The increased deployment of multi-robot systems (MRS) in various fields has led to the need for analysis of system-level performance. However, creating consistent metrics for MRS is challenging due to the wide range of system and environmental factors, such as team size and environment size. This paper presents a new analytical framework for MRS based on dimensionless variable analysis, a mathematical technique typically used to simplify complex physical systems. This approach effectively condenses the complex parameters influencing MRS performance into a manageable set of dimensionless variables. We form dimensionless variables which encapsulate key parameters of the robot team and task. Then we use these dimensionless variables to fit a parametric model of team performance. Our model successfully identifies critical performance determinants and their interdependencies, providing insight for MRS design and optimization. The application of dimensionless variable analysis to MRS offers a promising method for MRS analysis that effectively reduces complexity, enhances comprehension of system behaviors, and informs the design and management of future MRS deployments.

翻译：多机器人系统(MRS)在各领域的广泛应用，催生了系统级性能分析的需求。然而，由于团队规模与环境尺寸等系统与环境因素差异显著，建立统一的MRS性能评估指标颇具挑战。本文提出一种基于无量纲变量分析的MRS分析框架——该数学方法通常用于简化复杂物理系统。此方法将影响MRS性能的复杂参数有效凝练为可控的无量纲变量集。我们构建了融合机器人团队与任务核心参数的无量纲变量，并基于这些变量拟合团队性能参数模型。该模型成功识别了关键性能决定因素及其相互依存关系，为MRS设计与优化提供了理论依据。将无量纲变量分析应用于MRS，展现出降低系统复杂度、增强系统行为认知、指导未来MRS部署设计管理的显著优势，为MRS分析提供了有效方法论。