Escape from an Orbiting Pursuer with a Nonzero Capture Radius

TL;DR

This paper analyzes a pursuit-evasion problem where a slower pursuer with a nonzero capture radius attempts to contain a faster evader within a circular region, providing insights into capture conditions and escape strategies.

Contribution

It offers a detailed analysis of capture conditions, effects of key parameters, and reachability for evaders in a pursuit-evasion scenario with a nonzero capture radius.

Findings

Identified worst-case initial positions for capture

Demonstrated effects of speed ratio and capture radius

Mapped reachable escape regions for the evader

Abstract

This paper explores a multi-agent containment problem, where a fast evader, modeled having constant speed and using constant heading, attempts to escape a circular containment region that is orbited by a slower pursuer with a nonzero capture radius. The pursuer is constrained to move along the edge of the containment region and seeks to capture the evader. This paper presents an in-depth analysis of this pursuer-evader containment scenario. First, multiple types of capture conditions for a single-pursuer case are analyzed defining the worst-case initial position for the pursuer. Second, a parametric study is performed to demonstrate the effects of speed ratio, capture radius, and initial location of the evader. Finally, a reachability analysis is performed to investigate the viable escape headings and reachable regions by the evader. This work provides a foundation for the analysis of escape under more general evader inputs as well as a multiple-pursuer version of the scenario.