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.
Overview Review SLAM Reducing complexity State Augmentation Partitioned Updates Sparsification Data association Batch Gating SIFT Multi-Hypothesis Future works
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.
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 }
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.
SLAM algorithm Prediction Update
7 EKF State Space Model Prediction Update where
Maintaining values: Bel(x t,m) and its covariance matrix P t. Map with N landmarks:(3+2N)-dimensional Gaussian. 8 EKF-SLAM
Overview Review SLAM Reducing complexity State Augmentation Partitioned Updates Sparsification Data association Batch Gating SIFT Multi-Hypothesis Future works
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 State Augmentation Prediction : Solution : State Augmentation Separating the state into an augmented states Update only affected matrixes Static
State Augmentation Covariance prediction State Augmentation Static O(N 3 ) O(N)
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
Partitioned Updates Local State : Global State:Periodically registers Updated by Local SLAM
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
Covariance prediction Sparsification using the information form O(N 3 ) O(N)
Overview Review SLAM Computational complexity State Augmentation Partitioned Updates Sparsification Data association Batch Gating SIFT Multi-Hypothesis Future works
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?
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
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
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 …
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
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