Several interesting problems in multi-robot systems can be cast in the framework of distributed optimization. Examples include multi-robot task allocation, vehicle routing, target protection, and surveillance. While the theoretical analysis of distributed optimization algorithms has received significant attention, its application to cooperative robotics has not been investigated in detail. In this paper, we show how notable scenarios in cooperative robotics can be addressed by suitable distributed optimization setups. Specifically, after a brief introduction on the widely investigated consensus optimization (most suited for data analytics) and on the partition-based setup (matching the graph structure in the optimization), we focus on two distributed settings modeling several scenarios in cooperative robotics, i.e., the so-called constraint-coupled and aggregative optimization frameworks. For each one, we consider use-case applications, and we discuss tailored distributed algorithms with their convergence properties. Then, we revise state-of-the-art toolboxes allowing for the implementation of distributed schemes on real networks of robots without central coordinators. For each use case, we discuss its implementation in these toolboxes and provide simulations and real experiments on networks of heterogeneous robots.

翻译：多机器人系统中的若干重要问题可置于分布式优化框架下建模，例如多机器人任务分配、车辆路径规划、目标防护与区域监控等。尽管分布式优化算法的理论分析已受到广泛关注，但其在协作机器人领域的应用尚未得到深入探讨。本文系统阐述了如何通过恰当的分布式优化框架解决协作机器人学中的典型场景。具体而言，在简要介绍广泛研究的共识优化（最适用于数据分析）和基于图分割的优化框架（与优化中的图结构相匹配）之后，我们重点讨论两种能够建模多机器人协作场景的分布式设置——即约束耦合优化与聚合优化框架。针对每种框架，我们结合具体应用案例，探讨了相应的定制化分布式算法及其收敛特性。随后，我们综述了当前先进的工具箱技术，这些工具使得无需中央协调器的真实机器人网络能够实现分布式优化方案。针对每个应用案例，我们详细讨论了其在相关工具箱中的实现方式，并通过异构机器人网络的仿真与实物实验进行验证。