A Pursuit-Evasion Problem of Multiple Pursuers from the Biological-inspired Perspective

The pursuit-evasion problem is common in both nature and the artificial intelligence area. We consider the multi-player pursuit-evasion problem of multiple pursuers with communication constraints on an evader. Besides, the velocity of all pursuers is varying, and the initial positions do not need to be on the circle. The conditions for successful capture, including distance conditions and quantity conditions, are defined in this paper. Furthermore, the capture strategy and escape strategy are designed from the biological-inspired perspective. We realize collision avoidance, gathering, and direction alignment between pursuers by introducing repulsion, attraction, and alignment functions in the pursuer strategy. Then, we observe the sharp phase-transition between the capture zone and escape zone and fit the relevant phase-transition lines by varying the repulsion-coefficient and attraction-coefficient. Based on the coherent analysis for pursuit-evasion behaviour, the relationship between the parameters and the outcome can be obtained.