Control of coleader formations in the plane

This paper addresses the n-agent formation shape maintenance problem in the plane. We consider a class of directed information architectures associated with so called minimally persistent coleader formations. The formation shape is specified by certain interagent distances. Only one agent is responsible for maintaining each distance. We propose a control law where each agent executes its control using only the relative position measurements of agents it must maintain its distance to. The resulting nonlinear closed-loop system has a manifold of equilibria; thus the linearized system is nonhyperbolic. We apply center manifold theory to show local exponential stability of the desired formation shape that circumvents the non-compactness of the equilibrium manifold. Choosing stabilizing gains is possible if a certain submatrix of the rigidity matrix has all leading principal minors nonzero, and we show that this condition holds for all minimally persistent coleader formations with generic agent positions.