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Localization

Localization. David Johnson cs6370. Basic Problem. Go from this to this. [Thrun, Burgard & Fox (2005)]. Kalman Filter. [Thrun, Burgard & Fox (2005)]. Kalman Limitations. Need initial state and confidence Doesn’t solve global localization “kidnapped robot” problem

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Localization

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  1. Localization David Johnson cs6370

  2. Basic Problem • Go from this to this

  3. [Thrun, Burgard & Fox (2005)]

  4. Kalman Filter [Thrun, Burgard & Fox (2005)]

  5. Kalman Limitations • Need initial state and confidence • Doesn’t solve global localization • “kidnapped robot” problem • Only tracks one hypothesis at a time • Similar landmarks confuse it

  6. Global methods • We have used PDFs and Kalman Filter to represent and update robot state in one position • Global methods represent probability of robot state everywhere at once • Pick the peak as actual location • Based on Bayes filter, Markov model • Tracks a belief “bel” about where it is • Side note: there is a multi-hypothesis KF that tracks multiple Gaussians at once.

  7. Markov Localization [Thrun, Burgard & Fox (2005)]

  8. Global Localization • The research is how to efficiently represent the global belief

  9. Grid Localization • Developed out of Moravec’s occupancy maps for probabilistic mapping

  10. Occupancy maps • Only have to represent x,y location • Store probability that a cell is filled • Threshold into definitely empty or filled • How is a mobile robot different?

  11. Grid Localization [Thrun, Burgard & Fox (2005)]

  12. Grid Localization [Thrun, Burgard & Fox (2005)]

  13. Grid Localization [Thrun, Burgard & Fox (2005)]

  14. Grid Localization [Thrun, Burgard & Fox (2005)]

  15. Grid Localization [Thrun, Burgard & Fox (2005)]

  16. Grid Localization [Thrun, Burgard & Fox (2005)]

  17. Illustrative Example: Robot Localization t=0 Prob 0 1

  18. Illustrative Example: Robot Localization t=1 Prob 0 1

  19. Illustrative Example: Robot Localization t=2 Prob 0 1

  20. Illustrative Example: Robot Localization t=3 Prob 0 1

  21. Illustrative Example: Robot Localization t=4 Prob 0 1

  22. Trajectory 1 2 3 4 Illustrative Example: Robot Localization t=5 Prob 0 1

  23. Grid-based Localization

  24. How do we get information to the cells? • Pick closest obstacle • Precompute at each cell what the closest obstacle should be and a confidence to add to the cell if a match is made. • Only update confident cells • May cause loss of global property • How to do motion model? • Gaussian blur of grid

  25. (Sequential) Monte Carlo filters Bootstrap filters Condensation Interacting Particle Approximations Survival of the fittest … Particle Filters

  26. Representing Robot Location Y X

  27. Sampling as Representation Y X

  28. Particle Filter [Thrun, Burgard & Fox (2005)]

  29. Visualization of Particle Filter unweighted measure compute importance weights  p(xt-1|z1:t-1) resampling move particles predict p(xt|z1:t-1)

  30. Particle Filters – motion model

  31. 1. Prediction Phase – motion model u Motion Model

  32. 2. Measurement Phase Sensor Model

  33. 3. Resampling Step

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