Informed Steiner Trees: Sampling and Pruning for Multi-Goal Path Finding in High Dimensions

We interleave sampling based motion planning methods with pruning ideas from minimum spanning tree algorithms to develop a new approach for solving a Multi-Goal Path Finding (MGPF) problem in high dimensional spaces. The approach alternates between sampling points from selected regions in the search space and de-emphasizing regions that may not lead to good solutions for MGPF. Our approach provides an asymptotic, 2-approximation guarantee for MGPF. We also present extensive numerical results to illustrate the advantages of our proposed approach over uniform sampling in terms of the quality of the solutions found and computation speed. Note to Practitioners—MGPF is concerned with finding a collision-free, near-optimal path for a robot visiting a set of target configurations. This problem arises in applications that use robotic manipulators such as advanced manufacturing, surface inspection, package sorting, and in other logistical applications where the cost of the traveling between any two configurations of a robot cannot be readily determined a-priori. As robots are expected to perform a large number of tasks, the sequencing of these tasks become important specifically when the travel costs are challenging to estimate. This paper provides an approach to handle this problem in higher dimensions with theoretical guarantees as well as provides simulation results on a broad class of environments to corroborate its performance with respect to the state of the art.