Particle Filtering. CSE 473: Artificial Intelligence Particle Filters. Representation: Particles. Particle Filtering: Elapse Time

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1 CSE 473: Arificil Inelligence Pricle Filers Dieer Fo Universiy of Wshingon [Mos slides were creed by Dn Klein nd Pieer Abbeel for CS88 Inro o AI UC Berkeley. All CS88 merils re vilble h://i.berkeley.ed.] Filering: roime solion Pricle Filering Someimes X is oo big o se ec inference X my be oo big o even sore BX E.g. X is coninos X 2 my be oo big o do des Solion: roime inference Trck smles of X, no ll vles Smles re clled ricles Time er se is liner in he nmber of smles B: nmber needed my be lrge In memory: lis of ricles, no ses This is how robo locliion works in rcice Reresenion: Pricles Pricle Filering: Else Time Or reresenion of PX is now lis of N ricles smles Generlly, N << X Soring m from X o cons wold defe he oin P roimed by nmber of ricles wih vle So, mny my hve P = 0! More ricles, more ccrcy For now, ll ricles hve weigh of Pricles: 3,3 2,3 3,3 3,2 3,3 3,2,2 3,3 3,3 2,3 Ech ricle is moved by smling is ne osiion from he rnsiion model This is like rior smling smles freqencies reflec he rnsiion robbiliies Here, mos smles move clockwise, b some move in noher direcion or sy in lce This cres he ssge of ime If enogh smles, close o ec vles before nd fer consisen Pricles: 3,3 2,3 3,3 3,2 3,3 3,2,2 3,3 3,3 2,3 Pricles: 3,2 2,3 3,2 3, 3,3 3,2,3 2,3 3,2 2,2 Pricle Filering: Observe Pricle Filering: Resmle Slighly rickier: Don smle observion, fi i Similr o likelihood weighing, downweigh smles bsed on he evidence Pricles: 3,2 2,3 3,2 3, 3,3 3,2,3 2,3 3,2 2,2 Rher hn rcking weighed smles, we resmle N imes, we choose from or weighed smle disribion i.e. drw wih relcemen Pricles: 3,2 w=.9 2,3 w=.2 3,2 w=.9 3, w=.4 3,3 w=.4 3,2 w=.9,3 w=. 2,3 w=.2 3,2 w=.9 2,2 w=.4 As before, he robbiliies don sm o one, since ll hve been downweighed in fc hey now sm o N imes n roimion of Pe Pricles: 3,2 w=.9 2,3 w=.2 3,2 w=.9 3, w=.4 3,3 w=.4 3,2 w=.9,3 w=. 2,3 w=.2 3,2 w=.9 2,2 w=.4 This is eqivlen o renormliing he disribion Now he de is comlee for his ime se, conine wih he ne one New Pricles: 3,2 2,2 3,2 2,3 3,3 3,2,3 2,3 3,2 3,2

2 Rec: Pricle Filering Pricles: rck smles of ses rher hn n elici disribion Else Weigh Resmle Pricle Filers in Roboics Pricles: 3,3 2,3 3,3 3,2 3,3 3,2,2 3,3 3,3 2,3 Pricles: 3,2 2,3 3,2 3, 3,3 3,2,3 2,3 3,2 2,2 Pricles: 3,2 w=.9 2,3 w=.2 3,2 w=.9 3, w=.4 3,3 w=.4 3,2 w=.9,3 w=. 2,3 w=.2 3,2 w=.9 2,2 w=.4 New Pricles: 3,2 2,2 3,2 2,3 3,3 3,2,3 2,3 3,2 3,2 [Demos: ghosbsers ricle filering L5D3,4,5] Robo Locliion In robo locliion: We know he m, b no he robo s osiion Observions my be vecors of rnge finder redings Se sce nd redings re yiclly coninos works bsiclly like very fine grid nd so we cnno sore BX Pricle filering is min echniqe Byes Filer for Robo Locliion Byes Filers: Frmework GPBsed WiFi Sensor Model Given: Srem of observions nd cion d : d = {, 2!,, } Sensor model P. Acion model P,. Men Prior robbiliy of he sysem se P. Wned: Esime of he se X of dynmicl sysem. The oserior of he se is lso clled ief: = P, 2!,, Vrince CSE57: Probbilisic 5/3/7 Roboics = P,!,, Byes Byes Filers =h P,,,!, P,,!, Mrkov =h P P,,!, Mrginl. Mrkov ò ò = h P P, d = observion = cion = se = η P P,,,, P,,, d = h P P, P,,!, d 2

3 Mrkov Assmion Piecewise Consn ief 0 :, :, : = :, :, : =, Underlying Assmions Sic world Indeenden noise Perfec model, no roimion errors Piecewise Consn Reresenion Proimiy Sensor Model =<, y, q > Lser sensor Sonr sensor Probbilisic Kinemics Robo moves from, y,q o ', y',. q ' Odomery informion = d. ro, d ro2, drns Probbilisic Kinemics Odomery informion is inherenly noisy. d 2 2 rns = ' + y' y d = n2 y' y, ' q ro d = q q d ro2 ' ro, y,q d d rns ro ', y', q ' d ro2, 3

4 Sonrs nd Occncy Grid M Lserbsed Locliion Msem Torgide Minerv SmleBsed Densiy Aroimion Pricle ses cn be sed o roime densiies The more ricles fll ino n inervl, he higher he robbiliy of h inervl How o drw smles form fncion/disribion? Imornce Smling Princile Pricle Filers We cn se differen disribion g o genere smles from f By inrodcing n imornce weigh w, we cn ccon for he differences beween g nd f w = f / g f is ofen clled rge g is ofen clled roosl 4

5 5 w = Sensor Informion: Imornce Smling ò ' d ' ', Robo Moion w = Sensor Informion: Imornce Smling Robo Moion ò ' d ' ', drw i from drw i from i, Imornce fcor for i :,, disribion roosl rge disribion i w µ = = h, ò = d h Pricle Filer Algorihm Sr Smled Moion Model

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8 Pricle Filer Locliion Sonr 47 [Video: globlfloor.gif] 8

9 Aibo Sensor Model Disribions for P Locliion for AIBO robos WiFiBsed Peole Trcking WiFi Sensor Model Trcking Emle Men Vrince 9

10 Adive Smling KLDSmling Sonr Ad nmber of ricles on he fly bsed on sisicl roimion mesre KLDSmling Lser Robo Ming SLAM: Simlneos Locliion And Ming We do no know he m or or locion Se consiss of osiion AND m! Min echniqes: Klmn filering Gssin HMMs nd ricle mehods DPSLAM, Ron Prr [Demo: PARTICLESSLAMmingnew.vi] Ming wih Lser Scnner RoBlckwellied Ming wih ScnMching MIT Roboics 205 Dieer Fo: RGBD Perceion in Roboics M: Inel Reserch Lb Sele 0

11 Loo Closre Emle RoBlckwellied Ming wih Scn Mching 3 ricles m of ricle m of ricle 3 m of ricle 2 M: Inel Reserch Lb Sele RoBlckwellied Ming wih Scn Mching M: Inel Reserch Lb Sele Emle Inel Lb 5 ricles for imes fser hn relime P4, 2.8GH 5cm resolion dring scn mching cm resolion in finl m Work by Grisei e l. Odoor Cms M 30 ricles m km miles odomery 20cm resolion dring scn mching 30cm resolion in finl m Work by Grisei e l.