Motion Planning via Manifold Samples

TL;DR

This paper introduces a modular motion planning framework that combines geometric analysis of low-dimensional spaces with sampling methods, improving efficiency over traditional algorithms like PRM.

Contribution

The authors propose sampling entire low-dimensional manifolds in configuration spaces, enabling more accurate connectivity analysis and faster planning than point sampling methods.

Findings

Framework achieves significant speedup over PRM.

Manifold sampling improves connectivity analysis.

Modular design allows independent optimization.

Abstract

We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably simpler sampling-based approaches that are appropriate for higher dimensions. In order to facilitate the transfer of advanced geometric algorithms into practical use, we suggest taking samples that are entire low-dimensional manifolds of the configuration space that capture the connectivity of the configuration space much better than isolated point samples. Geometric algorithms for analysis of low-dimensional manifolds then provide powerful primitive operations. The modular design of the framework enables independent optimization of each modular component. Indeed, we have developed, implemented and optimized a primitive operation for complete and exact combinatorial analysis of a certain set of manifolds, using arrangements of curves of rational functions and concepts of generic programming. This in turn enabled us to implement our framework for the concrete case of a polygonal robot translating and rotating amidst polygonal obstacles. We demonstrate that the integration of several carefully engineered components leads to significant speedup over the popular PRM sampling-based algorithm, which represents the more simplistic approach that is prevalent in practice. We foresee possible extensions of our framework to solving high-dimensional problems beyond motion planning.