Probabilistic Pursuit-Evasion Games: A One-Step Nash Approach

This paper addresses the control of a team of autonomous agents pursuing a smart evader in a nonaccurately mapped terrain. By describing this problem as a partial information Markov game, we are able to integrate map-learning and pursuit. We propose receding horizon control policies, in which the pursuers and the evader try to respectively maximize and minimize the probability of capture at the next time instant. Because this probability is conditioned to distinct observations for each team, the resulting game is nonzero-sum. When the evader has access to the pursuers’ information, we show that a Nash solution to the one-step nonzero-sum game always exists. Moreover, we propose a method to compute the Nash equilibrium policies by solving an equivalent zero-sum matrix game. A simulation example is included to show the feasibility of the proposed approach. †This research was supported by Honeywell, Inc. on DARPA contract B09350186, and Office of Naval Research.