AVOIDANCE TRAJECTORIES FOR DRIVER ASSISTANCE SYSTEMS VIA SOLVERS FOR OPTIMAL CONTROL PROBLEMS∗

Abstract. Avoidance trajectories for driver assistance systems is an important and active field of research in car industry. Assistance systems with active braking maneuvers rely on car models, e.g. the single-track model, which are modeled as control problems. The formulation of suitable objective functions serves as a tool to realize collision detection and avoidance. In two scenarios for overtaking maneuvers, an optimal trajectory is computed via fixing a secure target state or by computing reachable sets from the initial starting point. First numerical experiments show approximations to optimal trajectories, controls and reachable sets. The sensitivity analysis in both, the optimal trajectory and the reachable set, reveal parameters that significantly influence the solution. Key words. sensitivity analysis; direct discretization methods; optimal control; reachable sets AMS subject classifications. 90C31, 49K40, 49M3