Multi-Agent Coordination to High-Dimensional Target Subspaces

In this paper, we consider a coordination problem to high-dimensional target subspaces for networked multi-agent systems. It is a general form of multi-agent coordination which includes a wide range of applications, e.g., rendezvous, alignment, formation and so on. This paper discusses a fundamental issue of this coordination: what kind of network topology enables us to achieve this coordination via distributed and relative control. We derive necessary and sufficient conditions of such network graphs, and show that the connectivity in terms of cliques (i.e., complete subgraphs) plays a crucial role. This result is a natural extension of the well-known result of the consensus control, and provides us with a unified control strategy for various coordination tasks. Numerical examples are given to illustrate the validity of the obtained analysis results.