Fast trajectory planning for Dubins vehicles under cumulative probability of radar detection

This paper studies a minimum-time trajectory planning problem under radar detection, where a Dubins vehicle aims to approach a target under a limited probability of being detected. Since the probability is accumulated along the vehicle's trajectory in an integral form, we have to address a non-convex constrained functional optimization problem. To this end, Pontryagin's minimum principle is adopted to derive the optimality conditions, based on which we obtain a set of parameterized trajectories that contain all optimal ones. By leveraging the design of intermediate points, fast algorithms are proposed to approximately compute a minimum-time trajectory among the set. Simulations are performed to validate the effectiveness and efficiency of the proposed algorithms.