The GraphSLAM Algorithm Daniel Holman CS 5391: AI Robotics March 12, 2014

Introduction The SLAM Problem Given a robot’s control signals and observations of nearby features, calculate a map of the features and robot path Full SLAM Problem Calculate the entire path of the robot, or all poses from time 1 to t rather than simply the pose at time t GraphSLAM provides a solution to the offline full SLAM problem

GraphSLAM GraphSLAM - Describes the SLAM problem as a sparse graph Each node in the graph represents a robot pose or a feature of the map Each edge in the graph corresponds to a nonlinear constraint of either the motion or measurement models

EKFSlam vs. GraphSLAM EKFSlam Online, Proactive As a filter, only maintain posterior pose at t No time dependence for memory allocation Represents information though mean vector and covariance matrix Best estimate of robot pose and map Updating covariance is computationally expensive, particularly for large maps GraphSLAM Offline, Batch, “lazy” Estimates posterior for all poses 1:t Graph increases linearly over time Represents information as soft constraints, less expensive to compute Adds an additional inference phase in which information is transformed to estimate state Can revise past data association, multiple linearization: produce more accurate maps

Sum of all constraints is nonlinear least squares problem Thrun, Sebastian, Wolfram Burgard, and Dieter Fox. Probabilistic robotics. MIT press, 2005.

Inference Map and path are obtained from linearized information matrix and information vector If each feature is only seen locally once, the graph represented by constraints is linear and thus can be reordered as a band-ordered diagonal matrix Realistically, features are seen at multiple time steps, computing full inverse of can be expensive

Inference

Thrun, Sebastian, Wolfram Burgard, and Dieter Fox. Probabilistic robotics. MIT press, 2005.

Feature Recovery

Thrun, Sebastian, Wolfram Burgard, and Dieter Fox. Probabilistic robotics. MIT press, 2005.

Conclusion Addresses full SLAM problem: calculates posteriors for full robot path along with map Constructs a sparse graph of nonlinear constraints between poses and sensed features, and motion commands into soft constraints between consecutive poses Performs inference by mapping the graph into an isomorphic information matrix and vector, defined over all pose variables and the entire map Construct linear information form, reduction of the form to remove the map, and solves resulting optimization problem over robot poses