Lecture 08: Localization and Mapping II
- 1. Introduction to RoboticsLocalization and Mapping IIMarch 8, 2010
- 2. Last week’s exercise: Path-PlanningSo far: Signal processing, feedback controlNew: algorithmsDijkstraA*
- 8. Markov LocalizationDiscrete, finite number of possible poses (grid, topological map)p(A) : probability that A is truep(A|B) : probability that A is true knowing Bp(A^B)=p(A|B)p(B)
- 9. Bayes rulep(A|B)=p(B|A)p(A)/p(B)p(loc|sensing)=p(sensing|loc)p(loc)/p(sensing)Example: I believe to be at location X and think that I see a door. What’s the likelihood tobe at X? The higher the likelihood to see a door at X, the higher the likelihood that I amat X.
- 10. Markov LocalizationBut: I know more than that! I have an estimate on how much I moved and where I were Before!0.330.330.33p(l’t-1)ot0.10.70.2(example depends on error-model for ot)
- 11. Markov LocalizationTwo step processAction update based on proprioceptionPerception update based on exterioceptionp(loc|sensing)=p(sensing|loc)p(loc)/p(sensing)
- 12. Example 1: topological mapDetect open/close doors using sonarp(n|i)=p(i|n)p(n)
- 13. Example 1: topological map
- 14. Example 2: Grid map3D (x,y, theta) leads to 3D gridSame approach for updating belief using perception and action
- 15. Reducing the complexity of Markov LocalizationInstead of maintaining a high-granularity belief state, perform random sampling.Problem: Completeness“Particle filter”
- 16. Example 3: Grid map/Particle FilterW. Burgard
- 17. Example 3: Grid map/Particle FilterW. Burgard
- 18. Example 3: Grid map/Particle FilterW. Burgard
- 19. Example 3: Grid map/Particle FilterW. Burgard
- 20. Example 3: Grid map/Particle Filter(scan 13)W. Burgard
- 21. Example 3: Grid map/Particle Filter(scan 21)W. Burgard
- 22. Exercise: Mapping and Localization in RobotStadiumTopological Map vs. Grid MapComplete representation vs. Particle FilterLocalization sensor? Features?Odometry (action update)?
- 23. HomeworkSections 5.7 and 5.8 (pages 244-256)Next week: DESIGN REVIEW, 15min per group