Prying Pedestrian Surveillance-Evasion: Minimum-Time Evasion from an Agile Pursuer

A new surveillance-evasion differential game is posed and solved in which an agile pursuer (the prying pedestrian) seeks to remain within a given surveillance range of a less agile evader that aims to escape. In contrast to previous surveillance-evasion games, the pursuer is agile in the sense of being able to instantaneously change the direction of its velocity vector, while the evader is constrained to have a finite maximum turn rate. Both the game of kind, concerned with conditions under which the evader can escape, and the game of degree, concerned with the evader seeking to minimize the escape time while the pursuer seeks to maximize it, are considered. The game-of-degree solution is surprisingly complex compared to solutions to analogous pursuit-evasion games with an agile pursuer because it exhibits dependence on the ratio of the pursuer’s speed to the evader’s speed. It is, however, surprisingly simple compared to solutions to classic surveillance-evasion games with a turn-limited pursuer.