Convex Tours of Bounded Curvature

TL;DR

This paper introduces an efficient algorithm for planning the shortest bounded-curvature path around obstacles within a convex workspace, optimizing curvature constraints for a point moving along a convex path.

Contribution

It presents the first linear-time algorithm to find the minimal curvature path around obstacles in a convex environment.

Findings

Algorithm runs in O(m+n) time.

Successfully finds the path with minimal curvature.

Applicable to convex workspaces with polygonal obstacles.

Abstract

We consider the motion planning problem for a point constrained to move along a smooth closed convex path of bounded curvature. The workspace of the moving point is bounded by a convex polygon with m vertices, containing an obstacle in a form of a simple polygon with $n$ vertices. We present an O(m+n) time algorithm finding the path, going around the obstacle, whose curvature is the smallest possible.