1. SLAM: Simultaneous Localization and Mapping: Part II BY TIM BAILEY AND HUGH DURRANT-WHYTE Presented by Chang Young Kim These slides are based on: Probabilistic Robotics, S. Thrun, W. Burgard, D. Fox, MIT Press, 2005 Many images are also taken from Probabilistic Robotics. http://www.probabilistic-robotics.com

2. Overview Review SLAM  Reducing complexity State Augmentation Partitioned Updates Sparsification  Data association Batch Gating SIFT Multi-Hypothesis Future works

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

4. Terminology Robot State (or pose):  Position and heading  Robot Controls:  Robot motion and manipulation  Sensor Measurements:  Range scans, images, etc.  Landmark or Map:  Landmarks or Map z t u t x t = ( x ; y ; µ ) x 1 : t = f x 1 ; x 2 ; ::: ; x t g u 1 : t = f u 1 ; u 2 ; ::: ; u t g z 1 : t = f z 1 ; z 2 ; ::: ; z t }

5. Terminology Observation model: or  The probability of a measurement z t given that the robot is at position x t and map m. Motion Model:  The posterior probability that action u t carries the robot from x t-1 to x t.

6. SLAM algorithm Prediction Update

7. 7 EKF State Space Model Prediction Update where

8. Maintaining values: Bel(x t,m) and its covariance matrix P t. Map with N landmarks:(3+2N)-dimensional Gaussian. 8 EKF-SLAM

9. Overview Review SLAM  Reducing complexity State Augmentation Partitioned Updates Sparsification  Data association Batch Gating SIFT Multi-Hypothesis Future works

10. Complexity O(N 3) with N landmarks due to the covariance matrix and matrix multiplication of Jacobian. Can handle hundreds of dimensions? It can be reduced by approximation methods:  State Augmentation for the prediction stage  Partitioned Updates for the update stage  Sparsification using an information form 10 EKF-SLAM : Complexity

11. 11 State Augmentation Prediction : Solution : State Augmentation Separating the state into an augmented states Update only affected matrixes Static

12. State Augmentation Covariance prediction State Augmentation Static O(N 3 ) O(N)

13. 13 Partitioned Updates Update : Solution : Partitioned Update with local submap. Confines the map to a small local region. Only Updates the small local region. Updates the whole map only at a much lower frequency

14. Partitioned Updates Local State : Global State:Periodically registers Updated by Local SLAM

15. State Bel(x t,m) and covariance matrix P t are Gaussian probability density which, implicitly describes the two central moments of Gaussian Using Moment or Information Form Sparsification P t Y t Many of none diagonal components are very close to 0  they can be set to zero. Sparsification

16. Covariance prediction Sparsification using the information form O(N 3 ) O(N)

17. Overview Review SLAM  Computational complexity State Augmentation Partitioned Updates Sparsification  Data association Batch Gating SIFT Multi-Hypothesis Future works

18. Data Association Problem A robust SLAM must consider possible data associations Solutions: three key methods :  Batch Gating  SIFT  Multi-Hypothesis Which observation belongs to which landmark?

19. Batch Gating Basic Principle of Batch: RANSAC Gating : constrained by robot position estimation  If true robot movement is ==> the left case is chosen by using the gating

20. Batch Gating is not enough for reliable data association SIFT features have “landmark-quality” for SLAM  SIFT correspondences tend to be reliable and recognizable under variable conditions Gating  If true robot movement is ==> the left case is chosen by using the gating SIFT

21. Multi-Hypothesis Data Association Multi-hypothesis data association  Generate a separate track estimate for each association hypothesis.  Low-likelihood tracks are pruned FastSLAM is inherently a Multi-hypothesis solution because its data association is done on a per-particle basis. Landmark 1Landmark 2Landmark M … x, y,  Landmark 1Landmark 2Landmark M … x, y,  Particle #1 Landmark 1Landmark 2Landmark M … x, y,  Particle #2 Particle N …

22. Per-Particle Data Association Was the observation generated by the red or the blue landmark? P(observation|red) = 0.3P(observation|blue) = 0.7 Per-particle data association  Pick the most probable match If the probability is too low, generate a new landmark

23. Future Woks Large scale mapping  including many vehicles  in mixed environments  with sensor networks and dynamic landmark. The delayed data-fusion concept instead of batch association and iterative smoothing to improve estimation quality and robustness