Particle Filters In Robotics or: How the World Became To Be One Big Bayes Network - PowerPoint PPT Presentation

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  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

  15. Monte Carlo Localization With: Frank Dellaert

  16. 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

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

  18. The SLAM Problem with known data association

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

  20. Kalman Filter Mapping: O(N2)

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

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

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

  24. 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

  25. 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]

  26. The FastSLAM Algorithm .2 .7 .1

  27. 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

  28. 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

  29. 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

  30. 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

  31. 3 Examples Particles + Kalman filters Particles + Point Estimators Particles + Particles

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

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

  34. 3 Examples Particles + Kalman filters Particles + Point Estimators Particles + Particles

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

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

  37. Multi-Robot Mapping

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

  39. 3 Examples Particles + Kalman filters Particles + Point Estimators Particles + Particles

  40. Tracking Moving Features With: Michael Montemerlo

  41. Tracking Moving Entities Through Map Differencing

  42. Map-Based People Tracking With: Michael Montemerlo

  43. Autonomous People Following With: Michael Montemerlo

  44. 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!

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

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

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

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