This document discusses localization and mapping for robotics. It introduces topics like gyroscopes, odometry, GPS, and landmarks for localization. It discusses uncertainty models using Gaussian distributions and error propagation. Methods for belief representation are presented, including parametric single/multi hypothesis and non-parametric particle filters. Environment representations like continuous, discrete, and topological maps are described. The document provides an example of Google Maps and discusses belief representation in topological maps. It also covers multi-hypothesis belief representation, sensor data to topological maps using exact and Voronoi decompositions, and adaptive cell-size. The document assigns homework on navigation algorithms and reactive vs. deliberative planning.

1. Introduction to RoboticsLocalization and Mapping I March 1, 2010

2. Last week’s exercise RobotStadium Introduction to SVN (versioning/collaboration tool) Tasks Locomotion: need to get up and run Perception: need to orient itself Communicate: need to share information Localize: need to reason about space Deliberate: need to plan what to do next Share the load: 1 or 2 tasks per student Present your plan in 2 weeks in class – be specific

3. Localization

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

5. Uncertainty Models: The Gaussian Distribution

6. 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

7. Differential Wheel Robot Odometry

8. Error propagation Wheel-Slip f=

9. Error Propagation

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

11. Environment Representation Continuous Discrete Topological Vectors Array Graph

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

13. Belief representation in topological maps

14. Multi-Hypothesis Belief Representation

15. From Sensor Data to Topological Maps Exact Decomposition

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

17. Adaptive Cell-Size

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

19. 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

20. Homework Section 5.6 (pages 212-244)