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# Lecture 07: Localization and Mapping I

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### Lecture 07: Localization and Mapping I

1. 1. Introduction to RoboticsLocalization and Mapping I<br />March 1, 2010<br />
2. 2. Last week’s exercise<br />RobotStadium<br />Introduction to SVN (versioning/collaboration tool)<br />Tasks<br />Locomotion: need to get up and run<br />Perception: need to orient itself<br />Communicate: need to share information<br />Localize: need to reason about space<br />Deliberate: need to plan what to do next<br />Share the load: 1 or 2 tasks per student<br />Present your plan in 2 weeks in class – be specific<br />
3. 3. Localization<br />
4. 4. Localization<br />Gyroscope<br />Odometry<br />Control input<br />GPS<br />Landmarks<br />Sensor input with different uncertainties. <br />What is the overall uncertainty of the estimate?<br />
5. 5. Uncertainty Models: The Gaussian Distribution<br />
6. 6. Error Propagation<br />Intuition: the more sensitive the estimated quantity is to perception error, the more this sensor should be weighted<br />Covariance matrix<br />Representing output<br />uncertainties<br />Function relating sensor input<br />to output quantities<br />Covariance matrix<br />representing input<br />uncertainties<br />
7. 7. Differential Wheel Robot Odometry<br />
8. 8. Error propagation<br />Wheel-Slip<br />f=<br />
9. 9. Error Propagation<br />
10. 10. Belief representation<br />Parametric, single hypothesis<br />Parametric, multi hypothesis<br />Non-parametric, multi hypothesis(particle filter)<br />
11. 11. Environment Representation<br />Continuous<br />Discrete<br />Topological<br />Vectors<br />Array<br />Graph<br />
12. 12. Example: Google Maps<br />Continuous, Discrete or Topological?<br />
13. 13. Belief representation in topological maps<br />
14. 14. Multi-Hypothesis Belief Representation<br />
15. 15. From Sensor Data to Topological Maps<br />Exact Decomposition<br />
16. 16. Voronoi Decomposition<br />Points on lines have the same distance to neighboring obstacles<br />Voronoi edges correspond to the safest path<br />