1Time-Optimal Motion Strategies for Capturing an Omnidirectional Evader using a Differential Drive Robot

Abstract—In this paper, we consider the problem of capturing an omnidirectional evader using a Differential Drive Robot (DDR) 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 as long as possible. The goal of the pursuer is to capture the evader as soon as possible. In this work, 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 towards 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