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

Abstract

This paper is concerned with a variation of a pursuit-evasion game called the Reconnaissance game, in which an Intruder attempts to approach a territory of interest (target region) and return to a safe zone (retreat region) in the presence of a faster Defender. The target and retreat regions are taken to be disjoint closed half-planes. The objective of the Intruder is two-fold: 1) minimize the distance between her position and the target region and 2) escape to the retreat region before being captured by the Defender. The Defender, on the other hand, strives to maximize the same distance and, if possible, capture the Intruder outside the retreat region. The game is decomposed into a series of two subgames: a Target game and an Escape game. A closed-form solution to each subgame, including the Value function and state-feedback saddle-point strategies, is derived separately. Furthermore, winning regions and barrier surfaces are constructed analytically. Numerical simulation results are presented to showcase the efficacy of the proposed solutions