In this work, non-cooperative competitive games between two unmanned ground robots using Nonlinear Model Predictive Control (NMPC) while incorporating obstacle avoidance techniques are studied. The objective of the first player (pursuer) is to minimize the relative distance and orientation between itself and the second player (evader) while avoiding obstacles, whereas the evader does the opposite. The Pursuit-Evasion Game (PEG) being a typical class of a differential game is formulated as a zero-sum game with two homogeneous players in five different game scenarios. The objective function of each player is formulated as a double optimization problem and is solved separately using NMPC techniques. The optimal trajectory of each player is computed iteratively by considering the best response of the opponent player. The level of information is assumed to be symmetric. Simulations of various scenarios show the winning possibility of each player.

Non-cooperative game problems such as pursuitevasion require a solution approach that takes into consideration the strategy of the opponents. To predict the strategy of an opponent in a game, its full information is required and more computation time would be spent. However, this requirement of the opponent's full information is not realistic. Also, the computation time required by the game-theoretic algorithm (GTA) could make the controller unimplementable for some systems. Conversely, Model Predictive Control (MPC) could be use to solve the same problem using only the states information on the opponent by solving minimization or maximization cost functions. In this paper, we compared the GTA and MPC algorithm using two autonomous nonholonomic ground robots. Several simulations were conducted in the absence and presence of obstacles, using different initial conditions. The results obtained showed that the MPC algorithm can achieve similar performance.