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

TL;DR

This paper introduces and solves a new differential game where an agile pursuer aims to keep an evader within surveillance range, analyzing conditions for escape and minimum escape time with novel complexity considerations.

Contribution

It presents a new surveillance-evasion game with an agile pursuer and finite turn-rate evader, providing solutions for both escape conditions and minimum escape time.

Findings

The game-of-degree solution depends on the speed ratio.

The solution is more complex than pursuit-evasion games with an agile pursuer.

The solution is simpler than classic turn-limited pursuit-evasion games.

Abstract

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, whilst 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 whilst 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 since 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.