Collision Avoidance Strategies for a Three Player Game

Collision avoidance strategies for a game with three players, two pursuers and one evader, are constructed by determining the semi-permeable curves that form the barrier. The vehicles are assumed to have the same capabilities, speed and turn-rates. The game is assumed to be played on a two-dimensional plane. The usable part and its boundary are first determined along with the strategy along the boundary. Semi-Permeable curves are evolved from the boundary and closure of the barrier is determined from the condition that leads to intersection of two semi-permeable curves. As in the game of two cars, universal curves and the characteristics that terminate and eminate from the universal curve are used to fill voids on the barrier surface. This study benefits from the following published work on barriers for differential games, Isaacs [1], Merz [2, 3], Pachter and Getz [4], Bardi [5], Falcone and Bardi [6], Patsko and Turova [7] and Mitchell, Bayen and Tomlin [8].