A new class of pursuer strategies for the discrete-time lion and man problem

This paper addresses a discrete-time pursuit-evasion game, known as the lion and man problem. The pursuer is chasing the evader within the positive quadrant of a two-dimensional environment and wins the game when it reaches the evader position. A new family of pursuer strategies is proposed, which relies on the minimization of a user-defined function of the environment coordinates. The approach guarantees capture in finite time, no matter which is the strategy adopted by the evader. The degree of freedom associated to the choice of the function to be minimized enhances the flexibility of the pursuer strategy. Moreover, numerical simulations show the superiority of the proposed solution with respect to the most common pursuit strategies available in the literature.