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Lecture 08: Localization and Mapping II
- 1. Introduction to RoboticsLocalization and Mapping II March 8, 2010
- 2. Last week’s exercise: Path-Planning So far: Signal processing, feedback control New: algorithms Dijkstra A*
- 3. Localization Odometry GPS Control input Landmarks Gyroscope
- 4. Localization Odometry GPS Local Global Control input Landmarks Gyroscope
- 8. Markov Localization Discrete, finite number of possible poses (grid, topological map) p(A) : probability that A is true p(A|B) : probability that A is true knowing B p(A^B)=p(A|B)p(B)
- 9. Bayes rule p(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 to be at X? The higher the likelihood to see a door at X, the higher the likelihood that I am at X.
- 10. Markov Localization But: I know more than that! I have an estimate on how much I moved and where I were Before! 0.33 0.33 0.33 p(l’t-1) ot 0.1 0.7 0.2 (example depends on error-model for ot)
- 11. Markov Localization Two step process Action update based on proprioception Perception update based on exterioception p(loc|sensing)=p(sensing|loc)p(loc)/p(sensing)
- 12. Example 1: topological map Detect open/close doors using sonar p(n|i)=p(i|n)p(n)
- 13. Example 1: topological map
- 14. Example 2: Grid map 3D (x,y, theta) leads to 3D grid Same approach for updating belief using perception and action
- 15. Reducing the complexity of Markov Localization Instead of maintaining a high-granularity belief state, perform random sampling. Problem: Completeness “Particle filter”
- 16. Example 3: Grid map/Particle Filter W. Burgard
- 17. Example 3: Grid map/Particle Filter W. Burgard
- 18. Example 3: Grid map/Particle Filter W. Burgard
- 19. Example 3: Grid map/Particle Filter W. 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 RobotStadium Topological Map vs. Grid Map Complete representation vs. Particle Filter Localization sensor? Features? Odometry (action update)?
- 23. Homework Sections 5.7 and 5.8 (pages 244-256) Next week: DESIGN REVIEW, 15min per group