On corner cutting in multi-obstacle avoidance problems

One challenging and not extensively studied issue in obstacle avoidance is the corner cutting problem. Avoidance constraints are usually imposed at the sampling time without regards to the intra-sample behavior of the dynamics. This paper improves upon state of the art by describing a multi-obstacle environment over a hyperplane arrangement scaffolding, provides a piecewise description of the "shadow" regions and represents them into a combined mixed integer and predictive control formulation. Furthermore, over-approximation constraints which reduce to strictly binary formulations are discussed in detail. Illustrative proofs of concept, comparisons with the state of the art and simulation results over a classical multi-obstacle avoidance problem validate the benefits of the proposed approach.