Optimal Control and the Aircraft Radar Evasion Problem

This paper considers the problem of optimal path planning for unmanned aerial vehicles in the presence of radar-guided surface-to-air missiles. The goal is to generate trajectories that ensure that the aerial vehicle visit a given set of way points while avoiding a given set of known locations of radar units. In this paper we first discuss the general radar evasion problem. Given that the aircraft equations of motion are nonholonomically constrained, the main mathematical tools used in this paper stem from nonlinear differential geometry. Hence, we introduce the constrained dynamic interpolation optimal control problem and state the optimality conditions. We then apply these conditions to the radar evasion problem. Finally, we provide numerical simulations that illustrate the ideas proposed in this paper.