Optimal Saddle-Point Strategy of Reach-Avoid Game in Three-Dimensional Space

Reach-avoid game with two pursuers and one evader in three dimensions is the main topic of this paper. While the adversary tries to approach the plane, two pursuers establish a cooperative team, each with different speeds, to defend the plane against one evader via capture. The isochronous surfaces, i.e., Apollonius spheres, separate the dominance regions of both sides to determine the saddle points and value functions of the systems involved in the game of degree. Moreover, it is proved that the state-feedback optimal strategies are Nash Equilibrium. The possible degeneration of the cooperative team is also analyzed. At last, several simulation experiments are conducted to demonstrate the optimality of the proposed strategies.