The Turret-Runner-Penetrator Differential Game
A. Von Moll, D. Shishika, Z. Fuchs, M. Dorothy
Published in American Control Conference, 2021
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 terminated. In this paper, 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 and ends up being terminated in order that the Penetrator can be guaranteed to hit the target circle. We formulate the Turret-Runner-Penetrator scenario as a differential game over the Value of the subsequent game of $minmax$ terminal angle which takes place between the Turret and Penetrator once the Runner has been terminated. The solution to the Game of Degree, including equilibrium Turret, Runner, and Penetrator strategies, as well as the Value function are given. In addition, the Game of Kind solution, which is the manifold of states in which the Penetrator will be terminated exactly on the target circle, is constructed numerically.