Control of acyclic formations of mobile autonomous agents

This paper proposes distributed control laws for maintaining the shape of a formation of mobile autonomous agents in the plane for which the desired shape is defined in terms of prescribed distances between appropriately chosen pairs of agents. The formations considered are directed and acyclic where each given distance is maintained by only one of the associated pair of agents and there is no cycle in the sensing graph. It is shown that, except for a thin set of initial positions, the gradient-like control law can always cause a formation to converge to a finite limit in an equilibrium manifold for which all distance constraints are satisfied. The potential applicability of a control law using target positions is also discussed.