Horizontal and Orthogonal Defensive Formations for Two Weak Pursuers and One Evader Game

Defensive formation of the pursuers is critical to the result of the two pursuers and one evader differential games. This article focuses on the horizontal defensive formation as well as the orthogonal defensive formation for the end game of homing missile interception, in which the payoff function is the minimal terminal miss of the pursuers. In particular, in the horizontal formation, it is proved that there exists an optimal initial distance between the two pursuers with a heuristic approach; in the orthogonal formation, it is deduced that the evader's optimal strategy depends on the maximum acceleration ratio of the evader and the pursuer. In addition, the two defensive formations are compared, implying that the horizontal formation gives a lesser miss than the orthogonal formation. Simulation results agree with the theoretical analysis.