemappingprocess.Ourapproachhasseveraldesirableproperties.First,byincorpo-ratingtheresultsofthepeopletrackerthealignmentofthescansbecomesmorerobust.Additionally,theresultingmapsaremoreaccurate,sincemeasurementscorruptedbypeoplewalkingbyarelteredout.Empiricalresults,describedinthispaper,illustratethatourapproachsucceedsinlearningaccuratelarge-scale2dand3dmapsofpopulatedenvironmentswithrangescannersevenifseveralpersonsareinthevicinityoftherobot.3TrackingPeopleinRangeScansTodetectpeopleandtrackpeopleinthevicinityoftherobot,oursystemappliesasample-basedvariantofProbabilisticDataAssociationFilters(JPDAFs)[8].Thisapproachisdescribedinthefollowingsection.Addi-tionally,wewilldescribehowweadaptthenumberofpersonsbeingtrackedandhowtoimplementthistechniqueusingdatagatheredwiththelaser-rangendersofamovingmobilerobot.3.1SamplebasedJointProbabilisticDataAssociationFilters(SJPDAFs)SupposethereareKpersonsandletXt=fxt1;:::;xtKgbethestatesofthesepersonsattimet.Notethateachxtiisarandomvariablerangingoverthestatespaceofasingleperson.Furthermore,letZ(t)=fz1(t);:::;zmt(t)gdenoteafeaturesetobservedattimet,wherezj(t)isonefeatureofsuchaset.Ztisthesequenceofallfeaturesetsuptotimet.Thekeyquestionwhentrackingmultiplepersonsishowtoassigntheobservedfeaturestotheindividualobjects.IntheJPDAFframework,ajointassociationeventisasetofpairs(j;i)2f0;:::;mtgf1;:::;Kg.Eachuniquelydetermineswhichfeatureisassignedtowhichobject.Pleasenote,thatintheJPDAFframework,thefeaturez0(t)isusedtomodelsituationsinwhichanobjecthasnotbeendetected,i.e.nofeaturehasbeenfoundforobjecti.Letjidenotethesetofallvalidjointassociationeventswhichassignfeaturejtotheobjecti.Attimet,theJPDAFconsiderstheposteriorprobabilitythatfeaturejiscausedbyobjecti:ji=X2jiP(jZt):(1)2 Figure1.Typicallaserrangenderscan.Twoofthelocalminimaarecausedbypeoplewalkingbytherobot(leftimage).Featuresextractedfromthescan,thegrey-levelrepresentstheprobabilitythataperson'slegsareattheposition(center).Occlusiongrid,thegrey-levelrepresentstheprobabilitythatthepositionisoccluded(rightimage).3.3LaserbasedImplementationInoursystemweapplytheSJPDAFtoestimatethetrajectoriesofpersonsinrangescans.Sincethelaserrangescannersmountedonourplatformsareataheightofapprox.40cm,thebeamsarereectedbythelegsofthepeoplewhichtypicallyappearaslocalminimainthescans.TheselocalminimaareusedasthefeaturesfortheSJPDAF(seeleftandcenterimageofFigure1).Unfortunately,thereareotherobjectswhichproducepatternssimilartopeople.Todistinguishthesestaticobjectsfrommovingpeopleoursystemadditionallyconsidersthedifferencesbetweenoccupancyprobabilitygridsbuiltfromconsecutivescans.ThiswholeprocessisillustratedinFigure2.Pleasenote,thatwealsoperformascan-matchingtoaligneachpairconsecutivescans.Therefore,thestaticaspectsoftheenvironmentcanbeidentiedandlteredoutaccurately. Figure2.Fromlefttoright,top-down:theoccupancymapforthecurrentscan,theoccupancymapforthepreviousscan,theresultingdifferencemap,andthefusionofthedifferencemapwiththefeaturemapsforthescandepictedinFigure1.Finally,wehavetodealwithpossibleocclusions.Wethereforecomputeaso-called“occlusionmap”containingforeachpositioninthevicinityoftherobottheprobabilitythatthecorrespondingpositionisnotvisiblegiventhecurrentrangescan.SeerightpartofFigure1.TheinformationaboutoccludedareasisusedtoavoidthattheSJPDAFlosestrackofapersonwheneveritistemporarilyoccluded.Figure3showsatypicalsituation,inwhicharobotequippedwithtwolaser-rangescannersistrackinguptofourpersonsinitsvicinity.Ascanbeseenfromthegure,ourapproachisrobustagainstocclusionsandcanquicklyadapttochangingsituationsinwhichadditionalpersonsenterthescene.Forexample,inthelowerleftimagetheupperrightpersonisnotvisibleintherangescan,sinceitisoccludedbythepersonthatisclosetotherobot.Theknowledgethatthesampleslieinanoccludedareapreventstherobotfromdeletingthecorrespondingsampleset.Instead,thesamplesonlyspreadout,whichrepresentsthegrowinguncertaintyoftherobotaboutthepositionoftheperson.4 Figure3.Trackingpeopleusinglaserrange-nderdata.Upperpartshowstherawsensordatawiththecoloredsamplesets.Lowerpartshowstherangevalueswiththelocalminimamarkedwiththecolorofthecorrespondingsampleset.4ComputingConsistentMapsOurcurrentsystemisabletolearn2dand3dmapsusingrangescansrecordedwithamobilerobot.Inbothcases,theapproachisincremental.Mathematically,wecalculateasequenceofposes^l1;^l2;:::andcorrespondingmapsbymaximizingthemarginallikelihoodofthet-thposeandmaprelativetothe(t�1)-thposeandmap:^lt=argmaxltfp(stjlt;^m(^lt�1;st�1))p(ltjut�1;^lt�1)g(7)Inthisequationthetermp(stjlt;^m(^lt�1;st�1))istheprobabilityofthemostrecentmeasurementstgiventheposeltandthemap^m(^lt�1;st�1)constructedsofar.Thetermp(ltjut�1;^lt�1)representstheprobabilitythattherobotisatlocationltgiventherobotwaspreviouslyatposition^lt�1andhascarriedout(ormeasured)themotionut�1.Theresultingpose^ltisthenusedtogenerateanewmap^mviathestandardincrementalmap-updatingfunctionpresentedin[24]:^m(^lt;st)=argmaxmp(mj^lt;st)(8)Theoverallapproachcanbesummarizedasfollows:Atanypointt�1intimetherobotisgivenanestimateofitspose^lt�1andamap^m(^lt�1;st�1).Aftertherobotmovedfurtheronandaftertakinganewmeasurementst,therobotdeterminesthemostlikelynewpose^lt.Itdoesthisbytradingofftheconsistencyofthemeasurementwiththemap(rsttermontheright-handsidein(7))andtheconsistencyofthenewposewiththecontrolactionandthepreviouspose(secondtermontheright-handsidein(7)).Themapisthenextendedbythenewmeasurementst,usingthepose^ltastheposeatwhichthismeasurementwastaken.ItremainstodescribehowweactuallymaximizeEquation(7).Oursystemappliestwodifferentapproachesdependingonwhethertheunderlyingscansare2dor3dscans.5 Tocomputethelikelihoodofabeambgiventhecurrentmap^m(^lt�1;st�1),werstdeterminetheexpecteddistancee(b;^m(^lt�1;st�1))totheclosestobstacleinthemeasurementdirection.Thisisefcientlycarriedoutusingray-tracingtechniquesbasedonaspatialtilingandindexing[25]ofthecurrentmap. Figure5.TheprobabilisticmeasurementmodelgivenasamixtureofaGaussianandauniformdistributionanditsapproximationbypiecewiselinearfunctions.Thenwecomputethelikelihoodofthemeasureddistancegiventheexpecteddistance,i.e.wedeterminethequantityp(bje(b;^m(^lt�1;st�1)))usingthemixturecomputedfore(b;^m(^lt�1;st�1)).Tospeedupcomputation,weapproximatethisdensitybypiecewiselinearfunctions(seealsoFigure5).Assumingthatthebeamscontainedinstareindependent,wecomputethelikelihoodofthewholescanasp(stjlt;^m(^lt�1;st�1))=Yb2stp(bje(b;^m(^lt�1;st�1))):(9)TomaximizeEquation7weagainapplyahillclimbingtechnique.4.3IntegratingPeopleTrackingResultsintotheMapBuildingProcessThegoalofintegratingtheresultsofthepeopletrackerintoamappingprocesscanbedividedintwosubjects:1.toimprovethealignmentbetweenthescansand2.tolteroutcorruptedmeasurementsoriginatingfrompeoplewalkinginthevicinityoftherobot.Toconsidertheestimatedstatesofthepersonsduringthescanalignment,weneedtoknowtheprobabilityP(hitx;yjXt)thatabeamendingatpositionhx;yiisreectedbyaperson.Inourcurrentimplementation,weconsidertheindividualpersonsindependently:P(hitx;yjXt)=1�KYi=1�1�P(hitx;yjxti):(10)InthisequationP(hitx;yjxti)isthelikelihoodthatabeamendingatpositionhx;yiisreectedbypersoni,giventhestatextiofthatperson.Tocomputethisquantity,weconstructatwo-dimensionalandnormalizedhistogrambycountinghowmanysamplesrepresentingthebeliefaboutxtifallintoeachbin.Nowsupposexbandybarethecoordinatesofthecellinwhichthebeambends.Accordingly,wecancomputetheprobabilityP(hitbjxti)thatabeambisreectedbyapersonasP(hitbjXt)=P(hitxb;ybjXt):(11)Itremainstodescribe,howweincorporatethequantityhb=P(hitbjXt)intothescanalignmentandregistrationprocess.Ifweconsiderallbeamsasindependent,thelikelihoodp(stjlt;^m(^lt�1;st�1))ofthemostrecentmeasurementgiveallpreviousscansisobtainedas:p(stjlt;^m(^lt�1;st�1))=Yb2stp(bj^m(^lt�1;st�1)))(1�hb):(12)7 Thus,duringthescanalignmentweweigheachbeambaccordingtotheprobability1�P(hitbjXt).Pleasenotethatthisisageneralformofasituationinwhichitisexactlyknownwhetherornotbisreectedbyaperson.Ifbisknowntobereectedbyaperson,hbequals1suchthatbdoesnotchangethelikelihoodofthescan(seeFigs6and7). (a)(b)(c)(d)Figure6.ExamplesituationinwhichthequantityP(hitx;yjXt)(imaged)iscomputedbycombiningthehistogramsforthreeindividualtrackers(imagea-c). Figure7.TheweightofalaserbeamiscomputedaccordingtothevalueP(hitx;yjXt)ofthecellinwhichitends.Thesecondtaskistolteroutbeamsreectedbypersonstoavoidspuriousobjectsintheresultingmaps.InourcurrentsystemwecomputeaboundingboxforeachsamplesetStiandintegrateonlythosebeamswhoseendpointdoesnotlieinanyoftheboundingboxes.Tocopewiththepossibletimedelayofthetrackers,wealsoignorecorrespondingbeamsofseveralpreviousandnextscansbeforeandafterthepersonwasdetected.Pleasenote,thatonegenerallycanbemoreconservativeduringthemapgenerationprocess,becausetherobotgenerallyscanseverypartoftheenvironmentquiteoften.However,duringscanalignment,atooconservativestrategymayresultintoofewremainingbeamswhichleadstoreducedaccuracyoftheestimatedpositions.5ExperimentsTheapproachdescribedabovehasbeenimplementedandtestedondifferentroboticplatformsandbasedonextensiveoff-lineexperimentscarriedoutwithrecordeddata.Thegoaloftheexperimentsdescribedinthissectionistoillustratethattheintegrationofpeopledetectiontechniquesintothemappingprocessleadstobettermapssincetheresultingalignmentsaremoreaccurateandsincebeamsreectedbypersonsarelteredoutwhichreducesthenumberofspuriousobjects.Pleasenotethatourcurrentimplementationcantrackseveralpeopleinreal-time,sothatthetimetomapanenvironmentisnotinuencedbyusingthisinformation.5.1Learning2dMapsTherstexperimentswerecarriedoutusingthePioneer2robotSamintheemptyexhibitionhalloftheByzan-tineMuseuminAthens,Greece.Thesizeofthisenvironmentis30mx45m.Figure8showstherobotduringthemappingprocess.Therewere15peoplewalkingthroughtheenvironmentwhiletherobotwasmappingit.ThemapobtainedwithoutlteringmeasurementsreectedbypersonsisshownintheleftimageofFigure9.TheresultobtainedwithournewalgorithmisshownintherightimageofFigure9.Bothmapsarehigh-resolution8 Figure11.OccupancygridmapscreatedforthepopulatedcorridorenvironmentoftheUniversityofBonnwithout(upperimage)andwithpeopleltering(lowerimage).5.2ImprovedRobustnessBesidesthefactthattheresultingmapsarebetter,lteringpeopleincreasestherobustnessofthemappingprocess.Todemonstratethiswehavecarriedoutaseriesofexperimentsinwhichweaddedrandomnoisetotheposesintheinputdataandcomparedtheperformanceofourmappingstrategywithandwithoutpeopleltering.Weperformed50experimentsforeachnoiselevel.Figure12showsthenumbersofmapscontainingatranslationalerrorlargerthan200cmforthedifferentnoisevalues.Inthisgurethex-axiscorrespondstothestandarddeviationoftheGaussiannoiseaddedtoeachodometryreading.They-axisisthenumberofmapsinwhichthetranslationalerrorafterregistrationexceeds200cm.Ascanbeeseenbythegure,theuseoftheinformationprovidedbythepeopletrackersignicantlyincreasestheaccuracyofthepositionestimationduringthemappingprocess. Figure12.Numberofmapswithtranslationalerrorlargerthan2mcomputedwithoutpeopleltering(lightgrey)andusingpeopleltering(darkgrey)forincreasinglevelsofnoiseinodometry.5.3Learning3dMapsThelastexperimentwascarriedouttoanalyzetheperformanceofoursystemwhenlearningthree-dimensionalmaps.ForthisexperimentweusedthePioneer2ATplatform(seeFigure13(left))equippedwithtwolaser10 Figure13.Pioneer2ATrobotHerbertfor3doutdoormapping(left)andtypicalsituationinwhichpeoplewalkthroughthesceneduringmapping(right). Figure14.Spuriousobjectscausedbypeoplewalkingthroughtheenvironment.range-scanners.Whereastherstscanner,thatismountedinfrontoftherobot,isusedfortrackingpeople,thesecondscanner,thatismountedonanAMTECwristmodule,isusedtoscanthe3dstructureoftheenvironment.Figure13(right)showsatypicalscenarioduringthisexperimentperformedonouruniversitycampus.Here,sev-eralpeoplewerewalkingthroughthescenewhiletherobotwasscanningit.Figure15(left)depictsthemodelobtainedafteraligningtwoscansofthesameenvironment.Inthismodel,thepeopleappearasthree-dimensionalcurves.Figure14containsamagniedviewofthecorrespondingportionofthemap.Ifweintegratetheinfor-mationobtainedfromthepeopletracker,however,thesespuriousobjectsarecompletelyremoved(seerightimageofFigure15).Thenumberoftrianglesinthesemodelsare416.800withoutlteringand412.500withltering.Pleasenote,thatthisexperimentalsoillustratestheadvantageofusingatrackingsystemoverapurefeature-basedapproach.Duetothedisplacementofthescanners,peoplearenotalwaysvisibleinbothscanners.Accordingly,apurelyfeature-basedapproachlike[33]willaddobjectstothe3dmodelwhenevertheyarenotdetectedbytherstscanner.Oursystem,however,canpredictpositionsofpersonsinthecaseofocclusionsandthuscanlteroutthecorrespondingreadingsevenifthefeaturesaremissing.6ConclusionsInthispaperwepresentedaprobabilisticapproachtomappinginpopulatedenvironments.ThekeyideaofthistechniqueistouseSample-basedJointProbabilisticDataAssociationFilters(SJPDAFs)totrackpeopleinthedataobtainedwiththesensorsoftherobot.Theresultsofthepeopletrackingareintegratedintothescanalignmentprocessandintothemapgenerationprocess.Thisleadstotwodifferentimprovements.First,theresultingposeestimatesarebetterandsecond,theresultingmapscontainlessspuriousobjectsthanthemapscreatedwithout11 Figure15.Three-dimensionalmapofabuilding(left)andpeopleltered(right).lteringpeople.Ourtechniquehasbeenimplementedandtestedondifferentroboticplatformsaswellasforgenerating2dand3dmaps.Theexperimentsdemonstratethatourapproachcanseriouslyreducethenumberofbeamscorruptedbypeoplewalkingthroughtheenvironment.Additionally,extensivesimulationexperimentsillustratethattheposeestimatesaresignicantlybetteriftheresultsofthetrackingsystemareincorporatedduringtheposeestimation.AcknowledgmentsThisworkhaspartlybeensupportedbytheECundercontractnumberIST-2000-29456.References[1]K.O.Arras,R.Philippsen,M.deBattista,M.Schilt,andR.Siegwart.AnavigationframeworkformultiplemobilerobotsanditsapplicationsattheExpo.02exhibition.InProc.oftheIROS-2002WorkshoponRobotsinExhibitions,2002.[2]M.Bennewitz,W.Burgard,andS.Thrun.UsingEMtolearnmotionbehaviorsofpersonswithmobilerobots.InProc.oftheIEEE/RSJInternationalConferenceonIntelligentRobotsandSystems(IROS),2002.[3]P.BeslandN.McKay.Amethodforregistrationof3dshapes.Trans.Patt.Anal.Mach.Intell.14(2),pages239–256,1992.[4]D.BeymerandKonoligeK.Trackingpeoplefromamobileplatform.InIJCAI-2001WorkshoponReasoningwithUncertaintyinRobotics,2001.[5]H.Bui,S.Venkatesh,andG.West.Trackingandsurveillanceinwide-areaspatialenvironmentsusingtheAbstractHiddenMarkovModel.Intl.J.ofPatternRec.andAI,2001.[6]W.Burgard,A.B.Cremers,D.Fox,D.H¨ahnel,G.Lakemeyer,D.Schulz,W.Steiner,andS.Thrun.Experi-enceswithaninteractivemuseumtour-guiderobot.ArticialIntelligence,114(1-2),2000.[7]J.A.Castellanos,J.M.M.Montiel,J.Neira,andJ.D.Tard´os.TheSPmap:Aprobabilisticframeworkforsimultaneouslocalizationandmapbuilding.IEEETransactionsonRoboticsandAutomation,15(5):948–953,1999.[8]I.J.Cox.Areviewofstatisticaldataassociationtechniquesformotioncorrespondence.InternationalJournalofComputerVision,10(1):53–66,1993.[9]G.Dissanayake,H.Durrant-Whyte,andT.Bailey.Acomputationallyefcientsolutiontothesimultaneouslocalisationandmapbuilding(SLAM)problem.InICRA'2000WorkshoponMobileRobotNavigationandMapping,2000.12 [30]S.Thrun.Aprobabilisticonlinemappingalgorithmforteamsofmobilerobots.InternationalJournalofRoboticsResearch,20(5):335–363,2001.[31]S.Thrun,W.Burgard,andD.Fox.Areal-timealgorithmformobilerobotmappingwithapplicationstomulti-robotand3Dmapping.InProc.oftheIEEEInternationalConferenceonRobotics&Automation(ICRA),2000.[32]S.Waldherr,S.Thrun,R.Romero,andD.Margaritis.Template-basedrecognitionofposeandmotiongesturesonamobilerobot.InProc.oftheNationalConferenceonArticialIntelligence(AAAI),1998.[33]C.-C.WangandC.Thorpe.Simultaneouslocalizationandmappingwithdetectionandtrackingofmovingobjects.InProc.oftheIEEEInternationalConferenceonRobotics&Automation(ICRA),2002.[34]Q.Zhu.HiddenMarkovmodelfordynamicobstacleavoidanceofmobilerobotnavigation.IEEETransac-tionsonRoboticsandAutomation,7(3),1991.14