1. Robótica Móvil CC5316 Clase 16: SLAM
Semestre Primavera 2012
Profesor: Pablo Guerrero

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. Chicken-or-Egg A map is needed for localizing a robot
SLAM is a chicken-or-egg problem
A map is needed for localizing a robot
A good pose estimate is needed to build a map
Thus, SLAM is regarded as a hard problem in robotics
A variety of different approaches to address the SLAM problem have been presented
Probabilistic methods outperform most other techniques

4. Structure of the Landmark-based SLAM-Problem

5. SLAM Applications
Indoors
Space
Undersea
Underground

6. Map Representations
Examples:
City map, subway map, landmark-based map

7. Representations Grid maps or scans Landmark-based
[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;…

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

9. Why is SLAM a hard problem?
Robot pose
uncertainty
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

10. 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!

11. Graphical Model of Online SLAM:

12. Graphical Model of Full SLAM:

13. Algoritmos más usados
EKF SLAM
Fast-SLAM

14. Kalman Filter Algorithm
Algorithm Kalman_filter( mt-1, St-1, ut, zt):
Prediction:
Correction:
Return mt, St

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

16. Classical Solution – The EKF
Blue path = true path Red path = estimated path Black path = odometry
Approximate the SLAM posterior with a high-dimensional Gaussian [Smith & Cheesman, 1986] …
Single hypothesis data association

17. EKF-SLAM
Map Correlation matrix

18. EKF-SLAM
Map Correlation matrix

19. EKF-SLAM
Map Correlation matrix

20. Properties of KF-SLAM (Linear Case)
[Dissanayake et al., 2001]
Theorem:
The determinant of any sub-matrix of the map covariance matrix decreases monotonically as successive observations are made.
In the limit the landmark estimates become fully correlated

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

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

23. Data Acquisition
[courtesy by E. Nebot]

24. Raw Odometry (no SLAM)
GPS (for reference)
Odometry

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

26. Estimated Trajectory
[courtesy by E. Nebot]

27. EKF-SLAM: Complexity
Cost per step: O(n2), quadratic in the number of landmarks: O(n2)
Total cost to build a map with n landmarks: O(n3)
Memory: O(n2)
Approaches exist that make EKF-SLAM
O(n^1.5) / O(n2.5) / O(n)

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

29. FastSLAM Filtro Rao-Blackwellized
Un filtro de partículas estima la pose del robot
Cada partícula contiene un mapa
El mapa está hecho de N EKF’s independientes

30. Ejemplo Trayectoria Partícula