Lecture 08: Localization and Mapping II
- 1. Introduction to RoboticsLocalizationand Mapping IIMarch 8, 2010
- 2. Last week’s exercise:Path-PlanningSo far: Signal processing, feedback controlNew: algorithmsDijkstraA*
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- 8. Markov LocalizationDiscrete, finitenumber 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: Ibelieve 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: Iknow 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 stepprocessAction update based on proprioceptionPerception update based on exterioceptionp(loc|sensing)=p(sensing|loc)p(loc)/p(sensing)
- 12. Example 1: topologicalmapDetect open/close doors using sonarp(n|i)=p(i|n)p(n)
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- 14. Example 2: Gridmap3D (x,y, theta) leads to 3D gridSame approach for updating belief using perception and action
- 15. Reducing the complexityof Markov LocalizationInstead of maintaining a high-granularity belief state, perform random sampling.Problem: Completeness“Particle filter”
- 16. Example 3: Gridmap/Particle FilterW. Burgard
- 17. Example 3: Gridmap/Particle FilterW. Burgard
- 18. Example 3: Gridmap/Particle FilterW. Burgard
- 19. Example 3: Gridmap/Particle FilterW. Burgard
- 20. Example 3: Gridmap/Particle Filter(scan 13)W. Burgard
- 21. Example 3: Gridmap/Particle Filter(scan 21)W. Burgard
- 22. Exercise: Mapping andLocalization in RobotStadiumTopological Map vs. Grid MapComplete representation vs. Particle FilterLocalization sensor? Features?Odometry (action update)?
- 23. HomeworkSections 5.7 and5.8 (pages 244-256)Next week: DESIGN REVIEW, 15min per group