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