1. HCI/ComS 575X: Computational Perception Instructor: Alexander Stoytchev http://www.cs.iastate.edu/~alex/classes/2006_Spring_575X/

2. Particle Filters HCI/ComS 575X: Computational Perception Iowa State University, SPRING 2006 Copyright © 2006, Alexander Stoytchev February 22, 2006

3. Sebastian Thrun, Wolfram Burgard and Dieter Fox (2005). Probabilistic Robotics MIT Press.

4. F. Dellaert, D. Fox, W. Burgard, and S. Thrun (1999). "Monte Carlo Localization for Mobile Robots", IEEE International Conference on Robotics and Automation (ICRA99), May, 1999.

5. Ioannis Rekleitis (2004). A Particle Filter Tutorial for Mobile Robot Localization. Technical Report TR-CIM-04-02, Centre for Intelligent Machines, McGill University, Montreal, Quebec, Canada.

6. Odometry Errors

7. Raw range data, position indexed by odometry [Thrun, Burgard & Fox (2005)]

8. Resulting Occupancy Grid Map [Thrun, Burgard & Fox (2005)]

10. Grid Localization [Thrun, Burgard & Fox (2005)]

11. Grid Localization [Thrun, Burgard & Fox (2005)]

12. Grid Localization [Thrun, Burgard & Fox (2005)]

13. Grid Localization [Thrun, Burgard & Fox (2005)]

14. Grid Localization [Thrun, Burgard & Fox (2005)]

15. Grid Localization [Thrun, Burgard & Fox (2005)]

16. Now Let’s Compare that With Some of the Other Methods

17. Markov Localization [Thrun, Burgard & Fox (2005)]

18. Kalman Filter [Thrun, Burgard & Fox (2005)]

19. Particle Filter [Thrun, Burgard & Fox (2005)]

20. Sample-based Localization (sonar)

22. Importance Sampling Ideally, the particles would represent samples drawn from the distribution p(x|z). –In practice, we usually cannot get p(x|z) in closed form; in any case, it would usually be difficult to draw samples from p(x|z). We use importance sampling: –Particles are drawn from an importance distribution. –Particles are weighted by importance weights. [ http://www.fulton.asu.edu/~morrell/581/ ]

23. Monte Carlo Samples (Particles) The posterior distribution p(x|z) may be difficult or impossible to compute in closed form. An alternative is to represent p(x|z) using Monte Carlo samples (particles): –Each particle has a value and a weight x x [ http://www.fulton.asu.edu/~morrell/581/ ]

24. In 2D it looks like this [http://www.ite.uni-karlsruhe.de/METZGER/DIPLOMARBEITEN/dipl2.html]

25. Objective-Find p(x k |z k,…,z 1 ) The objective of the particle filter is to compute the conditional distribution p(x k |z k,…,z 1 ) To do this analytically, we would use the Chapman-Kolmogorov equation and Bayes Theorem along with Markov model assumptions. The particle filter gives us an approximate computational technique. [ http://www.fulton.asu.edu/~morrell/581/ ]

26. Initial State Distribution x0x0 x0x0 [ http://www.fulton.asu.edu/~morrell/581/ ]

27. State Update x0x0 x 1 = f 0 (x 0, w 0 ) x1x1 [ http://www.fulton.asu.edu/~morrell/581/ ]

28. Compute Weights x1x1 x1x1 p(z 1 |x 1 ) x1x1 Before After [ http://www.fulton.asu.edu/~morrell/581/ ]

29. Resample x1x1 x1x1 [ http://www.fulton.asu.edu/~morrell/581/ ]

30. Example

31. Robot Pose

32. Odometry Motion Model

33. Sampling From the Odometry Model

34. Motion Model

36. Velocity model for different noise parameters

37. Sampling from the velocity model

38. In Class Demo of Particle Filters

39. THE END