Lecture 09: Localization and Mapping III

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Lecture 09: Localization and Mapping III

  1. 1. Introduction to RoboticsLocalization and Mapping III<br />March 29, 2010<br />
  2. 2. Before Break<br />Bayes Rule<br />Markov localization<br />Robot location expressed as probability on a grid<br />Action update: probabilities are updated using the motion model<br />Perception update: probabilities are updated using sensing model<br />Particle filter<br />Limit number of possible robot location to a small number of particles<br />Last exercise<br />
  3. 3. Kalman Filter: Intuition<br />1. Predict<br />2. Update<br />
  4. 4. Basics: Fuse two Measurements<br />Multiple measurements<br />Actual value<br />Mean-square error<br />Weights 1/<br />Optimal error<br />
  5. 5. Kalman Filter<br />Measurement<br />Kalman Filter Gain<br />
  6. 6. Example: Map-based localization<br />
  7. 7. 1. Prediction<br />Error propagation law<br />
  8. 8. 2. Observation<br />
  9. 9. 3. Measurement Prediction<br />Observations in Map frame<br />Z(k+1)=h(z,p(k+1|k))<br />
  10. 10. 4. Matching<br />Observations - Predicted features (based on estimated position) -> “Innovation”<br />Measurement noise<br />Position error<br />
  11. 11. 5. Estimation<br />
  12. 12. Take home messages: Kalman Filter<br />Optimal way to fuse uncertain observations<br />Overall variance always decreases<br />Recipe<br />Predict new measurement<br />Observe sensors<br />Update measurement weighted by validity of observation (“Innovation”)<br />Drawback: Assumes uncertainty to be Gaussian!<br />
  13. 13. Simultaneous Localization and Mapping<br />Hen-Egg Problem:<br />Need map to localize<br />Need location to map<br />Brainstorming: how can we solve this problem using the tools we have just seen? Hint: map consists of distinct features.<br />
  14. 14. Feature-based SLAM<br />
  15. 15. Feature-based SLAM<br />
  16. 16. Feature-based SLAM<br />
  17. 17. Feature-based SLAM<br />
  18. 18. Feature-based SLAM<br />
  19. 19. Feature-based SLAM<br />
  20. 20. From Localization to SLAM<br />
  21. 21. FastSLAM (Montemerlo et al. 2002)<br />Sample Gaussian distribution using particle filter<br />Update particles using motion estimate<br />Estimate sensor-input and prediction for each particle<br />Resample particles (higher weight for particles with good matching)<br />Each particle maintains map features (Gaussian distribution)<br />
  22. 22. Key problems in SLAM<br />Recognize place already visit<br />Dynamic environments<br />Recent directions<br />3D pointclouds<br />Visual features (SIFT, SURF etc.)<br />
  23. 23. Organization<br />Next week: Planning and Navigation<br />Week 12 + 13: Debates<br />http://courses.csail.mit.edu/6.141/spring2009/pub/debates/Debates.html<br />Week 14: Graduate student presentations<br />Week 15: Final presentations<br />Reading: Chapter 6 (pages 257-305) <br />Final exam: Monday, May 3 7:30 p.m. - 10:00 p.m.<br />

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