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Probabilistic Robotics
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  1. Probabilistic Robotics Localization EKF Updated by: Muneem

  2. Localization Taxonomy • Local vs. Global localization. • Static vs. Dynamic environments. • Passive vs. Active approaches. • Single-robot vs. Multirobot localization.

  3. Localization “Using sensory information to locate the robot in its environment is the most fundamental problem to providing a mobile robot with autonomous capabilities.” [Cox ’91] • Given • Map of the environment. • Sequence of sensor measurements. • Initial pose (for position tracking) • Wanted • Estimate of the robot’s position. • Problem classes • Position tracking • Global localization • Kidnapped robot problem (recovery)

  4. Topics • Table 7.2: EKF with known correspondences. • Table 7.3: EKF with unknown correspondences.

  5. Nonlinear Dynamic Systems • Most realistic robotic problems involve nonlinear functions Motion Update Measurement Update

  6. EKF Algorithm • Extended_Kalman_filter( mt-1,St-1, ut, zt): • Prediction: • Correction: • Returnmt,St

  7. EKF_localization ( mt-1,St-1, ut, zt,m):Prediction: Jacobian of g w.r.t location Jacobian of g w.r.t control Motion noise Predicted mean Predicted covariance

  8. EKF_localization ( mt-1,St-1, ut, zt,m):Correction: Predicted measurement mean Jacobian of h w.r.t location Pred. measurement covariance Kalman gain Updated mean Updated covariance

  9. Table 7.2: EKF with known correspondences • Given • Map of the environment: Feature-based map • Unique “landmarks” present • Know the positional coordinates of each landmark • Know the correspondence (label) of each landmark • Measurements from many sensors • Initial pose • Pages 176-183 of chapter 6

  10. Table 7.2: EKF with known correspondences • Models Used • Motion Model: Velocity-Based

  11. 1. previous pose Jacobian in motion update 2. 3. Jacobian which approximates a linear transformation

  12. Motion Noise Covariance Matrix 4. Predicted pose in motion update 5. 6. Predicted covariance in motion update Measurement Noise Covariance Matrix 7.

  13. 8. For all observed features do: 9. Known correspondence of ith feature Relative distance to jth landmark 10. Predicted measurement to jth landmark 11. Jacobian wrt robot location 12.

  14. 13. Updated measurement covariance 14. Kalman Gain Matrix 15. Updated pose estimate contributed by ith feature 16. End for 17. Final pose estimate from all i features 18. 19. 20. Return

  15. Table 7.3: EKF with unknown correspondences • Given • Map of the environment: Feature-based map • Unique “landmarks” present • Know the positional coordinates of each landmark • Measurements from many sensors • Initial pose

  16. unknown Steps 1-8 are identical to that of Table 7.2 8. For all observed features do: 9. For all landmarks k in the map m, do: 10. 11. Maximize the likelihood of measurement given any possible landmark in map 12. 13. End for 14.

  17. Table 7.3: EKF with unknown correspondences 15. Kalman Gain Matrix 16. Updated pose estimate contributed by ith feature 17. End for 18. Final pose estimate from all i features 19. 20. Return