Attacker Dispersal Surface in the Turret Defense Differential Game
A. Von Moll, Z. Fuchs
Published in IFAC World Congress on Automatic Control, 2020
The characteristics for the solution to the Turret Defense Differential Game are explored over the parameter space. We collapse the five natural parameters of capture radius, attacker speed, turret turn rate, time penalty constant, and look-angle penalty constant into two composite parameters in order to facilitate the analysis. There exist three singular surfaces in the game, two of which have an analytic form, and one which can only be obtained numerically. We focus on the latter: the Attacker Dispersal Surface, wherein the attacker can choose between an indirect or direct route to capture. For certain parameter settings, the Attacker Dispersal Surface is present, while for others, the surface is absent. These regions in the parameter space are identified, and the numerical procedures to do so are detailed. Backwards shooting of the optimal state and adjoint dynamics features prominently in the procedures. Two pieces of numerical evidence are utilized to indicate the presence or absence of the Attacker Dispersal Surface.