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Probabilistic Robotics

Probabilistic Robotics. SLAM. The SLAM Problem. A robot is exploring an unknown, static environment. Given: The robot’s controls Observations of nearby features Estimate: Map of features Path of the robot. Structure of the Landmark-based SLAM-Problem. Indoors. Undersea. Underground.

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Probabilistic Robotics

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  1. Probabilistic Robotics SLAM

  2. The SLAM Problem A robot is exploring an unknown, static environment. Given: • The robot’s controls • Observations of nearby features Estimate: • Map of features • Path of the robot

  3. Structure of the Landmark-based SLAM-Problem

  4. Indoors Undersea Underground Space SLAM Applications

  5. Representations • Grid maps or scans [Lu & Milios, 97; Gutmann, 98: Thrun 98; Burgard, 99; Konolige & Gutmann, 00; Thrun, 00; Arras, 99; Haehnel, 01;…] • Landmark-based [Leonard et al., 98; Castelanos et al., 99: Dissanayake et al., 2001; Montemerlo et al., 2002;…

  6. Why is SLAM a hard problem? SLAM: robot path and map are both unknown Robot path error correlates errors in the map

  7. Why is SLAM a hard problem? • In the real world, the mapping between observations and landmarks is unknown • Picking wrong data associations can have catastrophic consequences • Pose error correlates data associations Robot pose uncertainty

  8. SLAM: Simultaneous Localization and Mapping • Full SLAM: • Online SLAM: Integrations typically done one at a time Estimates entire path and map! Estimates most recent pose and map!

  9. Graphical Model of Online SLAM:

  10. Graphical Model of Full SLAM:

  11. robot motion current measurement map constructed so far Scan Matching Maximize the likelihood of the i-th pose and map relative to the (i-1)-th pose and map. Calculate the map according to “mapping with known poses” based on the poses and observations.

  12. Kalman Filter Algorithm • Algorithm Kalman_filter( mt-1,St-1, ut, zt): • Prediction: • Correction: • Returnmt,St

  13. Kalman Filter Algorithm Knowncorrespondences

  14. Kalman Filter Algorithm Unknowncorrespondences

  15. Kalman Filter Algorithm UnknownCorrespondences(cont’d)

  16. (E)KF-SLAM • Map with N landmarks:(3+2N)-dimensional Gaussian • Can handle hundreds of dimensions

  17. Classical Solution – The EKF • Approximate the SLAM posterior with a high-dimensional Gaussian [Smith & Cheesman, 1986] … • Single hypothesis data association

  18. EKF-SLAM Map Correlation matrix

  19. EKF-SLAM Map Correlation matrix

  20. EKF-SLAM Map Correlation matrix

  21. Properties of KF-SLAM (Linear Case) [Dissanayake et al., 2001] Theorem: In the limit the landmark estimates become fully correlated

  22. Victoria Park Data Set [courtesy by E. Nebot]

  23. Victoria Park Data Set Vehicle [courtesy by E. Nebot]

  24. Data Acquisition [courtesy by E. Nebot]

  25. SLAM [courtesy by E. Nebot]

  26. Map and Trajectory Landmarks Covariance [courtesy by E. Nebot]

  27. Landmark Covariance [courtesy by E. Nebot]

  28. Estimated Trajectory [courtesy by E. Nebot]

  29. EKF SLAM Application [courtesy by John Leonard]

  30. EKF SLAM Application odometry estimated trajectory [courtesy by John Leonard]

  31. EKF-SLAM Summary • Quadratic in the number of landmarks: O(n2) • Convergence results for the linear case. • Can diverge if nonlinearities are large! • Has been applied successfully in large-scale environments. • Approximations reduce the computational complexity.

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