Curvature-Bounded Traversability Analysis in Motion Planning for Mobile Robots

We consider the geometric problem of deciding whether a narrow planar passage can be traversed by a curve that satisfies prespecified upper bounds on its curvature. This problem is of importance for path- and motion-planning of autonomous mobile robots, particularly when vehicle dynamical constraints are considered during planning. For a special case of narrow passages, namely, rectangular channels, we present a fast numerical algorithm to determine if a given channel may be traversed via curvature-bounded paths. We demonstrate that the proposed algorithm can affirm traversability in cases where the most recent result in the literature fails.

I. Introduction

Consider the following problem in planar geometry: Let be a polygon, with two of its edges designated as the entry and exit edges. Determine if there exists a continuously differentiable curve of finite length and with no cusps, such that this curve lies entirely within the polygon , the endpoints of this curve lie on the entry and exit edges, and the curvature of this curve satisfies, pointwise, a prespecified upper bound. The bound on the curvature may vary over the region enclosed by .