On determining optimal strategies in pursuit games in the plane

Pursuit games have application to robotics: the pursuer models a moving obstacle and the evader models a robot that tries to reach a goal region without colliding with the moving obstacle, at each moment the robot does not know the future trajectory of the obstacle. The motion of the pursuer and the evader is controlled by their sets of permissible velocities, called indicatrices. We allow indicatrices that are more general than the simple motion (i.e., velocities are bounded by an L(2)-norm circle). We provide sufficient condition for a pursuit game to ''have value'', in this case we give optimal strategies for the pursuer and the evader. We prove that the pursuit game in which the pursuer and the evader are convex objects moving with simple motion ''has value''.