Control Strategies for Multiplayer Target-Attacker-Defender Differential Games with Double Integrator Dynamics

This paper presents a method for deriving optimal controls and assigning attacker-defender pairs in a target-attacker-defender differential game between an arbitrary numbers of attackers and defenders, all of which are modeled using double integrator dynamics. It is assumed that each player has perfect information about the states and controls of the players within a certain range of themselves, but they are unaware of any players outside of this range. Isochrones are created based on the time-optimal trajectories needed for the players to reach any point in the shortest possible time. The intersections of the players' isochrones are used to determine whether a defender can intercept an attacker before the attacker reaches the target. Sufficient conditions on the detection range of the defenders and the guaranteed capture despite perturbations of the attackers off the nominal trajectories are derived. Then, in simulations with multiple players, attacker-defender pairs are assigned so that the maximum number of attackers are intercepted in the shortest possible time.