Guarding a Non-Maneuverable Translating Line with an Attached Defender

TL;DR

This paper analyzes a differential game where a defender attached to a translating line segment aims to intercept an attacker, deriving strategies and barrier surfaces to determine winning regions.

Contribution

It introduces a novel target-guarding game with an attached defender, deriving equilibrium strategies and the value function considering the target's translation.

Findings

Derived equilibrium strategies for attacker and defender.

Identified barrier surfaces dividing winning regions.

Validated results through simulations.

Abstract

In this paper we consider a target-guarding differential game where the defender must protect a linearly translating line-segment by intercepting an attacker who tries to reach it. In contrast to common target-guarding problems, we assume that the defender is attached to the target and moves along with it. This assumption affects the defenders' maximum speed in inertial frame, which depends on the target's direction of motion. Zero-sum differential game of degree for both the attacker-win and defender-win scenarios are studied, where the payoff is defined to be the distance between the two agents at the time of game termination. We derive the equilibrium strategies and the Value function by leveraging the solution for the infinite-length target scenario. The zero-level set of this Value function provides the barrier surface that divides the state space into defender-win and attacker-win regions. We present simulation results to demonstrate the theoretical results.