Ballistic motion planning

This paper addresses the motion planning problem of a jumping point-robot. Each jump consists in a ballistic motion linking two positions in contact with obstacle surfaces. A solution path is thus a sequence of parabola arcs. The originality of the approach is to consider non-sliding constraints at contact points: slipping avoidance is handled by constraining takeoff and landing velocity vectors to 3D friction cones. Furthermore the magnitude of these velocities is bounded. The ballistic motion lying in a vertical plane, we transform the 3D problem into a 2D one. We then solve the motion equations. The solution gives rise to an exact steering method computing a jump path between two contact points while respecting all constraints. The method is integrated into a standard probabilistic roadmap planner. Probabilistic completeness is proven. Simulations illustrate the performance of the approach.