On Global Stability of Planar Formations

Formation control is concerned with the design of control laws that stabilize agents at given distances from each other, with the constraint that an agent's dynamics only depends on a subset of other agents. We show in this technical note that a broad class of control laws fails to stabilize a simple formation with four agents. The novelty of the approach used in this technical note lies in the use of bifurcation theory to show that, for almost all control laws, there exists a stable undesired equilibrium.