1. Probabilistic Robotics SLAM

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

3. 3 Structure of the Landmark- based SLAM-Problem

4. 4 SLAM Applications Indoors Space Undersea Underground

5. 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. 6 Why is SLAM a hard problem? SLAM: robot path and map are both unknown Robot path error correlates errors in the map

7. 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. 8 SLAM: Simultaneous Localization and Mapping Full SLAM: Online SLAM: Integrations typically done one at a time Estimates most recent pose and map! Estimates entire path and map!

9. 9 Graphical Model of Online SLAM:

10. 10 Graphical Model of Full SLAM:

11. 11 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. robot motion current measurement map constructed so far

12. 12 Scan Matching Example

13. 13 Kalman Filter Algorithm 1. Algorithm Kalman_filter(  t-1,  t-1, u t, z t ): 2. Prediction: 3. 4. 5. Correction: 6. 7. 8. 9. Return  t,  t

14. 14 Kalman Filter Algorithm Known correspondences

15. 15 Kalman Filter Algorithm Unknown correspondences

16. 16 Kalman Filter Algorithm Unknown Correspondences (cont’d)

17. 17 Map with N landmarks:(3+2N)-dimensional Gaussian Can handle hundreds of dimensions (E)KF-SLAM

18. 18 Classical Solution – The EKF Approximate the SLAM posterior with a high- dimensional Gaussian [Smith & Cheesman, 1986] … Single hypothesis data association

19. 19 EKF-SLAM Map Correlation matrix

20. 20 EKF-SLAM Map Correlation matrix

21. 21 EKF-SLAM Map Correlation matrix

22. 22 Properties of KF-SLAM (Linear Case) Theorem: In the limit the landmark estimates become fully correlated [Dissanayake et al., 2001]

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

24. 24 Victoria Park Data Set Vehicle [courtesy by E. Nebot]

25. 25 Data Acquisition [courtesy by E. Nebot]

26. 26 SLAM [courtesy by E. Nebot]

27. 27 Map and Trajectory Landmarks Covariance [courtesy by E. Nebot]

28. 28 Landmark Covariance [courtesy by E. Nebot]

29. 29 Estimated Trajectory [courtesy by E. Nebot]

30. 30 EKF SLAM Application [courtesy by John Leonard]

31. 31 EKF SLAM Application odometry estimated trajectory [courtesy by John Leonard]

32. 32 EKF-SLAM Summary Quadratic in the number of landmarks: O(n 2 ) 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.