Capturing a Differential Drive Robot With a Dubins Car

Abstract

This work addresses the pursuit-evasion problem of capturing a Differential Drive Robot (DDR) with a Dubins Car (DC) in minimum time. We model the problem as a zero-sum differential game, and using differential game theory, we compute the time-optimal motion strategies of the players near the end of the game. We unveil the existence of three singular surfaces: an Evader’s Dispersal Surface (EDS), a Transition Surface (TS), where the DDR switches its controls, and a Pursuer’s Universal Surface (PUS). A particular set of motion strategies for the players is used at each singular surface. To compute our solution, we assume that both players have the same maximum speed and a bounded turning ratio. Considering the previous setting, the game’s outcome only depends on the particular motion capabilities of the players. From previous results in the literature and those presented in the current paper, we can establish that a DDR has an advantage when it plays as a pursuer or as an evader compared to a Dubins Car performing the same role.

Keywords

• Differential games
• optimal control
• Pursuit-evasion
• robotics