Edge Nearest Neighbor in Sampling-Based Motion Planning

TL;DR

This paper introduces a new neighborhood finder for sampling-based motion planning that improves efficiency by better exploiting exploration properties, with theoretical and experimental validation.

Contribution

It implements a hierarchical neighborhood finder for RRT, demonstrating enhanced efficiency and proposing a variant of RRG that better explores narrow passages.

Findings

More efficient algorithms demonstrated experimentally.

Theoretically improved exploration of narrow passages.

Hierarchical data structures enhance nearest neighbor queries.

Abstract

Neighborhood finders and nearest neighbor queries are fundamental parts of sampling based motion planning algorithms. Using different distance metrics or otherwise changing the definition of a neighborhood produces different algorithms with unique empiric and theoretical properties. In \cite{l-pa-06} LaValle suggests a neighborhood finder for the Rapidly-exploring Random Tree RRT algorithm \cite{l-rrtnt-98} which finds the nearest neighbor of the sampled point on the swath of the tree, that is on the set of all of the points on the tree edges, using a hierarchical data structure. In this paper we implement such a neighborhood finder and show, theoretically and experimentally, that this results in more efficient algorithms, and suggest a variant of the Rapidly-exploring Random Graph RRG algorithm \cite{f-isaom-10} that better exploits the exploration properties of the newly described subroutine for finding narrow passages.