Apollonius Partitions Based Pursuit-evasion Game Strategies by Q-Learning Approach

This paper studies a classical single pursuer and single evader pursuit-evasion game. The pursuer attempts to capture the slower evader who aims to extend its lifetime during the game. To simplify this question, requiring the evader to take fixation strategy which is choosing the farthest point in its current dominant region as aimpoint and moving at a constant speed. Assuming the pursuer is faster than the evader. Then, the speed ratio is a constant. The instaneous state space will be partitioned into pursuer's dominant zone and evader's dominant zone by the generalized Apollonius circle. The pursuit strategy is based on minimizing the area of the evader's dominant region. Furthermore, we propose a supermodular game for this game. Thus, the existence of the Nash equilibrium is guaranteed. Simulation results based on Q-learning are presented to solve the problem, which shows the effectiveness of this method.