1. Introduction to RoboticsLocalization and Mapping III March 29, 2010

2. Before Break Bayes Rule Markov localization Robot location expressed as probability on a grid Action update: probabilities are updated using the motion model Perception update: probabilities are updated using sensing model Particle filter Limit number of possible robot location to a small number of particles Last exercise

3. Kalman Filter: Intuition 1. Predict 2. Update

4. Basics: Fuse two Measurements Multiple measurements Actual value Mean-square error Weights 1/ Optimal error

5. Kalman Filter Measurement Kalman Filter Gain

6. Example: Map-based localization

7. 1. Prediction Error propagation law

8. 2. Observation

9. 3. Measurement Prediction Observations in Map frame Z(k+1)=h(z,p(k+1|k))

10. 4. Matching Observations - Predicted features (based on estimated position) -> “Innovation” Measurement noise Position error

11. 5. Estimation

12. Take home messages: Kalman Filter Optimal way to fuse uncertain observations Overall variance always decreases Recipe Predict new measurement Observe sensors Update measurement weighted by validity of observation (“Innovation”) Drawback: Assumes uncertainty to be Gaussian!

13. Simultaneous Localization and Mapping Hen-Egg Problem: Need map to localize Need location to map Brainstorming: how can we solve this problem using the tools we have just seen? Hint: map consists of distinct features.

14. Feature-based SLAM

15. Feature-based SLAM

16. Feature-based SLAM

17. Feature-based SLAM

18. Feature-based SLAM

19. Feature-based SLAM

20. From Localization to SLAM

21. FastSLAM (Montemerlo et al. 2002) Sample Gaussian distribution using particle filter Update particles using motion estimate Estimate sensor-input and prediction for each particle Resample particles (higher weight for particles with good matching) Each particle maintains map features (Gaussian distribution)

22. Key problems in SLAM Recognize place already visit Dynamic environments Recent directions 3D pointclouds Visual features (SIFT, SURF etc.)

23. Organization Next week: Planning and Navigation Week 12 + 13: Debates http://courses.csail.mit.edu/6.141/spring2009/pub/debates/Debates.html Week 14: Graduate student presentations Week 15: Final presentations Reading: Chapter 6 (pages 257-305) Final exam: Monday, May 3 7:30 p.m. - 10:00 p.m.