Formation control in multi-player pursuit evasion game with superior evaders

In this paper, we consider a multi-pursuer multi-evader pursuit evasion game where some evaders' maximal speeds are higher than those of all pursuers. In multi-player pursuit evasion game, hierarchical framework is applied widely in order to decompose the original complicated multi-player game into multiple small scale games, i.e. one-pursuer one-evader games and multi-pursuer single-evader games. The latter is especially required for superior evaders. Although usually only suboptimal results are obtained, the resulted decentralized approaches are favored by researchers from the point view of communication aspect for practical applications. Based on our previous work, for a multi-pursuer single-superior- evader game on a plane, we first study the number of pursuers which necessitates the capture. Regarding each player as a mass point, a moving planar coordinate system is fixed on the evader. Then formation control is used for pursuers in their pursuit strategies deriving to 1) avoid collision between pursuers; 2) reduce the distance between each pursuer and the evader over the evolution of game; 3) keep the pursuers' angular distribution around the evader invariant during the pursuit process and enclose the superior evader within the union of each pursuer's capture domain at the end of game. The validity of our method is illustrated by two simulation examples.