Qualitative Criterion for Interception in a Pursuit/Evasion Game

TL;DR

This paper presents a qualitative criterion for interception in pursuit/evasion games, using future cones to determine conditions under which interception is always possible, akin to a Nash equilibrium.

Contribution

It introduces a novel criterion based on future cones to assess the existence of interception solutions in pursuit/evasion scenarios.

Findings

Interception is always possible if the target's future cone is within the interceptor's future cone after some initial time.

The criterion provides a necessary and sufficient condition for guaranteed interception.

The condition resembles a Nash equilibrium in pursuit/evasion games.

Abstract

A qualitative account is given of a differential pursuit/evasion game. A criterion for the existence of an intercept solution is obtained using future cones that contain all attainable trajectories of target or interceptor originating from an initial position. A sufficient and necessary conditon that an opportunity to intercept always exist is that, after some initial time, the future cone of the target be contained within the future cone of the interceptor. The sufficient condition may be regarded as a kind of Nash equillibrium.