1. Introduction to RoboticsLocalization and Mapping I October 18, 2010

2. Midterm Harder than last final Less time than final No recital But: less than 3/3.5 need to work! Understand midterm => good shape for finals

3. Last 2 week’s exercises Ratslife Tasks Vision Mapping Navigation Planning Strategy Share the load: 1 or 2 tasks per student Present your plan in 2 weeks in class – be specific

4. Last lecture: The Gaussian Distribution

5. Error Propagation Intuition: the more sensitive the estimated quantity is to perception error, the more this sensor should be weighted Covariance matrix Representing output uncertainties Function relating sensor input to output quantities Covariance matrix representing input uncertainties

6. Today Sensors for localization Error propagation for localization Position representation Planning

7. Localization

8. Localization Gyroscope Odometry Control input GPS Landmarks Sensor input with different uncertainties. What is the overall uncertainty of the estimate?

9. Differential Wheel Robot Odometry

10. Step-by-Step

11. How does the error build up? Ingredient 1: variance on wheel-speed / slip Ingredient 2: variance on previous position estimate Relation between wheel-speed and position Derivative wrt error Derivative wrt position

12. Error propagation Wheel-Slip f=

13. Step-by-Step

14. Belief representation

15. Belief representation Parametric, single hypothesis Parametric, multi hypothesis Non-parametric, multi hypothesis(particle filter)

16. Environment Representation Continuous Discrete Topological Vectors Array Graph

17. Example: Google Maps Continuous, Discrete or Topological?

18. Belief representation in topological maps

19. Multi-Hypothesis Belief Representation

20. From Sensor Data to Topological Maps Exact Decomposition

21. Voronoi Decomposition Points on lines have the same distance to neighboring obstacles Voronoi edges correspond to the safest path

22. Adaptive Cell-Size

23. Reactive vs. Deliberative Planning So far Move randomly Use heuristics (follow wall, spiral, …) Use landmarks (infrared beacons, magnet wire) Use gradients / feedback control (Exercise 2) Today Deliberative planning Reason on abstract representation

24. Exercise: Navigation Algorithms Find the shortest path from A to B Choose the map representation Devise an algorithm to extract path

25. Dijkstra’s Shortest Path Routing

26. A* Shortest Path Routing Heuristic path cost biases search toward goal Heuristic here: Manhattan distance Extra rule: Always start from cell with lowest cost

27. Homework Section 5.6 (pages 212-244)