Mathematical aspects of decentralized control of formations in the plane
It offers theoretical tools for researchers working on decentralized control of multi-agent systems, but is primarily a survey/tutorial rather than presenting new results.
This paper provides mathematical foundations for decentralized formation control, extending stability concepts to manifolds and introducing robustness for nonlinear systems, then formalizes the problem class and summarizes known results.
In formation control, an ensemble of autonomous agents is required to stabilize at a given configuration in the plane, doing so while agents are allowed to observe only a subset of the ensemble. As such, formation control provides a rich class of problems for decentralized control methods and techniques. Additionally, it can be used to model a wide variety of scenarios where decentralization is a main characteristic. We introduce here some mathematical background necessary to address questions of stability in decentralized control in general and formation control in particular. This background includes an extension of the notion of global stability to systems evolving on manifolds and a notion of robustness of feedback control for nonlinear systems. We then formally introduce the class of formation control problems, and summarize known results.