Turret–Runner–Penetrator Differential Game With Role Selection

Abstract

A scenario is considered in which two cooperative Attackers aim to infiltrate a circular target guarded by a Turret. The engagement plays out in the two-dimensional plane; the holonomic Attackers have the same speed and move with simple motion and the Turret is stationary, located at the target circle’s center, and has a bounded turn rate. When the Turret’s look angle is aligned with an Attacker, that Attacker is neutralized. In this article, we focus on a region of the state space, wherein only one of the Attackers is able to reach the target circle—and even then, only with the help of its partner Attacker. The Runner distracts the Turret until it is neutralized, which allows the Penetrator to gain a positional advantage and guarantee success in hitting the target circle. We formulate the Turret–Runner–Penetrator scenario as a differential game over the value of the subsequent game of min/max terminal angle, which takes place between the Turret and Penetrator once the Runner has been neutralized. The solution to the game of degree, including equilibrium Turret, Runner, and Penetrator strategies, as well as the Value function is given. The case in which the Penetrator can reach the target before the Turret can neutralize the Runner is formulated and solved. Finally, the assumption of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> defined roles/goals is relaxed and the minimum of the solutions to the two fixed-role games is shown to be a global stackelberg equilibrium (GSE).