A Surveillance Game between a Differential Drive Robot and an Omnidirectional Agent: The Case of a Faster Evader

A fundamental task in mobile robotics is to keep an agent under surveillance using an autonomous robotic platform equipped with a sensing device. Using differential game theory, we study a particular setup of the previous problem. A Differential Drive Robot (DDR) equipped with a bounded range sensor wants to keep surveillance of an Omnidirectional Agent (OA). The goal of the DDR is to maintain the OA inside its detection region for as much time as possible, while the OA, having the opposite goal, wants to leave the regions as soon as possible. We formulate the problem as a zero-sum differential game, and we compute the time-optimal motion strategies of the players to achieve their goals. We focus on the case where the OA is faster than the DDR. Given the OA's speed advantage, a winning strategy for the OA is always moving radially outwards to the DDR's position. However, this work shows that even though the previous strategy could be optimal in some cases, more complex motion strategies emerge based on the players' speed ratio. In particular, we exhibit that four classes of singular surfaces may appear in this game: Dispersal, Transition, Universal, and Focal surfaces. Each one of those surfaces implies a particular motion strategy for the players.