Constrained Turret Defense with Fixed Final Time

In this paper, we extend existing turret defense differential game formulations involving a turn-constrained turret and mobile agent to include specified final time and a constraint. For the purposes of this analysis, the specified final time may represent some exogenous input, perhaps representing the time at which some other event will take place. As for the constraint, it represents a keep-out zone for the mobile agent. The scenario is formulated as a two-player, zero-sum differential game and solved via the method of characteristics (i.e., back-propagation of equilibrium trajectories). Three different trajectory types make up the solution: trajectories that end with the turret aligned with the mobile agent, trajectories that end with the mobile agent on the constraint boundary, and regular trajectories.