Reachability by paths of bounded curvature in convex polygons

Abstract

Let B be a point robot moving in the plane, whose path is constrained to forward motions with a curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has linear complexity.