Surveillance for Security as a Pursuit-Evasion Game

This work addresses a visibility-based target tracking problem that arises in autonomous surveillance for covert security applications. Consider a mobile observer, equipped with a camera, tracking a target in an environment containing obstacles. The interaction between the target and the observer is assumed to be adversarial in order to obtain control strategies for the observer that guarantee some tracking performance. Due to the presence of obstacles, this problem is formulated as a game with state constraints. Based on our previous work in [6] which shows the existence of a value function, we present an off-line solution to the problem of computing the value function using a Fast Marching Semi-Lagrangian numerical scheme, originally presented in [15]. Then we obtain the optimal trajectories for both players, and compare the performance of the current scheme with the Fully Discrete Semi-Lagrangian Scheme presented in [6] based on simulation results.