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

This paper studies a discrete-time pursuit evasion game 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. (C) 2019 Elsevier B.V. All rights reserved.