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

## TL;DR

This paper develops an analytical approach to assign tasks in a multiplayer reach-avoid game within convex domains, optimizing evader capture using barrier-based regions and simplified integer programming.

## Contribution

It introduces a novel analytical barrier method for task assignment in pursuit-evasion games, reducing computational complexity with a simplified integer programming approach.

## Key findings

- Analytical barriers effectively determine winning regions.
- Task assignment maximizes evader captures under optimal play.
- Simulation validates the proposed method's effectiveness.

## Abstract

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.