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.