Introduction to Mobile Robotics SLAM: Simultaneous Localization and Mapping

Transcription

1 Inroducion o Mobile Roboics SLAM: Simulaneous Localizaion and Mapping Wolfram Burgard, Maren Bennewiz, Diego Tipaldi, Luciano Spinello

2 Wha is SLAM? Esimae he pose of a robo and he map of he environmen a he same ime SLAM is hard, because a map is needed for localizaion and a good pose esimae is needed for mapping Localizaion: inferring locaion given a map Mapping: inferring a map given locaions SLAM: learning a map and locaing he robo simulaneously

3 The SLAM Problem SLAM has long been regarded as a chicken-or-egg problem: a map is needed for localizaion and a pose esimae is needed for mapping 3

4 SLAM Applicaions SLAM is cenral o a range of indoor, oudoor, in-air and underwaer applicaions for boh manned and auonomous vehicles. Examples: A home: vacuum cleaner, lawn mower Air: surveillance wih unmanned air vehicles Underwaer: reef monioring Underground: exploraion of mines Space: errain mapping for localizaion 4

5 SLAM Applicaions Indoors Undersea Space Underground 5

6 Map Represenaions Examples: Subway map, ciy map, landmark-based map Maps are opological and/or meric models of he environmen 6

7 Map Represenaions in Roboics Grid maps or scans, 2d, 3d [Lu & Milios, 97; Gumann, 98: Thrun 98; Burgard, 99; Konolige & Gumann, 00; Thrun, 00; Arras, 99; Haehnel, 01; Grisei e al., 05; ] Landmark-based [Leonard e al., 98; Caselanos e al., 99: Dissanayake e al., 2001; Monemerlo e al., 2002; 7

8 The SLAM Problem SLAM is considered a fundamenal problems for robos o become ruly auonomous Large variey of differen SLAM approaches have been developed The majoriy uses probabilisic conceps Hisory of SLAM daes back o he mid-eighies 8

9 Feaure-Based SLAM Given: The robo s conrols Relaive observaions Waned: Map of feaures Pah of he robo 9

10 Feaure-Based SLAM Absolue robo poses Absolue landmark posiions Bu only relaive measuremens of landmarks 10

11 Why is SLAM a hard problem? 1. Robo pah and map are boh unknown 2. Errors in map and pose esimaes correlaed 11

12 Why is SLAM a hard problem? The mapping beween observaions and landmarks is unknown Picking wrong daa associaions can have caasrophic consequences (divergence) Robo pose uncerainy 12

13 SLAM: Simulaneous Localizaion And Mapping Full SLAM: p( x :, m z1:, u1 : 0 Online SLAM: ) Esimaes enire pah and map! p ( x, m z1 :, u1: ) p( x1:, m z1:, u1: ) dx1dx2... dx 1 Esimaes mos recen pose and map! Inegraions (marginalizaion) ypically done recursively, one a a ime 13

14 Graphical Model of Full SLAM p( x1 : 1, m z1: 1, u1: 1) 14

15 Graphical Model of Online SLAM p( x 1, m z1: 1, u1: 1) p( x1: 1, m z1: 1, u1: 1) dx1dx2 dx 15

16 Moion and Observaion Model "Moion model" "Observaion model" 16

17 Remember he KF Algorihm 1. Algorihm Kalman_filer( -1, -1, u, z ): 2. Predicion: Correcion: Reurn, 17 u A B 1 T R A A 1 1 ) ( T T Q C C C K ) ( C z K C K I ) (

18 EKF SLAM: Sae represenaion Localizaion 3x1 pose vecor 3x3 cov. marix SLAM Landmarks simply exend he sae. Growing sae vecor and covariance marix! 18

19 EKF SLAM: Sae represenaion Map wih n landmarks: (3+2n)-dimensional Gaussian Can handle hundreds of dimensions 19

20 EKF SLAM: Filer Cycle 1. Sae predicion 2. Measuremen predicion 3. Measuremen 4. Daa associaion 5. Updae

21 EKF SLAM: Sae Predicion

22 EKF SLAM: Measuremen Predicion

23 EKF SLAM: Obained Measuremen

24 EKF SLAM: Daa Associaion

25 EKF SLAM: Updae Sep

26 EKF SLAM Map Correlaion marix 26

27 EKF SLAM Map Correlaion marix 27

28 EKF SLAM Map Correlaion marix 28

29 EKF SLAM: Correlaions Maer Wha if we negleced cross-correlaions? 29

30 EKF SLAM: Correlaions Maer Wha if we negleced cross-correlaions? Landmark and robo uncerainies would become overly opimisic Daa associaion would fail Muliple map enries of he same landmark Inconsisen map 30

31 SLAM: Loop Closure Recognizing an already mapped area, ypically afer a long exploraion pah (he robo closes a loop ) Srucurally idenical o daa associaion, bu high levels of ambiguiy possibly useless validaion gaes environmen symmeries Uncerainies collapse afer a loop closure (wheher he closure was correc or no) 35

32 SLAM: Loop Closure Before loop closure 36

33 SLAM: Loop Closure Afer loop closure 37

34 SLAM: Loop Closure By revisiing already mapped areas, uncerainies in robo and landmark esimaes can be reduced This can be exploied when exploring an environmen for he sake of beer (e.g. more accurae) maps Exploraion: he problem of where o acquire new informaion See separae chaper on exploraion 38

35 KF-SLAM Properies (Linear Case) The deerminan of any sub-marix of he map covariance marix decreases monoonically as successive observaions are made When a new landmark is iniialized, is uncerainy is maximal Landmark uncerainy decreases monoonically wih each new observaion [Dissanayake e al., 2001] 39

36 KF-SLAM Properies (Linear Case) In he limi, he landmark esimaes become fully correlaed [Dissanayake e al., 2001] 40

37 KF-SLAM Properies (Linear Case) In he limi, he covariance associaed wih any single landmark locaion esimae is deermined only by he iniial covariance in he vehicle locaion esimae. [Dissanayake e al., 2001] 41

38 EKF SLAM Example: Vicoria Park Daase 42

39 Vicoria Park: Daa Acquisiion [couresy by E. Nebo] 43

40 Vicoria Park: Esimaed Trajecory [couresy by E. Nebo] 44

41 Vicoria Park: Landmarks [couresy by E. Nebo] 45

42 EKF SLAM Example: Tennis Cour [couresy by J. Leonard] 46

43 EKF SLAM Example: Tennis Cour odomery esimaed rajecory [couresy by John Leonard] 47

44 EKF SLAM Example: Line Feaures KTH Bakery Daa Se [Wulf e al., ICRA 04] 48

45 EKF-SLAM: Complexiy Cos per sep: quadraic in n, he number of landmarks: O(n 2 ) Toal cos o build a map wih n landmarks: O(n 3 ) Memory consumpion: O(n 2 ) Problem: becomes compuaionally inracable for large maps! There exiss varians o circumven hese problems 49

46 SLAM Techniques EKF SLAM FasSLAM Graph-based SLAM Topological SLAM (mainly place recogniion) Scan Maching / Visual Odomery (only locally consisen maps) Approximaions for SLAM: Local submaps, Sparse exended informaion filers, Sparse links, Thin juncion ree filers, ec. 50

47 EKF-SLAM: Summary The firs SLAM soluion Convergence proof for linear Gaussian case Can diverge if nonlineariies are large (and he real world is nonlinear...) Can deal only wih a single mode Successful in medium-scale scenes Approximaions exiss o reduce he compuaional complexiy 51