A game of surveillance between an omnidirectional agent and a differential drive robot

Abstract

This paper addresses a surveillance problem between a Differential Drive Robot (DDR) and an Omnidirectional Agent (OA) in a Euclidean plane without obstacles. The agent is initially located inside the robot's detection region, and it wants to escape from it as soon as possible. The DDR, on the other hand, wants to delay the escape as much as possible. The pursuer's detection region is modelled as a circle centred at the pursuer's current location. In this work, the time-optimal motion strategies for the players are presented. Also, based on the players' initial configurations, we solve the decision problem of determining the winner of the game.