  We show in this paper that a small subset of agents of a formation of n
agents in Euclidean space can control the position and orientation of the
entire formation. We consider here formations tasked with maintaining
inter-agent distances at prescribed values. It is known that when the
inter-agent distances specified can be realized as the edges of a rigid graph,
there is a finite number of possible configurations of the agents that satisfy
the distance constraints, up to rotations and translations of the entire
formation. We show here that under mild conditions on the type of control used
by the agents, a subset of them forming a clique can work together to control
the position and orientation of the formation as a whole. Mathematically, we
investigate the effect of certain allowable perturbations of a nominal dynamics
of the formation system. In particular, we show that any such perturbation
leads to a rigid motion of the entire formation. Furthermore, we show that the
map which assigns to a perturbation the infinitesimal generator of the
corresponding rigid motion is locally surjective.
