From Constrained Delaunay Triangulations to Roadmap Graphs with Arbitrary Clearance

TL;DR

This paper introduces a novel, efficient refinement algorithm for constrained Delaunay triangulations that creates adaptable roadmap graphs for path planning with arbitrary obstacle clearance, simplifying and speeding up the process.

Contribution

It presents an original refinement algorithm that produces flexible roadmap graphs for path planning with arbitrary clearance, avoiding recomputation when clearance changes.

Findings

The algorithm is simpler than existing methods.

It is significantly more efficient.

The generated roadmap graphs support arbitrary obstacle clearance.

Abstract

This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be followed around a given set of obstacles. Our solution consists in an original refinement algorithm for constrained Delaunay triangulations, aimed at generating a roadmap graph suited for planning paths with arbitrary clearance. In other words, a minimum distance to the obstacles can be specified, and the graph does not have to be recomputed if this distance is modified. Compared to other solutions, our approach has the advantage of being simpler, as well as significantly more efficient.