1. CSE-473 Project 2 Monte Carlo Localization

2. Localization as state estimation

3. Markov Localization as State Estimation (2) Motion: Perception: … is optimal under the Markov assumption Kalman filters, Hidden Markov Models, DBN Markov!

4. [Schiele et al. 94], [Weiß et al. 94], [Borenstein 96], [Gutmann et al. 96, 98], [Arras 98] Kalman Filters

5. [Burgard et al. 96,98], [Fox et al. 99], [Konolige et al. 99] Piecewise constant

6. l Represent density by random samples l Estimation of non-Gaussian, nonlinear processes l Monte Carlo filter, Survival of the fittest, Condensation, Bootstrap filter, Particle filter l Filtering: [Handschin, 70], [Gordon et al., 93], [Kitagawa 96] l Computer vision: [Isard et al. 96, 98] l DBN: [Kanazawa et al., 95] Particle Filters

7. l Converges to true density Sample-based Density Representation

8. Importance Sampling Weight samples:

9. Sample-based Density Representation

10. Sensor Information: Importance Sampling

11. Robot Motion

12. Sensor Information: Importance Sampling

13. Robot Motion

14. l Set of samples S t = {, … } described by position l and weight p l Initialize sample set S 0 according to prior knowledge For each motion  do: l Sampling: Generate from each sample in S t-1 a new sample according to motion model l For each observation s do: l Importance sampling: Re-weight each sample with the likelihood l Resampling: Draw N samples from sample set S t according to their likelihood Monte Carlo Localization (SIR)

15. Motion Model P(l | a, l’) Model odometry error as Gaussian noise on  and 

16. Motion Model P(l | a, l’) Start

17. Global Localization (sonar)

18. Using Ceiling Maps for Localization [Dellaert et al. 99]

19. Vision-based Localization P(z|x) h(x) z

20. Vision-based Localization [CVPR-99]

21. Comparison to Grid-based Markov Localization (2) l Office environment: 20,000 samples versus 150 million states l NMAH: Global localization in 15 seconds instead of 4 minutes l Vision-based: Can track the position in situations in which grid-based approach fails

22. Condensation Tracking

23. Mixed-State Tracking

24. Tracking Multiple People

25. Multi-robot Localization: Idea [ISRR-99, Autonomous Robots-00]

26. Robot Detection Camera imageLaser scan

27. Multi-robot Localization l Combined belief state has dimension 3N complexity grows exponentially in number of robots l Factorial representation of the belief l Perform Markov localization for each robot and use detections to constrain the beliefs

28. Belief Update in Multi-robot Localization l The belief of robot m is updated whenever –it moves: –it senses: –it is detected by another robot n:

29. Density Trees [Koller et al., 98], [Moore et al., 97], [Omohundro, 91], [ICML-99] Integration of robot detection requires a density

30. Example Run

31. Experimental Results l 10 runs of global localization

32. Experimental Setup Heterogeneous Robots Laser Sonar

33. Example Run