Capturability in a two-target 'game of two cars'

The regions of capturability and draw are derived for a two-target pursuit-evasion differential game of two cars. Specifically, using geometric arguments, complete barrier surfaces are constructed that emanate from the boundaries of the usable parts of the targets of the faster and slower players. The targets are, respectively, a sector of a disk and a complete disk. The barrier surface emanating from the latter target provides a solution to the one-target game of two cars, while the regions of capturability in the two-target game of two cars are inferred from the combined effect of both barrier surfaces. Nomenclature / = right-hand side of the kinematic differential equations n = normal to the barrier surface r = weapon system range R = minimum turning radius R2 = Euclidian plane S] = one-dimensional thorus S = barrier surface t = time T = target set (terminal manifold) u = control variable w = speed x,y = position of the player in the plane a = half-squint angle of the weapon system 0 = maneuverability ratio =w1R2/w2R1 y = speed ratio =w 2 /w y 0 = heading T = time Subscripts