Euclidean Distance-Optimal Post-Processing of Grid-Based Paths

TL;DR

This paper introduces Homotopic Visibility Graph Planning (HVG), a novel post-processing method that guarantees path shortening within the same topological class, improving grid-based path planning in Euclidean space.

Contribution

The paper presents HVG, a new algorithm that guarantees the shortest path within a topological class, with proofs and experimental comparisons to existing methods.

Findings

HVG guarantees path length reduction within the same topological class.

Experimental results show HVG outperforms existing post-processing techniques.

HVG is proven to produce at least as short a path as the provably shortest within its class.

Abstract

Paths planned over grids can often be suboptimal in an Euclidean space and contain a large number of unnecessary turns. Consequently, researchers have looked into post-processing techniques to improve the paths after they are planned. In this paper, we propose a novel post-processing technique, called Homotopic Visibility Graph Planning (HVG) which differentiates itself from existing post-processing methods in that it is guaranteed to shorten the path such that it is at least as short as the provably shortest path that lies within the same topological class as the initially computed path. We propose the algorithm, provide proofs and compare it experimentally against other post-processing methods and any-angle planning algorithms.