Exponential stabilization of infinitesimally rigid formations

In this paper, we explore exponential stability of infinitesimally rigid formations under the distance-based control approach. We convert the formation maintenance problem into stabilization problem of the error dynamics, and analyze the stability of the equilibrium point of the error dynamics. A basic assumption is that the desired formation shape is represented by an infinitesimally rigid framework. From the fact that any infinitesimally rigid framework contains a infinitesimally minimally rigid subframework, we view the error dynamics as a perturbed system with vanishing perturbation. Then the nominal system is derived from the infinitesimally minimally rigid subframework with guaranteed exponential stability. Then we apply the perturbed system theory to show the exponential stability of the original system.