Containment strategies to capture one higher-speed evader in perfect encirclement formation

A pursuit-evasion game in which multiple lower-speed pursuers cooperate to capture a single higher-speed evader is considered in this work. The Cartesian oval-based method is used to separate the dominance regions for the evader and the pursuer with a positive capture radius. Firstly, the occupied angle of the Cartesian oval is derived and the perfect encirclement formation formed by Cartesian ovals is developed. Then given the initial state of the perfect encirclement formation with two, three, and four pursuers, the optimal cooperative containment strategies for the multiple pursuers to shrink the initial encirclement formation are developed. Furthermore, we prove that if the pursuers employ the proposed optimal containment strategies, the escaping path of the evader is avoided, thus ensuring the instantaneous nullification of escaping path during the entire game process.