A differential pursuit/evasion game of capture between an omnidirectional agent and a differential drive robot, and their winning roles

This paper addresses a differential pursuit/evasion game. The players are an omnidirectional agent (OA) and a differential drive robot (DDR). They move in an obstacle-free environment; the DDR is faster than the OA but it can only change its motion direction up to a bounded rate. First, we analyse the scenario in which the OA has as objective to capture a DDR in minimum time and the DDR wants to retard the capture as long as possible. We present the time optimal motion primitives of the players to achieve their goals. Later, we allow the agents to change the roles, namely, the DDR is allowed to play as the pursuer and the OA is allowed to play as the evader. This later analysis allows one to establish which is the winner role for each agent, based only on the initial position of the players and their maximum speed.