Interception in differential pursuit/evasion games

TL;DR

This paper introduces a geometric criterion using future cones to determine interception possibilities in differential pursuit/evasion games, with applications to vehicle interception and satellite warfare.

Contribution

It develops a novel topological cone-based criterion for interception in differential games, linking geometric conditions to Nash equilibrium concepts.

Findings

Future cone containment determines interception feasibility.

Equivalence of future cone conditions to known interception criteria.

Application to satellite interception, exemplified by the FengYun-1C case.

Abstract

A qualitative criterion for a pursuer to intercept a target in a class of differential games is obtained in terms of \emph{future cones}: Topological cones that contain all attainable trajectories of target or interceptor originating from an initial position. An interception solution exists after some initial time iff the future cone of the target lies within the future cone of the interceptor. The solution may be regarded as a kind of Nash equillibrium. This result is applied to two examples: 1. The game of Two Cars: The future cone condition is shown to be equivalent to conditions for interception obtained by Cockayne. \cite{ref2} 2. Satellite warfare: The future cone for a spacecraft or direct-ascent antisatellite weapon (ASAT) maneuvering in a central gravitational field is obtained and is shown to equal that for a spacecraft which maneuvers solely by means of a single velocity change at the cone vertex. The latter result is illustrated with an analysis of the January 2007 interception of the FengYun-1C spacecraft.