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Probabilistic Robotics

Delve into the complexities of Simultaneous Localization and Mapping (SLAM) in robotics. Explore landmark-based representations, Kalman Filter Algorithm, EKF-SLAM, and the challenges faced in mapping unknown environments. Unravel the intricacies of estimating the robot's path and constructing maps of features. Learn about SLAM applications in various spaces and the significance of data associations in SLAM.

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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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