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 their 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有趣问题可被纳入分布式优化的框架，例如多机器人任务分配、车辆路径规划、目标保护与监控等。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实际应用尚未得到深入研究。本文展示了如何通过适当的分布式优化配置来解决协作机器人中的典型场景。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）和基于分区的配置（匹配优化中的图结构）之后，我们重点研究两种能够建模协作机器人多种场景的分布式设置，即所谓的约束耦合与聚合优化框架。针对每种框架，我们分析了具体应用案例，并讨论了具有收敛性保证的定制化分布式算法。随后，我们回顾了无需中央协调器即可在真实机器人网络上实现分布式方案的最新工具包。对于每个应用案例，我们探讨了其在上述工具包中的实现方法，并提供了异构机器人网络的仿真与真实实验验证。