Modeling of the Target Interception Delay in an ADT-Game With Three Defenders

Abstract

The paper considers a variant of the flat Attacker-Defender-Target problem with 3 defenders. The problem is considered in simple motions in a flat setting: the target and the defenders move rectilinearly with constant velocity. The initial position of the target and the attacker is given. In this case, the motion of the target is determined by its initial velocity vector, and that of the defenders by the momentum and angle of release. All defenders are considered to be released immediately at the initial time of attack detection, as their release later may be noisy and de-mask the target for the attacker. The defenders are false targets (decoys). In fact, the task is to determine such trajectories of the defenders that the attacker first intercepts them and only then switches to pursuit of the main target. In this way, the time to intercept the primary target increases, and at some parameter values it may become unattainable for an attacker with limited energy resources. The study considers a model of the operation of the homing system of an autonomous attack vehicle based on proportional navigation, with the attacker first solving the problem of joint pursuit of targets, then circling the targets one by one. A software package was developed, numerical simulations were performed, and the optimal release angles of 3 defenders were determined for different target heading angles. For each of the cases considered, a solution was found in which the attacker lacks the energy resource to intercept the main target.