SEIF, EnKF, EKF SLAM - People @ EECS at UC Berkeley · 2015-12-01 · EKF-SLAM: prac6cal challenges...
Transcript of SEIF, EnKF, EKF SLAM - People @ EECS at UC Berkeley · 2015-12-01 · EKF-SLAM: prac6cal challenges...
SEIF,EnKF,EKFSLAM
PieterAbbeelUCBerkeleyEECS
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n Fromananaly6calpointofview==Kalmanfilter
n Difference:keeptrackoftheinversecovarianceratherthanthecovariancematrix[maFerofsomelinearalgebramanipula6onstogetintothisform]
n Whyinteres6ng?
n Inversecovariancematrix=0iseasiertoworkwiththancovariancematrix=infinity(caseofcompleteuncertainty)
n InversecovariancematrixisoPensparserthanthecovariancematrix---forthe“insiders”:inversecovariancematrixentry(i,j)=0ifxiiscondi6onallyindependentofxjgivensomeset{xk,xl,…}
n Downside:whenextendedtonon-linearseZng,needtosolvealinearsystemtofindthemean(aroundwhichonecanthenlinearize)
n SeeProbabilis6cRobo6cspp.78-79formorein-depthpros/consandProbabilis6cRobo6csChapter12foritsrelevancetoSLAM(thenoPenreferredtoasthe“sparseextendedinforma6onfilter(SEIF)”)
Informa6onFilter
n KalmanfilterexactunderlinearGaussianassump6ons
n Extensiontonon-linearseZng:
n ExtendedKalmanfilter
n UnscentedKalmanfilter
n ExtensiontoextremelylargescaleseZngs:
n EnsembleKalmanfilter
n SparseInforma6onfilter
n Mainlimita6on:restrictedtounimodal/Gaussianlookingdistribu6ons
n Canalleviatebyrunningmul6pleXKFs+keepingtrackofthelikelihood;butthisiss6lllimitedintermsofrepresenta6onalpowerunlessweallowaverylargenumberofthem
KFSummary
EKF/UKFSLAM
n State:(nR,eR,θR,nA,eA,nB,eB,nC,eC,nD,eD,nE,eE,nF,eF,nG,eG,nH,eH)
n Nowmap=loca6onoflandmarks(vs.gridmaps)
n Transi6onmodel:
n Robotmo6onmodel;Landmarksstayinplace
B E
FC
H
AG
D
R
SimultaneousLocaliza6onandMapping(SLAM)
n Inprac6ce:robotisnotawareofalllandmarksfromthebeginning
n Moreover:nouseinkeepingtrackoflandmarkstherobothasnotreceivedanymeasurementsabout
àIncrementallygrowthestatewhennewlandmarksgetencountered.
n Landmarkmeasurementmodel:robotmeasures[xk;yk],theposi6onoflandmarkkexpressedincoordinateframeaFachedtotherobot:n h(nR,eR,θR,nk,ek)=[xk;yk]=R(θ)([nk;ek]-[nR;
eR])
n OPenalsosomeodometrymeasurementsn E.g.,wheelencoders
SimultaneousLocaliza6onandMapping(SLAM)
VictoriaParkDataSetVehicle
[courtesy by E. Nebot]
DataAcquisi6on
[courtesy by E. Nebot]
VictoriaParkDataSet
[courtesy by E. Nebot]
Es6matedTrajectory
[courtesy by E. Nebot]
EKFSLAMApplica6on
[courtesy by J. Leonard]
12
EKFSLAMApplica6on
odometry estimated trajectory
[courtesy by John Leonard]
Landmark-basedLocaliza6on
EKF-SLAM:prac6calchallengesn Defininglandmarks
n Laserrangefinder:Dis6nctgeometricfeatures(e.g.useRANSACtofindlines,thenusecornersasfeatures)
n Camera:“interestpointdetectors”,textures,color,…
n OPenneedtotrackmul6plehypotheses
n Dataassocia6on/Correspondenceproblem:whenseeingfeaturesthatcons6tutealandmark---Whichlandmarkisit?
n Closingtheloopproblem:howtoknowyouareclosingaloop?
à Cansplitoffmul6pleEKFswheneverthereisambiguity;
à KeeptrackofthelikelihoodscoreofeachEKFanddiscardtheoneswithlowlikelihoodscore
n Computa6onalcomplexitywithlargenumbersoflandmarks.