Two-Player Reconnaissance Game with Half-Planar Target and Retreat Regions

TL;DR

This paper analyzes a differential game involving an Intruder and a faster Defender, where the Intruder aims to reconnoiter a half-plane target and retreat, with solutions derived for optimal strategies in each phase.

Contribution

The paper provides a complete closed-form solution for the differential game with half-plane regions, including value functions and equilibrium strategies for both phases.

Findings

Closed-form solutions for the game strategies are derived.

Numerical simulations demonstrate the effectiveness of the strategies.

The game model captures realistic reconnaissance scenarios with partial capture risk.

Abstract

This paper is concerned with the reconnaissance game that involves two mobile agents: the Intruder and the Defender. The Intruder is tasked to reconnoiter a territory of interest (target region) and then return to a safe zone (retreat region), where the two regions are disjoint half-planes, while being chased by the faster Defender. This paper focuses on the scenario where the Defender is not guaranteed to capture the Intruder before the latter agent reaches the retreat region. The goal of the Intruder is to minimize its distance to the target region, whereas the Defender's goal is to maximize the same distance. The game is decomposed into two phases based on the Intruder's myopic goal. The complete solution of the game corresponding to each phase, namely the Value function and state-feedback equilibrium strategies, is developed in closed-form using differential game methods. Numerical simulation results are presented to showcase the efficacy of our solutions.