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

TL;DR

This paper introduces a novel sampling and pruning method for multi-goal path finding in high-dimensional spaces, providing approximation guarantees and demonstrating improved solution quality and speed over traditional methods.

Contribution

It combines sampling-based motion planning with pruning strategies from minimum spanning trees to efficiently solve high-dimensional multi-goal path finding problems with theoretical guarantees.

Findings

Provides an asymptotic 2-approximation guarantee for MGPF.

Demonstrates improved solution quality over uniform sampling.

Shows faster computation times in numerical experiments.

Abstract

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.