Graph theoretic methods in the stability of vehicle formations

This paper investigates the stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a pre-specified (undirected) communication graph, G. The feedback control is based only on relative information about vehicle states shared via the communication links. We prove that a linear stabilizing feedback always exists provided that G is connected. Moreover, we show how the rate of convergence to formation is governed by the size of the smallest positive eigenvalue of the Laplacian of G. Several numerical simulations are used to illustrate the results.