Multiplayer Reach-avoid Game Research Articles

Collaborative Constrained Target-Reaching Control in a Multiplayer Reach-Avoid Game

Collaborative Constrained Target-Reaching Control in a Multiplayer Reach-Avoid Game

Cooperative Team Strategies for Multi-Player Perimeter-Defense Games

This paper studies a variant of the multi-player reach-avoid game played between intruders and defenders with applications to perimeter defense. The intruder team tries to score by sending as many intruders as possible to the target area, while the defender team tries to minimize this score by intercepting them. Finding the optimal strategies of the game is challenging due to the high dimensionality of the joint state space, and the existing works have proposed approximation methods to reduce the design of the defense strategy into assignment problems. However they suffer from either suboptimal defender performance or computational complexity. Based on a novel decomposition method, this paper proposes a scalable (polynomial-time) assignment algorithm that accommodates cooperative behaviors and outperforms the existing defense strategies. For a certain class of initial configurations, we derive the exact score by showing that the lower bound provided by the intruder team matches the upper bound provided by the defender team, which also proves the optimality of the team strategies.

Task Assignment for Multiplayer Reach–Avoid Games in Convex Domains via Analytical Barriers

This work considers a multiplayer reach-avoid game between two adversarial teams in a general convex domain which consists of a target region and a play region. The evasion team, initially lying in the play region, aims to send as many its team members into the target region as possible, while the pursuit team with its team members initially distributed in both play region and target region, strives to prevent that by capturing the evaders. We aim at investigating a task assignment about the pursuer-evader matching, which can maximize the number of the evaders who can be captured before reaching the target region safely when both teams play optimally. To address this, two winning regions for a group of pursuers to intercept an evader are determined by constructing an analytical barrier which divides these two parts. Then, a task assignment to guarantee the most evaders intercepted is provided by solving a simplified 0-1 integer programming instead of a non-deterministic polynomial problem, easing the computation burden dramatically. It is worth noting that except the task assignment, the whole analysis is analytical. Finally, simulation results are also presented.

On Guaranteed Capture in Multi-Player Reach-Avoid Games via Coverage Control

The main objective of this letter is to provide a control solution for guaranteed capture in multi-player reach-avoid (RA) games in the presence of different vehicle kinematic constraints. To that end, this letter seeks to convert the RA problem from the traditional game theoretic framework to a coverage control problem, which makes it more suitable to find solutions in the multi-agent context. Within this framework, a distributed coverage control law is provided, as well as formal capture guarantees that are verified via simulation..

Reach-Avoid Games With Two Defenders and One Attacker: An Analytical Approach.

This paper considers a reach-avoid game on a rectangular domain with two defenders and one attacker. The attacker aims to reach a specified edge of the game domain boundary, while the defenders strive to prevent that by capturing the attacker. First, we are concerned with the barrier, which is the boundary of the reach-avoid set, splitting the state space into two disjoint parts: 1) defender dominance region (DDR) and 2) attacker dominance region (ADR). For the initial states lying in the DDR, there exists a strategy for the defenders to intercept the attacker regardless of the attacker's best effort, while for the initial states lying in the ADR, the attacker can always find a successful attack strategy. We propose an attack region method to construct the barrier analytically by employing Voronoi diagram and Apollonius circle for two kinds of speed ratios. Then, by taking practical payoff functions into considerations, we present optimal strategies for the players when their initial states lie in their winning regions, and show that the ADR is divided into several parts corresponding to different strategies for the players. Numerical approaches, which suffer from inherent inaccuracy, have already been utilized for multiplayer reach-avoid games, but computational complexity complicates solving such games and consequently hinders efficient on-line applications. However, this method can obtain the exact formulation of the barrier and is applicable for real-time updates.

Defendable Region for the Multiplayer Reach-Avoid Game with Free Attacker-Defender Velocity Ratio

The multiplayer reach-avoid game plays an important role in the applications involving cooperative agents. Analyzing the defendable region for the multiplayer reach-avoid game is the prerequisite for designing the target assignment algorithms and the control laws for both sides of the teams. Since the attacker-defender velocity ratio could be different in different application scenarios, this paper studies the defendable region for the multiplayer reach-avoid game with free attacker-defender velocity ratio. That is to say, the velocity of attacker might be less than, equal to or greater than the velocity of the defender. In order to simplify the problem, the two-dimension one defender versus one attacker issue is first dealt with. Based on the attacker-defender moving time ratio, the concept of the breakthrough point is proposed in this paper. Then, the defendable region of the one versus one reach-avoid game is analyzed based on the concept of breakthrough point. And then the defendable region of the multiplayer reach-avoid game is considered and the defendable regions are classified as strongly defendable regions and weakly defendable regions according to whether the target assignment algorithm is necessary for the defenders. Finally, we illustrate our method by some simulation results.

Multiplayer Reach-Avoid Games via Pairwise Outcomes

A multiplayer reach-avoid game is a differential game between an attacking team with NA attackers and a defending team with ND defenders playing on a compact domain with obstacles. The attacking team aims to send M of the NA attackers to some target location, while the defending team aims to prevent that by capturing attackers or indefinitely delaying attackers from reaching the target. Although the analysis of this game plays an important role in many applications, the optimal solution to this game is computationally intractable when NA>1 or ND>1. In this paper, we present two approaches for the NA=ND=1 case to determine pairwise outcomes, and a graph theoretic maximum matching approach to merge these pairwise outcomes for an NA,ND>1 solution that provides guarantees on the performance of the defending team. We will show that the four-dimensional Hamilton-Jacobi-Isaacs approach allows for real-time updates to the maximum matching, and that the two-dimensional "path defense" approach is considerably more scalable with the number of players while maintaining defender performance guarantees.