Polyhedral potential field constructions for obstacle avoidance in a receding horizon formulation

Abstract

We revisit and enhance previous work pertaining to the use of polyhedral potential fields for motion planning in a receding horizon framework. We adapt the standard vertex-based mixed-integer (MI) representations of piecewise affine functions and propose three equivalent formulations which balance the complexity of the geometric representation with the size of the associated MI representation. In all cases, we arrive at formulations whose polyhedral support comes (either directly or as a refinement of it) from an associated hyperplane arrangement induced by the hyperplanes bounding the polyhedral obstacles.