Trajectory Optimization in Convex Underapproximations of Safe Regions
Jerry Ding and Claire Tomlin
Air Force Office of Scientific Research
This project is concerned with a computationally efficient method for optimizing an aircraft trajectory in a two-aircraft conflict scenario, under a noncooperative setting. It is assumed that the future trajectory of the uncontrolled aircraft is unknown, but that deterministic input bounds are given. The only sensor information available is assumed to be readings of the position of the uncontrolled aircraft at regularly sampled discrete time instants. Safety is ensured through the computation of unsafe reachable sets in a game theoretic framework. The reachable sets are then employed as constraints in a convex trajectory optimization program at each time step. We prove the safety property of the optimization program, and address the errors introduced by model linearization through a robustness analysis. Simulation results demonstrate that the trajectories generated by the proposed algorithm provide a tight bound on the feasible trajectories in the presence of uncertainties.