Convex Tours of Bounded Curvature
Résumé
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.