2. © sebastian thrun, CMU, 20001 CS226 Statistical Techniques In Robotics Monte Carlo Localization Sebastian Thrun (Instructor) and Josh Bao (TA) http://robots.stanford.edu/cs226 Office: Gates 154, Office hours: Monday 1:30-3pm

3. © sebastian thrun, CMU, 20002 Bayes Filters Bayes [Kalman 60, Rabiner 85] x = state t = time m = map z = measurement u = control Markov

4. © sebastian thrun, CMU, 20003 Bayes filters  Linear Gaussian: Kalman filters (KFs, EKFs)  Discrete: Hidden Markov Models (HMMs)  With controls: Partially Observable Markov Decision Processes (POMDPs)  Fully observable with controls: Markov Decision Processes (MDPs)  With graph-structured model: Dynamic Bayes networks (DBNs)

5. © sebastian thrun, CMU, 20004 Markov Assumption  Past independent of future given current state  Violated: Unmodeled world state Inaccurate models p(x’|x,u), p(z|x) Approximation errors (e.g., grid, particles) Software variables (controls aren’t random)

6. © sebastian thrun, CMU, 20005 x t-1 utut p(x t |x t-1,u t ) Probabilistic Localization map m laser datap(z|x,m)

7. © sebastian thrun, CMU, 20006 What is the Right Representation? Multi-hypothesis [Weckesser et al. 98], [Jensfelt et al. 99] Particles [Kanazawa et al 95] [de Freitas 98] [Isard/Blake 98] [Doucet 98] Kalman filter [Schiele et al. 94], [Weiß et al. 94], [Borenstein 96], [Gutmann et al. 96, 98], [Arras 98] [Nourbakhsh et al. 95], [Simmons et al. 95], [Kaelbling et al. 96], [Burgard et al. 96], [Konolige et al. 99] Histograms (metric, topological)

8. © sebastian thrun, CMU, 20007 Particle Filters

9. © sebastian thrun, CMU, 20008 Particle Filter Represent p ( x t | d 0..t,m) by set of weighted particles {x (i) t,w (i) t } draw x (i) t  1 from p(x t-1 |d 0..t  1,m ) draw x (i) t from p ( x t | x (i) t  1,u t  1,m ) Importance factor for x (i) t :

10. © sebastian thrun, CMU, 20009 Monte Carlo Localization (MCL)

11. © sebastian thrun, CMU, 200010 Monte Carlo Localization (MCL)  Take i-th sample  “Guess” next pose  Calculate Importance Weights  Resample

12. © sebastian thrun, CMU, 200011 Monte Carlo Localization

13. © sebastian thrun, CMU, 200012 Sample Approximations

14. © sebastian thrun, CMU, 200013 Monte Carlo Localization, cont’d

15. © sebastian thrun, CMU, 200014 Performance Comparison Monte Carlo localizationMarkov localization (grids)

16. © sebastian thrun, CMU, 200015 What Can Go Wrong? Model limitations/false assumptions  Map false, robot outside map  Independence assumption in sensor measurement noise  Robot goes through wall  Presence of people  Kidnapped robot problem Approximation (Samples)  Small number of samples (eg, n=1) ignores measurements  Perfect sensors  Resampling without robot motion  Room full of chairs (discontinuities)

17. © sebastian thrun, CMU, 200016 Localization in Cluttered Environments

18. © sebastian thrun, CMU, 200017 Kidnapped Robot Problem

19. © sebastian thrun, CMU, 200018 Probabilistic Kinematics map m

20. © sebastian thrun, CMU, 200019 Pitfall: The World is not Markov!

21. © sebastian thrun, CMU, 200020 Error as Function of Sensor Noise sensor noise level (in %) error (in cm) 1,000 samples

22. © sebastian thrun, CMU, 200021 dual mixed MCL Error as Function of Sensor Noise sensor noise level (in %) error (in cm)

23. © sebastian thrun, CMU, 200022 Avoiding Collisions with Invisible Hazards Raw sensorsVirtual sensors added