As the scale and complexity of multi-agent robotic systems are subject to a continuous increase, this paper considers a class of systems labeled as Very-Large-Scale Multi-Agent Systems (VLMAS) with dimensionality that can scale up to the order of millions of agents. In particular, we consider the problem of steering the state distributions of all agents of a VLMAS to prescribed target distributions while satisfying probabilistic safety guarantees. Based on the key assumption that such systems often admit a multi-level hierarchical clustered structure - where the agents are organized into cliques of different levels - we associate the control of such cliques with the control of distributions, and introduce the Distributed Hierarchical Distribution Control (DHDC) framework. The proposed approach consists of two sub-frameworks. The first one, Distributed Hierarchical Distribution Estimation (DHDE), is a bottom-up hierarchical decentralized algorithm which links the initial and target configurations of the cliques of all levels with suitable Gaussian distributions. The second part, Distributed Hierarchical Distribution Steering (DHDS), is a top-down hierarchical distributed method that steers the distributions of all cliques and agents from the initial to the targets ones assigned by DHDE. Simulation results that scale up to two million agents demonstrate the effectiveness and scalability of the proposed framework. The increased computational efficiency and safety performance of DHDC against related methods is also illustrated. The results of this work indicate the importance of hierarchical distribution control approaches towards achieving safe and scalable solutions for the control of VLMAS. A video with all results is available in https://youtu.be/0QPyR4bD2q0 .

翻译：随着多机器人系统的规模和复杂性持续增长，本文考虑一类称为超大规模多智能体系统（VLMAS）的系统，其维度可扩展至数百万个智能体。特别地，我们研究了在满足概率安全保证的前提下，将VLMAS所有智能体的状态分布引导至指定目标分布的问题。基于此类系统通常具有多层层次化集群结构（其中智能体被组织成不同层级的团簇）的关键假设，我们将这些团簇的控制与分布控制相关联，并提出了分布式层次化分布控制（DHDC）框架。所提出的方法包含两个子框架。第一个子框架为分布式层次化分布估计（DHDE），这是一种自下而上的层次化分布式算法，它将所有层级团簇的初始与目标配置关联为合适的高斯分布。第二个子框架为分布式层次化分布引导（DHDS），这是一种自上而下的层次化分布式方法，可将所有团簇和智能体的分布从初始状态引导至DHDE分配的目标状态。扩展到两百万个智能体的仿真结果证明了所提框架的有效性和可扩展性。同时展示了DHDC相比相关方法在计算效率和安全性能方面的提升。本研究表明，层次化分布控制方法对于实现VLMAS的安全可扩展控制具有重要意义。包含所有结果的视频可在https://youtu.be/0QPyR4bD2q0 获取。