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Map Building with Mobile Robots in Dynamic Environments Dirk H ahnel Rudolph Triebel Wolfram Map Building with Mobile Robots in Dynamic Environments Dirk H ahnel Rudolph Triebel Wolfram

Map Building with Mobile Robots in Dynamic Environments Dirk H ahnel Rudolph Triebel Wolfram - PDF document

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Map Building with Mobile Robots in Dynamic Environments Dirk H ahnel Rudolph Triebel Wolfram - PPT Presentation

Most of the techniques developed so far have been designed for situations in which the environment is static during the mapping process Dynamic objects however can lead to serious errors in the re sulting maps such as spurious objects or misalignmen ID: 22390

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robotsthatoperatesinapopulatedexhibition.Theirsystemuseslinefeaturesforlocalizationandhasbeenreportedtosuc-cessfullylterrange-measurementsreectedbypersons.Foxetal.[9]presentaprobabilistictechniquetoidentifyrangemeasurementsthatdonotcorrespondtothegivenmodeloftheenvironment.Theseapproaches,however,requireagivenandxedmapwhichisusedforlocalizationandfortheextractionofthefeaturescorrespondingtothepeople.Ourtechnique,incontrast,doesnotrequireagivenmap.Ratheritlearnsthemapfromscratchusingthedataacquiredwiththerobot'ssensors.Ouralgorithmrepeatedlyinterleavestheprocessofestimatingwhichbeamsarecausedbydynamicobjectswithamappingandlocalizationalgorithm.Therebyititerativelyimprovesitsestimatesandgeneratesmoreaccuratemodelsoftheenvironment.Fromamoregeneralperspective,theproblemofestimatingdynamicaspectsindatacanberegardedasanoutlierdetec-tionproblem,sincethespuriousmeasurementsaredataitemsthatdonotcorrespondtothestaticaspectsoftheenvironmentwhicharetobeestimated.Theidenticationofoutliersisanimportantsubtaskinvariousapplicationareassuchasdatamining[12,3,16],correspondenceestablishment[6,2],clus-tering[8],orstatistics[1].Inalltheseelds,errorsinthedatareducetheaccuracyoftheresultingmodelsandthuscanleadtoadecreasedperformancewheneverthelearnedmodelsareusedforpredictionorrobotnavigation,forexample.Theproblemconsideredinthispaperdiffersfromtheseapproachesinthefactthatoutlierscannotbedetectedsolelybasedontheirdistancetotheotherdataitems.Rather,themeasurementsrsthavetobeinterpretedandtransformedintoaglobalrepresen-tation(map)beforeindividualmeasurementscanbeidentiedasoutliers.3LearningMapsinDynamicEnvironmentsOurapproachtodiscovermeasurementsthatcorrespondtody-namicobjectsisstrictlystatistical.WeusethepopularEM-algorithmtoidentifydataitemsthatcannotbeexplainedbytherestofthedataset.Theinputtoourroutineisasequenceofdataitemsz=fz1;:::;zTg.Theoutputisamodelmob-tainedfromthesedataitemsafterincorporatingtheestimatesaboutspuriousmeasurements.Inessence,ourapproachseekstoidentifyamodelmthatmaximizesthelikelihoodofthedata.Throughoutthispaperweassumethateachmeasurementztconsistsofmultipledatazt;1;:::;zt;Nasitisthecase,forexample,forlaser-rangescans.Throughoutthispaperweas-sumethatthedatazt;narebeamsobtainedwithalaser-rangescanner.Toaccuratelymapadynamicenvironmentweneedtoknowwhichmeasurementsarecausedbydynamicobjectsandthere-forecansafelybeignoredinthealignmentandmapupdatingphase.Tocharacterizespuriousmeasurementsinthedataweintroduceadditionalvariablesct;nthattellusforeachtandeachn,whetherthedataitemzt;niscausedbyastaticobjectornot.Eachsuchvariablect;nisabinaryvariable,thatisei-ther0or1.Itis1ifandonlyifthezt;niscausedbyastaticobject.Thevectorofallthesevariableswillbedenotedbyc. Figure1:Beamcoveringzt;ncellsofamap.Forthesakeofsimplicity,wegivethederivationforbeamsthatareparalleltothex-axisofthemap.Inthiscase,thelengthzt;ndirectlycorrespondstothenumberofcellscov-eredbythisbeam.Wewilllaterdescribehowtodealwithbeamsthatarenotparalleltothex-axis.Letfbeafunctionthatreturnsforeachpositionxtoftherobot,eachbeamnum-bern,andeachkzt;ntheindexf(xt;n;k)ofk-theldcoveredbythatbeaminthemap(seeFigure1).Todeterminewhetherornotabeamisreectedbyadynamicobject,weneedtodenethelikelihoodofameasurementgiventhecur-rentmapmoftheenvironment,theposexoftherobot,andtheinformationaboutwhetherzt;nisreectedbyamaximumrangereading.Typically,maximum-rangereadingshavetobetreateddifferently,sincethosemeasurementsgenerallyarenotreectedbyanyobject.Throughoutthispaperweintro-duceindicatorvariablest;nwhichare1ifandonlyifzt;nisamaximumrangereadingand0,otherwise.Thelikelihoodofameasurementzt;ngiventhevalueofct;nandthemapmcanthusbecomputedas:p(zt;njct;n;xt;m)="zt;n�1Yk=0(1�mf(xt;n;k)))#t;n"[mf(xt;n;zt;n)]ct;n[1�mf(xt;n;zt;n)](1�ct;n)zt;n�1Yk=0(1�mf(xt;n;k))#(1�t;n)(1)Thersttermofthisequationspeciesthelikelihoodofthebeamgivenitisamaximumrangescan.Insuchasituation,wecomputethelikelihoodastheproductoftheprobabilitiesthatthebeamhascoveredthecells0tozt;n�1.Pleasenote,thatthecellinwhichthebeamendsdoesnotprovideanyinformationsincewedonotknow,whetherthereisanobjectornotgiventhebeamisamaximumrangereading.Therebytheprobabil-itythatabeamcoversacellkzt;nisequalto1�mf(xt;n;k).Thesecondrowofthisequationspecieshowtodealwiththecasethatacellthatreectsanon-maximumrangebeam.Ifzt;nisnotreectedbyadynamicobject,i.e.ct;n=1,thenthelikelihoodequalsmf(xt;n;zt;n).If,incontrast,zt;nisre-ectedbyadynamicobject,thelikelihoodis1�mf(xt;n;zt;n).Aswellasforthemaximumrangemeasurementswehavetop.2 considerinbothcasesthatthebeamhascoveredzt;n�1cellsbeforereachingcellf(xt;n;zt;n).Basedonthedenitionoftheobservationlikelihoodwenowwilldenethelikelihoodp(z;cjx;m)ofthedatawhichwetrytomaximizeinordertondthemostlikelymapoftheenvironment.p(z;cjx;m)=TYt=1p(zt;ctjxt;m)(2)=TYt=1p(zt;jxt;m)p(ctjxt;m)(3)=TYt=1p(zt;jxt;m)p(ct)(4)=TYt=1NYn=1p(zt;n;jct;n;xt;m)p(ct)(5)WeobtainEquation(3)fromEquation(2)byassumingthattheztandctareindependentgivenxtandm.Wefurthermoreconsiderctasindependentfromthelocationxtandthemapm,whichleadstoEquation(4).Finally,Equation(5)isde-rivedfromEquation(4)undertheusualassumption,thattheneighboringbeamsofasinglescanareindependentgiventhemapoftheenvironment.Maximizingp(z;cjx;m)isequivalenttomaximizingthecorrespondingloglikelihood,whichcanbederivedfromEquation(5)andEquation(1)bystraightforwardmathemat-icaltransformations:lnp(z;cjx;m)=lnTYt=1NYn=1p(zt;n;jct;n;xt;m)p(ct)=NTXt=1lnp(ct)+TXt=1NXn=1lnp(zt;n;jct;n;xt;m)=NTXt=1lnp(ct)+TXt=1NXn=1"(1�t;n)hct;nlnmf(xt;n;zt;n)+(1�ct;n)ln(1�mf(xt;n;zt;n))i+zt;n�1Xk=0ln(1�mf(xt;n;k))#(6)Sincethecorrespondencevariablescarenotobservableintherstplaceacommonapproachistointegrateoverthem,thatis,tooptimizetheexpectedloglikelihoodEc[lnp(c;zjx;m)jx;m;d]instead.Sincetheexpectationisalinearoperator,wecanmoveitinsidetheexpression.Byexploitingthefactthattheexpectationofct;nonlydependsonthecorrespondingmeasurementzt;nandthepositionxtoftherobotatthattime.wecanderivethefollowingequation:Ec[lnp(z;cjx;m)jz;x;m]= +TXt=1NXn=1"et;n(1�t;n)lnmf(xt;n;zt;n)+(1�et;n)(1�t;n)ln(1�mf(xt;n;zt;n))+zt;n�1Xk=0ln(1�mf(x;n;k))#(7)Forthesakeofbrevity,weusethetermet;n=Ec[ct;njzt;n;xt;m](8)inthisequation.Theterm =NTXt=1Ec[lnp(ct)jz;x;m](9)iscomputedfromthepriorp(ct)ofthemeasurementswhichisindependentofz,x,andm.Accordingly, canberegardedasaconstant.Unfortunately,optimizingEquation(7)isnotaneasyen-deavor.AtypicalapproachtomaximizeloglikelihoodsistheEMalgorithm.Intheparticularproblemconsideredherethisamountstogeneratingasequenceofmapsmofincreasinglikelihood.IntheE-Step,wecomputetheexpectationsaboutthehiddenvariablesc.IntheM-stepwethencomputethemostlikelymapmusingtheexpectationscomputedintheE-Step.Bothstepsaredescribedindetailintheremainderofthissection.IntheE-stepwecomputetheexpectationset;n=Ec[ct;njzt;n;xt;m]foreachct;ngiventhemeasurementzt;n,thelo-cationxtoftherobotandthecurrentmapm.Exploitingthefactthatet;nequalsp(ct;njzt;n;xt;m)andconsideringthetwocasesthatzt;nisamaximumrangereadingornot,weobtain:et;n=(p(ct;n),ift;n=1p(ct;n)t;n,otherwisewheret;n=1 p(ct;n)+(1�p(ct;n))(1 mf(xt;n;zt;n)�1)(10)Therstequationcorrespondstothesituationthatzt;nisamaximumrangereading.Then,et;ncorrespondstothepriorprobabilityp(ct;n)thatameasurementisreectedbyastaticobject.Thus,amaximumrangereadingdoesnotprovideanyevidenceaboutwhetherornotthecellinthemapinwhichthebeamendsiscoveredbyadynamicobject.IntheM-StepwewanttodeterminethevaluesformandxthatmaximizeEquation(7)aftercomputingtheexpectationset;np.3 Figure5:EvolutionofthemapduringEM.Theimagescorrespondstoiteration1,2,and6. Figure3:RobotSammappingthepopulatedexhibitionhalloftheByzantineMuseuminAthens(left).Intheresultingmap(right),themeasurementslabeledasdynamicareshowningrey/orange. Figure4:Evolutionoftheloglikelihood(Equation(6))duringtheindividualiterations.computethelikelihoodthatabeamcoversacelljofmas(1�mj).Otherwise,transversalbeamscoveringmorecellswouldaccumulatealowerlikelihood.Thesolutiontothisistoweighthebeamsaccordingtothelengthbywhichtheycoveracell.SupposeBisthesetofcellsinmcoveredbyabeam.Furthermoresupposeljisthelengthbywhichthebeamcoverseldj2B.Then,thelikelihoodofacoveringallcellsinBiscomputedasQj2B(1�mj)lj.4ExperimentsTheapproachdescribedabovehasbeenimplementedandtestedondifferentroboticplatforms,indifferentenvironmentsandwith2dand3ddata.Inallexperiments,weguredout,thatthesystemisrobusteveninhighlydynamicenvironments.Inoneexperimentcarriedoutwithafastmovingcar,thesys-temwasabletoaccuratelymaptheenvironmentevenifnoodometrydatawasgiven.4.1FilteringPeopleTherstexperimentswerecarriedoutusingthePioneer2robotSamintheemptyexhibitionhalloftheByzantineMu-seuminAthens,Greece.Thesizeofthisenvironmentis30mx45m.Therobottraveledcontinously57mwithanavg.speedof0.37m/sandamax.speedof0.96m/s.Figure3(left)showstherobotduringthemappingprocess.Therewere15peoplewalkingwithatypicalspeedthroughtheenvironmentwhiletherobotwasmappingit.Partiallytheystoppedandcontin-uedmoving.Themostlikelymapresultingfromtheappli-cationofourapproachisshowninatherightimageofFig-ure3.Thebeamslabeledasdynamicaredrawngrey/orangeinthisgure.Ascanbeseen,ourapproachcanreliablyiden-tifydynamicaspectsandisabletolearnmapsthatincludethestaticaspectsonly.Atthispointwewouldalsoliketomentionthattheresultingmapcontainsseriouslylessdynamicobjectsthanthemapobtainedwithourpreviousapproachpresentedin[11].Figure4plotstheevolutionofEc[lnp(c;zjx;m)jx;m;d]overthedifferentiterationsofouralgorithm.Itillustratesthatouralgorithminfactmaximizestheoverallloglikelihood.Pleasenote,thatthiscurvegenerallyisnotmonotonic,be-causeoftheincrementalmaximum-likelihoodsolutiontotheSLAMproblem.Slightvariationsintheposecanhaveneg-ativeeffectsinfuturesteps,sothatthemaplikelihoodcandecrease.However,weneverobservedsignicantdecreaseoftheloglikelihood.4.2ImprovedLocalizationAccuracyBesidesthefactthattheresultingmapscontainlessspuriousobjects,ourapproachalsoincreasesthelocalizationaccuracy.Ifdynamicobjectsarenothandledappropriatelyduringlocal-ization,matchingerrorsbecomemorelikely.Figure6showsatypicalmapweobtainedwhenmappingadenselypopu-latedenvironment.InthiscasewemappedapartoftheWeanHallCorridoratCarnegieMellonUniversityduringpeakof-cehourswhenmanypersonswerearound.Someofthemweretryingtoblocktherobot,sothattherobothadtomakedetoursaroundthem.Thereforetherobottraveled74mwithanavg.speedof0.15m/s(0.35m/smaximum).Despitethefact,thatthehugeamountofspuriousobjectsmakethemapvirtuallyuselessfornavigationtasks,themapalsoshowsse-riouserrorsinthealignment.Someoftheerrorsareindicatedbyarrowsinthecorrespondinggure.Figure7showsthemapgeneratedbyouralgorithm.Asthegureillustrates,thespuriousmeasurements(indicatedbygrey/orangedots)havebeenlteredoutcompletely.Addition-ally,thealignmentofthescansismoreaccurate.p.5 Figure6:MapobtainedinapopulatedcorridoroftheWeanHallatCarnegieMellonUniversityusingtherawinputdata. Figure7:Mapgeneratedbyouralgorithm.Figure5depictstheevolutionofapartofthemapinthediffer-entroundsoftheEM.Itshowshowthebeamscorrespondingtodynamicobjectsslowlyfadeoutandhowtheimprovedes-timatesaboutthesebeamsimprovethelocalizationaccuracy.4.3GeneratingLarge-ScaleOutdoorMapsToevaluatethecapabilityofourtechniquetodealwitharbi-traryfeatures,wemountedalaser-rangescanneronacaranddroveapproximately1kmthroughPittsburgh,PA,USA(Cor-nerbetweenCraigStreetandForbesAvenue).Themaximumspeedofthecarwas35MPHinthisexperiment.Wethenap-pliedourapproachtotherecordeddata.ThemapgeneratedbyouralgorithmisshowninFigure8.Whereastheblackdotscorrespondtothestaticobjectsinthescene,thewhitedotsarethosewhicharelteredoutusingourapproach.Again,mostofthedynamicsofthescenecouldberemoved.Onlyafewcarscouldnotbeidentiedasdynamicobjects.Thisismainlybecausewequicklypassedcarswaitingforturnsandbecausewedrovealongthepathonlyonce.Pleasealsonote,thatduetothelackofaGPS,themaphadtobecomputedwithoutanyodometryinformation.4.4GeneratingTextured3DMapsTodemonstratethatourapproachisnotlimitedto2drangedata,wecarriedoutseveralexperimentswiththemobilerobotRobin(seeFigure9)whichisequippedwithalaser-scanner Figure8:Mapofanoutdoorsceneafterlteringdynamicobjects. Figure9:ThemobilerobotRobinusedtogeneratetextured3dmodels(left).Beamsreectedbyapersonareisolatedfromtherestofthedata.Thisisachievedbycomputingaboundingboxaroundthosebeamsperceivedwiththehorizontalscannerthatareidentiedascorrespondingtodynamicobjects(centerandright). Figure10:Textured3dmodelofapersonidentiedasadynamicobject.mountedonanAMTECpan/tiltunit.Ontopofthisscannerweinstalledacamerawhichallowsustoobtaintextured3dmapsofanenvironment.Additionally,thisrobotcontainsahorizontallyscanninglaserrangenderwhichweusedinourexperimentstodeterminedynamicobjects.Tolabelthebeamsinthe3ddataasdynamicweuseaboundingboxaroundthedynamic2dpoints.Tolterdynamicobjectsinthetex-turesrecordedwithRobin'scameraswechooseforeverypoly-gonthatimagewhichhasthehighestlikelihoodofcontainingstaticaspectsonly.TheleftimageofFigure11showsonepar-ticularviewofamodelobtainedwithoutlteringofdynamicobjects.Thearrowindicatesapolygonwhosetexturecontainsfractionsofanimageofapersonwhichwalkedthroughthescenewhiletherobotwasscanningit.Afterapplyingourap-proachthecorrespondingbeamsandpartsofthepictureswerelteredout.TheresultingmodelshownintherightimageofFigure11thereforeonlycontainstexturesshowingstaticob-jects.4.5ExtractingTextured3dObjectsAdditionallytolteringdynamicobjectsandlearningstaticaspectsofenvironmentsouralgorithmcanalsobeusedtosep-aratedynamicobjectsfromtheenvironment.Thekeyideaistoextractallmeasurementsfromthe3ddatathatliewithinaboundingboxaroundthebeamswhoseprobabilitythattheyarereectedbydynamicobjectsexceeds0.7.Figure9showstwoviewsofatypical3ddatasetsobtainedwiththisapproach.Whereasthedatapointsbelongingtoadynamicobjectareshowninblack,therestofthedataisdepictedingrey.Againweusedthecameratomaptexturesonthe3ddatathatwerep.6 Figure11:Textured3dmodelsobtainedusingRobin.Theupperimageshowstheresultwithoutltering.Thelowerimageshowstheresultingmodelobtainedwithouralgorithm.identiedasbelongingtoadynamicobject.Figure10depictsthreeviewsoftheresultingmodel.Ascanbeseenfromthegure,ourapproachcanaccuratelyextractrealisticlookingtextured3dmodelsofdynamicobjects.5ConclusionsInthispaperwepresentedaprobabilisticapproachtomap-pingindynamicenvironments.OurapproachusestheEMalgorithmtointerleavetheidenticationofmeasurementsthatcorrespondtodynamicobjectswithamappingandlocaliza-tionalgorithm.Thiswayitincrementallyimprovesitsesti-mateaboutspuriousmeasurementsandthequalityofthemap.Thenallyobtainedmapscontainlessspuriousobjectsandalsoaremoreaccuratebecauseoftheimprovedrangeregis-tration.Ourtechniquehasbeenimplementedandtestedondiffer-entplatforms.Inseveralexperimentscarriedoutinindoorandoutdoorenvironmentswedemonstratedthatourapproachyieldsaccuratemapsevenifusedonafastmovingvehiclewithoutodometryinformation.Wealsopresentedanappli-cationtolearntextured3dmodelsofdynamicenvironments.Finally,weappliedouralgorithmtoextractdynamicobjectsfrom3ddata.Theresultsillustratethatourapproachcanreli-ablyestimatewhichbeamscorrespondtodynamicobjects.AcknowledgementsThisworkhaspartlybeensupportedbytheECundercontractnumberIST-2000-29456andbytheGermanSci-enceFoundation(DFG)undercontractnumberSFB/TR8-03.IthasalsobeensponsoredbyDARPA'sMARS,CoABS,andMICAProgramme(contractnumbersN66001-01-C-6018,NBCH1020014,F30602-98-2-0137,andF30602-01-C-0219)andbytheNSFundergrantnumbersIIS-9876136andIIS-9877033.References[1]V.BarnettandT.Lewis.OutliersinStatisticalData.Wiley,NewYork,1994.[2]P.BeslandN.McKay.Amethodforregistrationof3dshapes.Trans.Patt.Anal.Mach.Intell.14(2),pages239–256,1992.[3]C.E.BrodleyandM.A.Friedl.Identifyingandeliminatingmisla-beledtraininginstances.InProc.oftheNationalConferenceonArticialIntelligence(AAAI),1996.[4]W.Burgard,A.B.Cremers,D.Fox,D.H¨ahnel,G.Lakemeyer,D.Schulz,W.Steiner,andS.Thrun.Experienceswithaninteractivemuseumtour-guiderobot.ArticialIntelligence,114(1-2),2000.[5]J.A.Castellanos,J.M.M.Montiel,J.Neira,andJ.D.Tard´os.TheSPmap:Aprobabilisticframeworkforsimultaneouslocalizationandmapbuilding.IEEETransactionsonRoboticsandAutomation,15(5):948–953,1999.[6]I.J.CoxandS.L.Hingorani.Anefcientimplementationofreidsmultiplehypothesistrackingalgorithmanditsevaluationforthepurposeofvisualtracking.IEEETransactionsonPAMI,18(2):138–150,February1996.[7]G.Dissanayake,H.Durrant-Whyte,andT.Bailey.Acomputationallyefcientsolutiontothesimultaneouslocalisationandmapbuilding(SLAM)problem.InICRA'2000WorkshoponMobileRobotNavigationandMapping,2000.[8]R.Duda,P.Hart,andD.Stork.PatternClassication.Wiley-Interscience,2001.[9]D.Fox,W.Burgard,andS.Thrun.Markovlocalizationformobilerobotsindynamicenvironments.JournalofArticialIntelligenceResearch(JAIR),11:391–427,1999.[10]J.-S.GutmannandK.Konolige.Incrementalmappingoflargecyclicenvironments.InProc.oftheIEEEInt.Symp.onComputationalIntelligenceinRoboticsandAutomation(CIRA),1999.[11]D.H¨ahnel,D.Schulz,andW.Burgard.Mappingwithmobilerobotsinpopulatedenvironments.InProc.oftheIEEE/RSJInternationalConferenceonIntelligentRobotsandSystems(IROS),2002.[12]GeorgeH.John.Robustdecisiontrees:Removingoutliersfromdatabases.InFirstInternationalConferenceonKnowledgeDiscoveryandDataMining,pages174–179,1995”.[13]J.J.LeonardandH.J.S.Feder.Acomputationallyefcientmethodforlarge-scaleconcurrentmappingandlocalization.InProc.oftheNinthInt.Symp.onRoboticsResearch(ISRR),1999.[14]F.LuandE.Milios.Globallyconsistentrangescanalignmentforenvironmentmapping.AutonomousRobots,4:333–349,1997.[15]M.MontemerloandS.Thrun.Conditionalparticleltersforsimul-taneousmobilerobotlocalizationandpeople-tracking(slap).InProc.oftheIEEEInternationalConferenceonRobotics&Automation(ICRA),2002.[16]S.Ramaswamy,R.Rastogi,andS.Kyuseok.Efcientalgorithmsforminingoutliersfromlargedatasets.InProc.oftheACMSIGMODInterna-tionalConferenceonManagementofData,2000.[17]H.Shatkay.LearningModelsforRobotNavigation.PhDthesis,Com-puterScienceDepartment,BrownUniversity,Providence,RI,1998.[18]http://robotics.ep.ch/,2002.[19]S.Thrun.Aprobabilisticonlinemappingalgorithmforteamsofmo-bilerobots.InternationalJournalofRoboticsResearch,20(5):335–363,2001.[20]C.-C.WangandC.Thorpe.Simultaneouslocalizationandmappingwithdetectionandtrackingofmovingobjects.InProc.oftheIEEEInterna-tionalConferenceonRobotics&Automation(ICRA),2002.p.7