Formation Control in Multi-player Pursuit Evasion Game with Superior Evaders Xu Wang a , Jose B. Cruz Jr. a , Genshe Chen *b Khanh Pham c , Erik Blasch d a Department of Electrical and Computer Engineering, The Ohio State University, 205 Dreese Lab, 2015 Neil Ave., Columbus, OH 43210; b Intelligent Automation Inc., 15400 Calhoun Dr., Suite 400, Rockville, MD 20855 c AFRL/VSSV, Kirtland AFB, NM 87117 d AFRL/SNAA, WPAFB, OH 45433 ABSTRACT 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. Keywords: Pursuit evasion game, multi-player, superior evader, formation control 1. INTRODUCTION In multi-agent systems, where each agent is an individually controlled dynamics, cooperation between the agents of the same group may optimize the group level performance index. For some systems, cooperative relationship is required in order to allow the group to act as a whole and succeed in group mission. Formation control, which shapes the relative position and orientation of agents, is among the methods facilitating cooperation. Formation control has broad applications in spacecraft 1-3 , unmanned aerial vehicles 4-5 , unmanned ground vehicles 6 , autonomous underwater vehicles 7- 9 , mobile robots 10-12 and sensing network 13 . Usually, group formation is dynamic in order to accommodate the changing environment and/or tasks. In multi-pursuer multi-evader pursuit evasion games, formation control is very important for pursuers to develop optimal pursuit strategies. Here capture is defined as when an evader is within a pursuer’s capture zone—a circle if 2-dimension space or a sphere if 3-dimension space centered at the pursuer with certain radius. Based on a probabilistic map, reference 14 studied pursuers’ coordination scheme when pursuing a group of evaders in an unknown environment. 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. We call such evaders as “superior evaders” 15 to emphasize the fact that they have comparatively more advantageous control resources. In multi-player pursuit evasion game, hierarchical framework 14, 19 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 pursuers in order to maximally exploit their cooperation when confronting 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. For the autonomous systems of pursuers in multi-pursuer single- superior-evader games, how to exploit the cooperation between pursuers so that the superior evader can be captured successfully in the shortest time is the main problem. *gchen@i-a-i.com; phone 1 301 294-5218.