1. Particle Filters In Roboticsor: How the World Became To Be One Big Bayes Network Sebastian Thrun Carnegie Mellon University University of Pittsburgh

2. This Talk Robotics Research Today Particle Filters In Robotics 4 Open Problems

3. Robotics Yesterday

4. Robotics Today

5. Robotics Tomorrow?

6. This Talk Robotics Research Today Particle Filters In Robotics 4 Open Problems

7. Robotics @ CMU, 1997 with W. Burgard, A.B. Cremers, D. Fox, D. Hähnel, G. Lakemeyer, D. Schulz, W. Steiner

8. Robotics @ CMU, 1998 with M. Beetz, M. Bennewitz, W. Burgard, A.B. Cremers, F. Dellaert, D. Fox, D. Hähnel, C. Rosenberg, N. Roy, J. Schulte, D. Schulz

9. The Localization Problem fast-moving ambiguous identity non-statio- nary many objects static few objects one object uniquely identifiable local (tracking) global kidnapped • Objects • Robots • Other Agents

10. Probabilistic Localization • “Bayes filter” • HMMs • DBNs • POMDPs • Kalman filters • Particle filters • Condensation • etc m map z1 z3 z3 z2 observations . . . x1 x1 x1 x2 x2 x2 x3 xt robot poses robot poses u3 u3 u3 u3 ut ut ut u2 u2 u2 u2 controls controls map m laser data

11. Bayes Filter Localization [Nourbakhsh et al 94] [Simmons/Koenig 95] [Kaelbling et al 96]

12. What is the Right Representation? Multi-hypothesis Kalman filter [Weckesser et al. 98], [Jensfelt et al. 99] [Schiele et al. 94], [Weiß et al. 94], [Borenstein 96], [Gutmann et al. 96, 98], [Arras 98] Particles [Kanazawa et al 95] [de Freitas 98] [Isard/Blake 98] [Doucet 98] Histograms (metric, topological) [Nourbakhsh et al. 95], [Simmons et al. 95], [Kaelbling et al. 96], [Burgard et al. 96], [Konolige et al. 99]

13. Particle Filters For Localization

14. Monte Carlo Localization (MCL) With: Wolfram Burgard, Dieter Fox, Frank Dellaert

16. Monte Carlo Localization With: Frank Dellaert

18. Particle Filter in High Dimensions fast-moving ambiguous identity non-statio- nary many objects/features static few objects one object uniquely identifiable local (tracking) global kidnapped

19. Learning Mapsaka Simultaneous Localization and Mapping (SLAM) 70 m

20. The SLAM Problem with known data association

21. EKF Approach O(N2) [Smith, Self, Cheeseman, 1985]

22. Kalman Filter Mapping: O(N2)

23. EKS-SLAM for Underwater MappingCourtesy of Stefan Williams and Hugh Durrant-Whyte, Univ of Sydney

24. Particle Filtering in Low Dimensions! sample pose robot poses

25. Particle Filtering in High Dimensions?  sample map maps

26. Insight: Conditional Independence Factorization first developed by Murphy & Russell, 1999 1 Landmark 1 z1 z3 observations . . . x1 x2 x3 xt Robot poses u3 ut u2 controls z2 zt 2 Landmark 2

27. Rao-Blackwellized Particle Filters … robot poses landmark n=1 landmark n=N landmark n=2 … landmark n=1 landmark n=N landmark n=2 [Murphy 99, Montemerlo 02]

28. The FastSLAM Algorithm .2 .7 .1

29. FastSLAM - O(MN) O(M) Constant time per particle O(M) Constant time per particle O(MN) Linear time per particle • Update robot particles based on control ut • Incorporate observation zt into Kalman filters • Resample particle set M = Number of particles N = Number of map features

30. Ben Wegbreit’s Log-Trick n  4 ? T F new particle n  2 ? F T n  3 ? T F [i] [i] m3,S3 n  4 ? k  4 ? T T F F old particle k  2 ? n  2 ? k  6 ? n  6 ? T T F F T T F F k  1 ? n  1 ? k  3 ? n  3 ? k  1 ? n  5 ? k  3 ? n  7 ? T T F F T T F F T T F F T T F F [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] [i] m1,S1 m1,S1 m2,S2 m2,S2 m3,S3 m3,S3 m4,S4 m4,S4 m5,S5 m5,S5 m6,S6 m6,S6 m7,S7 m7,S7 m8,S8 m8,S8

31. FastSLAM - O(M logN) O(M) Constant time per particle O(MlogN) Log time per particle O(M logN) Log time per particle • Update robot particles based on control ut • Incorporate observation zt into Kalman filters • Resample particle set M = Number of particles N = Number of map features

32. Advantage of Structured PF Solution FastSLAM: O(MlogN) Moore’s Theorem: logN 30 M: discussed later + global uncertainty, multi-modal + non-linear systems + sampling over data associations Kalman: O(N2) 500 features

33. 3 Examples Particles + Kalman filters Particles + Point Estimators Particles + Particles

34. Outdoor Mapping (no GPS) • 4 km excursion With Juan Nieto, Eduardo Nebot, Univ of Sydney

35. With Juan Nieto, Eduardo Nebot, Univ of Sydney

36. 3 Examples Particles + Kalman filters Particles + Point Estimators Particles + Particles

37. Indoor Mapping • Map: point estimators (no uncertainty) • Lazy

38. Importance of Particle Filters Non-probabilistic Probabilistic, with samples

39. Multi-Robot Mapping

40. Multi-Robot Exploration DARPA TMR Texas DARPA TMR Maryland With: Reid Simmons and Dieter Fox

41. 3 Examples Particles + Kalman filters Particles + Point Estimators Particles + Particles

42. Tracking Moving Features With: Michael Montemerlo

43. Tracking Moving Entities Through Map Differencing

44. Map-Based People Tracking With: Michael Montemerlo

45. Autonomous People Following With: Michael Montemerlo

46. Advantage of Structured PF Solution + global uncertainty, multi-modal + non-linear systems + sampling over data associations Kalman: O(N2) FastSLAM: O(MlogN) 500 features Moore’s Theorem: logN 30 M: discussed now!

47. Worst-Case Environment ? … … N landmarks robot path … … Kalman filters: Maps (relative information) converges for linear-Gaussian case

48. Relative Map Error (Simulation) Kalman Filter Kalman Filter 250 particles error steps

49. Relative Map Error (Simulation) Kalman Filter Kalman Filter 250 particles 250 particles 100 particles 100 particles 2 particles error steps

50. Robot-To-Map Error (Simulation) Kalman Filter error 250 particles 100 particles 2 particles steps