Probabilistic Algorithms for Mobile Robot Mapping

1. Probabilistic Algorithms forMobile Robot Mapping Sebastian Thrun Carnegie Mellon & Stanford Wolfram Burgard University of Freiburg and Dieter Fox University of Washington LEP: Adapted, combining partially with Thrun’s Tutorial

2. Based on the paper A Real-Time Algorithm for Mobile Robot Mapping With Applications to Multi-Robot and 3D Mapping Best paper award at 2000 IEEE International Conference on Robotics and Automation (~1,100 submissions) Sponsored by DARPA (TMR-J.Blitch, MARS-D.Gage, MICA-S.Heise) and NSF (ITR(2), CAREER-E.Glinert, IIS-V.Lumelsky) Other contributors: Yufeng Liu, Rosemary Emery, Deepayan Charkrabarti, Frank Dellaert, Michael Montemerlo, Reid Simmons, Hugh Durrant-Whyte, Somajyoti Majnuder, Nick Roy, Joelle Pineau, …

3. This Talk Motivation SLAM (Kalman filters) Expectation Maximization Real Time Hybrid 3D Mapping with EM Open Problems

4. Museum Tour-Guide Robots With: Greg Armstrong, Michael Beetz, Maren Benewitz, Wolfram Burgard, Armin Cremers, Frank Dellaert, Dieter Fox, Dirk Haenel, Chuck Rosenberg, Nicholas Roy, Jamie Schulte, Dirk Schulz

5. The Nursebot Initiative With: Greg Armstrong, Greg Baltus, Jacqueline Dunbar-Jacob, Jennifer Goetz, Sara Kiesler, Judith Matthews, Colleen McCarthy, Michael Montemerlo, Joelle Pineau, Martha Pollack, Nicholas Roy, Jamie Schulte

6. The Localization Problem • Estimate robot’s coordinates s=(x,y,q) from sensor data • Position tracking (error bounded) • Global localization (unbounded error) • Kidnapping (recovery from failure) Ingemar Cox (1991): “Using sensory information to locate the robot in its environment is the most fundamental problem to provide a mobile robot with autonomous capabilities.” see also [Borenstein et al, 96]

7. Mapping: The Problem • Concurrent Mapping and Localization (CML) • Simultaneous Localization and Mapping (SLAM)

8. Mapping: The Problem • Continuous variables • High-dimensional (eg, 1,000,000+ dimensions) • Multiple sources of noise • Simulation not acceptable

9. Milestone Approaches Mataric 1990 Elfes/Moravec 1986 Kuipers et al 1991 Lu/Milios/Gutmann 1997

10. 3D Mapping Moravec et al, 2000 Konolige et al, 2001 Teller et al, 2000

11. Every state-of-the-art mapping algorithm is probabilistic. Take-Home Message Mapping is the holy grail in mobile robotics.

12. Robots are Inherently Uncertain • Uncertainty arises from four major factors: • Environment stochastic, unpredictable • Robot stochastic • Sensor limited, noisy • Models inaccurate

13. Probabilistic Robotics

14. Probabilistic Robotics Key idea: Explicit representation of uncertainty (using the calculus of probability theory) • Perception = state estimation • Action = utility optimization

15. Advantages of Probabilistic Paradigm • Can accommodate inaccurate models • Can accommodate imperfect sensors • Robust in real-world applications • Best known approach to many hard robotics problems

16. Pitfalls • Computationally demanding • False assumptions • Approximate

17. This Talk Motivation SLAM (Kalman filters) Expectation Maximization Real Time Hybrid 3D Mapping with EM Open Problems

18. The Localization Problem • Estimate robot’s coordinates s=(x,y,q) from sensor data • Position tracking (error bounded) • Global localization (unbounded error) • Kidnapping (recovery from failure) Ingemar Cox (1991): “Using sensory information to locate the robot in its environment is the most fundamental problem to provide a mobile robot with autonomous capabilities.” see also [Borenstein et al, 96]

19. p(s) s Probabilistic Localization [Simmons/Koenig 95] [Kaelbling et al 96] [Burgard et al 96]

20. d = data o = observation a = action t = time s = state Bayes Markov Markov Bayes Filters [Kalman 60, Rabiner 85]

21. Markov Assumption used above Knowledge of current state renders past, future independent: • “Static World Assumption” • “Independent Noise Assumption”

22. Bayes Filters are Familiar to AI! • Kalman filters • Hidden Markov Models • Dynamic Bayes networks • Partially Observable Markov Decision Processes (POMDPs)

23. p(s|a,s’,m) s’ s’ a a map m laser data p(o|s,m) observation o p(o|s,m) Localization With Bayes Filters

24. [Weckesser et al. 98], [Jensfelt et al. 99] Kalman filter Multi-hypothesis [Schiele et al. 94], [Weiß et al. 94], [Borenstein 96], [Gutmann et al. 96, 98], [Arras 98] Piecewise constant (metric, topological) Variable resolution (eg, trees) [Nourbakhsh et al. 95], [Simmons et al. 95], [Kaelbling et al. 96], [Burgard et al. 96], [Konolige et al. 99] [Burgard et al. 98] What is the Right Representation?

25. Idea: Represent Belief Through Samples • Particle filters • [Doucet 98, deFreitas 98] • Condensation algorithm • [Isard/Blake 98] • Monte Carlo localization • [Fox/Dellaert/Burgard/Thrun 99]

26. Monte Carlo Localization (MCL)

27. MCL: Importance Sampling

28. MCL: Robot Motion motion

29. MCL: Importance Sampling

30. draw s(i)t-1from b(st-1) draw s(i)tfrom p(st | s(i)t-1,at-1,m) Importance factor for s(i)t: Particle Filters Represents b(st) by set of weighted particles {s(i)t,w(i)t}

31. Monte Carlo Localization

32. Performance Comparison Markov localization (grids) Monte Carlo localization

33. Monte Carlo Localization • Approximate Bayes Estimation/Filtering • Full posterior estimation • Converges in O(1/#samples) [Tanner’93] • Robust: multiple hypothesis with degree of belief • Efficient: focuses computation where needed • Any-time: by varying number of samples • Easy to implement 

34. Distance filters: [Fox et al 1998] Pitfall: The World is not Markov!

35. Probabilistic Localization: Lessons Learned • Probabilistic Localization = Bayes filters • Particle filters: Approximate posterior by random samples

36. 70 m The Problem: Concurrent Mapping and Localization

37. Concurrent Mapping and Localization • Is a chicken-and-egg problem • Mapping with known poses is “simple” • Localization with known map is “simple” • But in combination, the problem is hard! • Today’s best solutions are all probabilistic!

38. Mapping: Outline Maximum likelihood: EM Posterior estimation: EKF (SLAM) Maximum likelihood: ML* Posterior estimation with known poses: Occupancy grids

39. Assume static map [Smith, Self, Cheeseman 90, Chatila et al 91, Durrant-Whyte et al 92-00, Leonard et al. 92-00] Mapping as Posterior Estimation

40. Kalman Filters • N-dimensional Gaussian • Can handle hundreds of dimensions

41. Underwater Mapping By: Louis L. Whitcomb, Johns Hopkins University

42. Underwater Mapping - Example “Autonomous Underwater Vehicle Navigation,” John Leonard et al, 1998

43. Underwater Mapping with SLAMCourtesy of Hugh Durrant-Whyte, Univ of Sydney

44. Mapping with Extended Kalman Filters Courtesy of [Leonard et al 1998]

45. Undistinguishable features Distinguishable features Posterior multi-modal  Posterior uni-modal  The Key Assumption • Inverse sensor model p(st|ot,m) must be Gaussian. • Main problem: Data association • In practice: • Extract small set of highly distinguishable features from sensor data • Discard all other data • If ambiguous, take best guess for landmark identity

46. Mapping Algorithms - Comparison

47. Mapping: Outline Maximum likelihood: EM Posterior estimation: EKF (SLAM) Maximum likelihood: ML* Posterior estimation with known poses: Occupancy grids

48. E-Step: Localization M-Step: Mapping with known poses Mapping with Expectation Maximization [Dempster et al, 77] [Thrun et al, 1998] [Shatkay/Kaelbling 1997]

49. map(1) Uncertainty Models for Motion

50. 16 landmarks 15 landmarks 27 landmarks 17 landmarks CMU’s Wean Hall (80 x 25 meters)