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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 the game the evader is at a distance L>l from the pursuer. The pursuer goal is to get closer from the evader than the capture distance l. The goal of the evader is to keep the pursuer at all time farther from it than this capture distance. In this paper, we found 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 also present the condition defining the winner of the game and we construct a solution over the entire reduced space.

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