A discrete-time pursuit–evasion game in convex polygonal environments

This paper studies a discrete-time pursuit–evasiongame within a convex polygonal environment. Building on solutions of the classic lion-and-man problem, two strategies are proposed for the pursuer, which guarantee exact capture in finite time and provide upper bounds on the time-to-capture at each move of the game. A numerical procedure for updating the so-called center of the game, which is instrumental for computing the lion's move, is devised. Numerical simulations show that optimizing the center position, with respect to a suitable cost function taking into account the structure of the environment, allows one to remarkably reduce the number of moves required to capture the evader.