Sparse Multilevel Roadmaps for High-Dimensional Robot Motion Planning

TL;DR

This paper introduces the sparse multilevel roadmap planner (SMLR), a novel algorithm that extends sparse roadmaps with multilevel abstractions for efficient high-dimensional robot motion planning, including challenging scenarios.

Contribution

The paper generalizes sparse roadmaps to multilevel abstractions using fiber bundles and restriction sampling, improving planning performance in high-dimensional spaces.

Findings

Outperforms traditional sparse roadmap planners on high-dimensional problems.

Effective in scenarios with narrow passages and infeasible configurations.

Demonstrates probabilistic completeness and near-optimality inheritance.

Abstract

Sparse roadmaps are important to compactly represent state spaces, to determine problems to be infeasible and to terminate in finite time. However, sparse roadmaps do not scale well to high-dimensional planning problems. In prior work, we showed improved planning performance on high-dimensional planning problems by using multilevel abstractions to simplify state spaces. In this work, we generalize sparse roadmaps to multilevel abstractions by developing a novel algorithm, the sparse multilevel roadmap planner (SMLR). To this end, we represent multilevel abstractions using the language of fiber bundles, and generalize sparse roadmap planners by using the concept of restriction sampling with visibility regions. We argue SMLR to be probabilistically complete and asymptotically near-optimal by inheritance from sparse roadmap planners. In evaluations, we outperform sparse roadmap planners on challenging planning problems, in particular problems which are high-dimensional, contain narrow passages or are infeasible. We thereby demonstrate sparse multilevel roadmaps as an efficient tool for feasible and infeasible high-dimensional planning problems.