标题： 基于细胞束的分布式多智能体协调 显示英文标题

标题： Distributed Multi-agent Coordination over Cellular Sheaves

摘要： 多智能体系统的协调技术种类繁多，通常利用专门为所涉及的系统类型或协调目标定制的求解器或控制器。 本文介绍了一种使用细胞层和非线性层拉普拉斯算子语言的一般统一框架，用于异构多智能体协调，这些概念是对图和图拉普拉斯算子的推广。 具体而言，我们引入了非线性同调规划的概念，该规划包含了无向图上的细胞层选择、非线性边势函数以及受限凸节点目标，构成了广泛类别协调问题的标准形式。 我们使用乘子交替方向法推导出一种分布式优化算法，用于解决这些非线性同调规划问题。 为了展示此框架的应用性，我们展示了如何将包括一致性、队形和群体运动在内的异构协调目标表示为非线性同调规划，并提供了数值模拟以证明我们的分布式求解算法的有效性。 显示英文摘要

摘要： Techniques for coordination of multi-agent systems are vast and varied, often utilizing purpose-built solvers or controllers with tight coupling to the types of systems involved or the coordination goal. In this paper, we introduce a general unified framework for heterogeneous multi-agent coordination using the language of cellular sheaves and nonlinear sheaf Laplacians, which are generalizations of graphs and graph Laplacians. Specifically, we introduce the concept of a nonlinear homological program encompassing a choice of cellular sheaf on an undirected graph, nonlinear edge potential functions, and constrained convex node objectives, which constitutes a standard form for a wide class of coordination problems. We use the alternating direction method of multipliers to derive a distributed optimization algorithm for solving these nonlinear homological programs. To demonstrate the applicability of this framework, we show how heterogeneous coordination goals including combinations of consensus, formation, and flocking can be formulated as nonlinear homological programs and provide numerical simulations showing the efficacy of our distributed solution algorithm.