An Isochron-Based Solution to the Target Defense Game Against a Faster Invader

Abstract

This letter studies a target defense game between two defenders and a faster moving invader. We propose a novel approach that solves the saddle point strategy from a family of time-to-capture isochrons. We show that the game can be viewed as a pursuit-evasion game between the invader and the isochrons, where the latter are controlled by the defenders. The optimal defending strategy is the one that forces the invader to isochrons with shorter time-to-capture most efficiently. The proposed method is validated in a special case with zero capture range, where we prove that the saddle point strategy is optimal regardless of other players' behaviors. In addition, the isochrons are shown to be semipermeable, and the barrier of the target defense game is solved.