Pursuit-evasion games with multi-pursuer vs. one fast evader

In a pursuit-evasion (PE) game, each pursuer attempts to minimize the distance between the pursuer (P) and the evader (E) and capture it in the shortest time, whereas the evader tries to maximize the distance to escape from being captured. In this paper, we deal with PE games with a fast evader which can match the speed of or outrun the pursuers. We apply the well-known Apollonius circles formed by the evader and each pursuer to analyze how the evader can find a better strategy to escape or prolong the capture time whenever a successful escape is not possible. Conversely, by observing the changing states of the evader, the pursuers cooperatively contain the evader by enclosing the evader inside a convex polygon, with its vertices being the pursuers' positions. Simulation results show the effectiveness of the proposed strategies as well as the limitations of a successful pursuit of an intelligent evader.