Reach‐avoid games with two heterogeneous defenders and one attacker

Abstract

This article addresses a reach-avoid game with two heterogeneous defenders and one attacker in a bounded, convex domain consisting of a target region and a play region. The attacker aims to reach the target region before being captured by any defenders, while the defenders strive to capture the attacker in advance. A simple geometric method is introduced that only considers the position relation between the reaching regions of the players and the boundary of the target region to construct the barrier of the two-player version reach-avoid game analytically. Next, based on the speed ratio between the defenders, the necessary and sufficient conditions suitable for the general game setups to judge which defender contributes to the barrier and decompose the problem into several two-player version subproblems are given. Then, the barrier of the original game is constructed analytically by combining these subproblems in all possible situations. The method provided an analytical expression of the barrier and has essentially no computation burden. Thus, the method is suitable for online applications. And solutions given in this work can be extended to general multiplayer situations and the game with complex setups for further research.

Reach‐Avoid Games with a Time Limit and Detection Range: A Geometric Approach

“…is theorem is also obtained and utilized in many works which have similar game setups [2][3][4]37]. In fact, when the attacker is initially located in the detection range, the original game in this work becomes the game that has already been studied by Yan et al [36].…”

“…us, the target of the attacker is to drive the game state x into S A , while the defender tries to force the state of the game into S D . Since the reach-avoid game terminates immediately when the attacker enters the Ω T , in this article, we assume that the initial position of the attacker lies in the play region Ω P to ensure that the game exists [37].…”

“…is kind of situation is also regarded as the equilibrium outcome. e set of the game's neutral states S N consists of three parts and can be delineated as [37].…”

Multiplayer reach-avoid differential games with simple motions: A review

“…Due to the usefulness of knowing the game winner before the game actually runs, huge progress has been made on the study of barriers (Yan et al, 2017;Shishika and Kumar, 2018;Yan et al, 2019a;Yan et al, 2020;Liang et al, 2022;Lee and Bakolas, 2021;Yan et al, 2021a;Yan et al, 2021b;Von Moll et al, 2022b;Chen and Yu, 2022).…”

“…This review is concerned with the M-RA differential games, with a particular interest in simple motions, which were first discussed by (Mitchell et al, 2005;Margellos and Lygeros, 2011;Zhou et al, 2012) and then extended into many variations and practical applications (Huang et al, 2014;Selvakumar and Bakolas, 2019;Fu and Liu, 2020). The problem is closely related to lifeline games (Garcia et al, 2019b;Yan et al, 2021a;Yan et al, 2021b;Chen and Yu, 2022), two-target differential games (Blaquière et al, 1969;Olsder and Breakwell, 1974;Pachter and Getz, 1980;Getz and Pachter, 1981) and target guarding differential games (Mohanan et al, 2018). Moreover, the problem has high relevance to scenarios involving underground vehicles guarding a building, unmanned aerial vehicles patrolling against illegal poachers and unmanned surface vehicles patrolling around a prohibited water area.…”