Mapping in Dynamic Environments

Transcription

1 Mapping in Dynaic Environens Wolfra Burgard Universiy of Freiburg, Gerany

2 Mapping is a Key Technology for Mobile Robos Robos can robusly navigae when hey have a ap. Robos have been shown o being able o deal wih a subsanial aoun of dynaics given a ap. An iproveen can be expeced once robo can dynaically updae heir aps

3 Siulaneous Localizaion and Mapping (SLAM) SLAM enables a robo o siulaneously esiae is posiion and ap. Typically he ap is assued o be saic. How can we exend SLAM o dynaic environens?

4 A Graphical Model for SLAM in Saic Environens u u 1 2 u x 0 x 1 x 2 x... z 1 z 2 z

5 A Graphical Model for SLAM in Dynaic Environens u u 1 2 u x 0 x 1 x 2 x z 1 z 2 z

6 Probabilisic Forulaion aps rajecory easureens conrols Scan aching, EKF, UKF, Paricle Filers, Maxiu likelihood esiaion (GraphSLAM)

7 Mapping by Filering Idea: Bayes filer over boh robo posiions and ap. Bel(, x ) = η p(z, x ) p(x, 1 x 1, 1,u 1 )Bel( 1, x 1 )d 1 dx 1 Independence of and x: Bel(, x ) = η p(z, x ) p(x x 1,u 1 )p( 1 )Bel( 1, x 1 )d 1 dx 1 In saic worlds: Bel (, x ) = η p( z, x ) p( x x 1, u 1) Bel( 1, x 1) d 1dx 1

8 Dynaic Environens 1. Generally, he ap is no saic while apping: People walking by, oving objecs. 2. Ofen he world changes over ie: Doors open or close, objecs are oved around, plans grow 3. Typical resuling probles: Bad alignens (localizaion), spurious objecs (apping)

9 Approaches o Deal wih Dynaic Environens 1. Do nohing 2. Change he sensor odel 3. Filering 4. Modeling

10 Occupancy Grid Maps Inroduced by Moravec and Elfes in 1985 Represen environen by a grid. Esiae he probabiliy ha a locaion is occupied by an obsacle. Key assupions Occupancy of individual cells is independen Bel( ) = P( u1, z2, u 1 = x, y Bel( [ xy ] Robo posiions are known! ), z )

11 Updaing Occupancy Grid Maps Typically updaed using inverse sensor odel and odds raio: Or log-odds raio : 1 ] [ 1 ] [ 1 ] [ ] [ ] [ ] [ ] [ ) ( 1 ) ( ) ( ) ( 1 ), ( 1 ), ( 1 1 ) ( + = xy xy xy xy xy xy xy Bel Bel P P x z P x z P Bel ( ) ( ) ) ( ln ) ( ln 1 ), ( ln 1 ), ( ln ) ( ) ( ] [ ] [ ] [ ] [ ] [ 1 ] [ xy xy xy xy xy xy P P x z P x z P B B + + = B

12 Using Bayes Rule in Dynaic Environens [Avos e al., 2002]

13 Iproveen: Muliple Levels of Maps Use a fixed ap o represen he saic aspecs only. Use a ap learned on he fly o represen he curren sae of he world. Cobine boh aps using a conservaive sraegy: x, y] Bel ( ) = ax ( [ x, y] [ x, ] Bel ( ), Bel ( )) [ y saic dynaic

14 Works Well in Pracice

15 Exaple: On-line Mapping wih Rhino [Burgard e al., 99]

16 Modeling Approach: Mapping in Populaed Environens Proble: How can we build aps while people are walking hrough he scene? Soluion: Feaure-based people racking. Appropriaely deal wih he corresponding beas during localizaion and ap updaing.

17 Proble Descripion Key quesions How any people are here? Where do hey go? Requireens Real ie Evenually no odel of he environen Robo in oion

18 Tracking wih a Moving Robo [Schulz e al., 01]

19 Reoving People Deecions Universiy of Bonn Byzanine Museu, Ahens

20 3D Maps in Populaed Environens

21 A Fly-Through

22 Filering Approach o Mapping in Dynaic Environens Proble: Ofen odels of non-saionary objecs are no available. Ofen we canno assue ha here is a separaion beween non-saionary and saic objecs. Soluion: Using EM o learn beas refleced by dynaic objecs.

23 The Measureen Model 1. pose a ie : x 0 1 n 2. bea n of scan : 3. axiu range reading: 4. bea refleced by dynaic objec: 5. bea refleced by saic objec: z, n ς, n = 1 ς and c, n = 0, n =, n = 0 and, n = ς c 0 1 f ( x, n, z,n ) p(z,n c,n, x, ) = z,n 1 k=0 z,n k=0 (1 f (x,n,k)) if ς,n =1 (1 f (x,n,k)) if ς,n = 0 and c,n = 0 z,n 1 k=0 f (x,n,z,n ) (1 f (x,n,k)) if ς,n = 0 and c,n =1

24 Applicaion of EM E-Sep: ς, n = 1 else M-Sep: Copue os likely ap using Bayes rule by considering he expecaions e,n during ap updaing and localizaion

25 Copuing he Mos Likely Map ˆ [] = argax J j=1 T =1 N n=1 (I( f (x, n, z,n ) = j) (1 ς,n ) (e,n ln j + (1 e,n )ln(1 j )) z,n 1 k=0 Suppose α j = T + I( f (x, n, k) = j) ln (1 j )) N =1 n=1 I( f (x, n, z,n ) = j) (1 ς,n ) e,n T N z,n 1 β j = I( f (x, n, z,n ) = j) (1 ς,n ) (1 e,n )+ I( f (x, n, k) = j) =1 n=1 k=0

26 Copuing he Mos Likely Map + = = J j j j j j 1 ] [ ) ln(1 ln arg ax ˆ β α We assue ha all cells j are independen: 0 1 = = j j j j j β α If we se Copuing he os likely ap aouns o couning how ofen a cell has refleced a easureen. j j j j β α α + = we obain

27 EM-based Esiaion of he Mos Likely Map M-Sep: E-Sep: Copue ap based on he expecaions e n Copue he expecaion e n ha bea n in scan is refleced by a dynaic objec given e n : Expecaion ha z n is refleced by a dynaic objec

28 Byzanine Museu, Ahens

29 Wean

30 Wean Hall (Hallway)

31 Pisburgh Craig Sree/Forbes Ave

32 Inegraing Laser & Iages Wolfra

33 Inegraing Laser & Iages Wolfra Dirk

34 Resuling Model

35 Modeling Low-Dynaics Environens are no saic Doors can be opened or closed Soe objecs are oved regularly How o odel low-dynaic aspecs? How o use such knowledge o iprove he capabiliies of a obile robo?

36 Door Exaple Possible saes in a corridor environen

37 Approach Segen he ap ino sub-aps Esiae possible saes for each sub-ap Sore he possible configuraions in he ap Use such a represenaion o iprove, e.g., he robo s localizaion abiliies

38 Mapping Resuls

39 Mapping Resuls

40 Exended MCL Esiae he pose of he robo and he curren sae of he environen We only esiae he sae of he curren sub-ap, he robo is in (sensor provides local inforaion) This avoids a large sae spaces of he robo (paricles): robo s pose sub-ap configuraion

41 Localizaion Accuracy Coparison SA-1

42 Dynaic Subaps Wha if he variey of he dynaics is oo large o allow he clusering approach? The alernaive is o re-ap dynaically depending on he observed changes. This allows o localize relaive o previously unseen objecs

43 Localizaion in Sei-saic Environens Teporary aps represen seisaic objecs in he environen Observaions are caused by boh saic and sei-saic objecs Odoery Robo pose Saic ap Observaions Sei-saic aps

44 Sei-saic Maps Local ap represening sei-saic objecs as observed by he robo while navigaing (Meory of unexpeced observaions) Saic ap wih hree differen sei-saic aps

45 Sei-saic Maps Represened as pose-graphs Consruced fro consecuive easureens Afer loop closure we perfor opiizaion

46 Localizaion wih Teporary Maps If observaion consisen wih saic ap, use saic ap for localizaion else selec sei-saic ap for localizaion. Mahalanobis disance for ap selecion If no ap is found, we creae one

47 Localizaion wih Teporary Maps Sei-saic aps are used if consisen wih he observaions. Oherwise hey are discarded

48 Localizaion wih Teporary Maps

49 Experiens Localizaion in large open spaces 30 paricles Laser ax-range se o 20 Sandard paricle filer Teporary aps

50 Suary Differen echniques for apping in dynaic environens Objec odeling Filering Learning sub-ap saes Increenally updaing aps The proble is no solved and key for longer auonoy