Optimal Path Trajectories in a Threat Environment

Minimizing the risk of detection in a hostile environment is a fundamental requirement of all military operations. Often the trajectory of a vehicle is dependent on other factors such as maximum travel time, fuel usage, and the like, which provide constraints on determining the optimal path of the vehicle. The risk to the vehicle is from detection and subsequent action by enemy forces. Often this detection is from radar. Here we investigate the single vehicle path planning problem to minimize radar exposure. We formulate the problem in a continuous way and present numerical results for a single threat radar. We also show how our approach can be extended to include a second threat radar. By extending our approach we believe that a feasible technique to determine the optimal path in a threat environment consisting of a network of multiple threat radars can be obtained, perhaps even undertaken by on-board systems.