Control of minimally persistent leader-remote-follower formations in the plane

This paper addresses the n-vehicle formation shape maintenance problem in the plane. The objective is to design decentralized motion control laws for each vehicle to restore formation shape in the presence of small perturbations from the desired shape. Formation shape is restored by actively controlling a certain set of interagent distances, and we assign the task of controlling a particular interagent distance to only one of the involved agents. We restrict our attention to a class of directed information architectures called minimally persistent leader-remote-follower. The nonlinear closed-loop system has a manifold of equilibria, which implies that the linearized system is nonhyperbolic. We apply center manifold theory to show local exponential stability of the desired formation shape. 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 leader-remote-follower formations with generic agent positions. Simulations are provided.