Receding Horizon Control for Uncertain Pursuit-Evasion Games

A robust technique for handling parameter and strategy uncertainty in a pursuit-evasion framework is developed. The method is a receding horizon controller valid for problem classes with singularly perturbed trajectories that approximates the optimal feedback solution with small loss in optimality. The receding horizon method is used to ensure the controller is robust to incorrect or extraneous information about an opposing player's dynamics or strategy. A simple analytic pursuit-evasion game motivates the method by demonstrating that the receding horizon solution closely approximates the optimal solution and may be solved much faster. Simulations of a nonlinear game show that the receding horizon controller is especially useful when it is unknown whether the opposing player is performing an active or passive maneuver. In several cases, the receding horizon controller is shown to become more effective than a game-optimal controller acting with an incorrect strategy estimate. The major limitation of the technique for a nonlinear system is the expensive solution time; therefore, the optimal control problem is translated to a nonlinear programming problem and the test cases are repeated. Finally, the test cases are run on hardware to validate the method for real-time practical operation. The singular-perturbation algorithm applied herein is valid only for a small subset of all pursuit and evasion games. Nonetheless, the methods developed here can in theory be used for any generic game scenario, given that sufficient computing power is available to find the numerical solutions.