In this paper, we consider the problem of capturing an omnidirectional evader using a differential drive robot in an obstacle-free environment. At the beginning of this game, the evader is at a distance L > l (the capture distance) from the pursuer. The goal of the evader is to keep the pursuer farther than this capture distance for as long as possible. The goal of the pursuer is to capture the evader as soon as possible. In this paper, we make the following contributions. We present closed-form representations of the motion primitives and time-optimal strategies for each player; these strategies are in Nash equilibrium, meaning that any unilateral deviation of each player from these strategies does not provide to such player benefit toward the goal of winning the game. We propose a partition of the playing space into mutually disjoint regions where the strategies of the players are well established. This partition is represented as a graph, which exhibits properties that guarantee global optimality. We also analyze the decision problem of the game and we present the conditions defining the winner.

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In this paper we consider the surveillance problem of tracking a moving evader by a nonholonomic mobile pursuer. We deal specifically with the situation in which the only constraint on the evader's velocity is a bound on speed (i.e., the evader is able to move omnidirectionally), and the pursuer is a nonholonomic, differential drive system having bounded speed.We formulate our problem as a game. Given the evader's maximum speed, we determine a lower bound for the required pursuer speed to track the evader. This bound allows us to determine at the beginning of the game whether or not the pursuer can follow the evader based on the initial system configuration. We then develop the system model, and obtain optimal motion strategies for both players, which allow us to establish the long term solution for the game. We present an implementation of the system model, and motion A preliminary version of portions of this work appeared in Murrieta-Cid et al., Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems 2005. R. Murrieta-Cid ( ) · U. Ruiz · J.L. Marroquin

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