Anchor Selection for SLAM Based on Graph Topology and Submodular Optimization

This article considers simultaneous localization and mapping (SLAM) problem for robots in situations where accurate estimates for some of the robot poses, termed anchors, are available. These may be acquired through external means, for example, by either stopping the robot at some previously known locations or pausing for a sufficient period of time to measure the robot poses with an external measurement system. The main contribution is an efficient algorithm for selecting a fixed number of anchors from a set of potential poses that minimizes estimated error in the SLAM solution. Based on a graph-topological connection between the D-optimality design metric and the tree-connectivity of the pose-graph, the anchor selection problem can be formulated approximately as a submatrix selection problem for reduced weighted Laplacian matrix, leading to a cardinality-constrained submodular maximization problem. Two greedy methods are presented to solve this submodular optimization problem with a performance guarantee. These methods are complemented by Cholesky decomposition, approximate minimum degree permutation, order reuse, and rank-1 update that exploit the sparseness of the weighted Laplacian matrix. We demonstrate the efficiency and effectiveness of the proposed techniques on public-domain datasets, Gazebo simulations, and real-world experiments.