3-D Multi-player Pursuit-evasion Game with a Faster Evader

This paper studies two kinds of multi-player pursuit-evasion games in 3-D space: Two-pursuer one-evader game and multi-pursuer one-evader game. The main challenges are that the evader has faster speed than a group of pursuers and the moving directions of the pursuers and faster evader are unknown to each other. First, the concept of occupied angle is introduced to represent the dominated spaces by the pursuers. Then, escape algorithm and pursuit algorithm are designed for the evader and pursuers, respectively. Finally, escape condition and capture condition of the faster evader and pursuers are presented. Some simulation examples are given to illustrate the theoretical results.