Non-linear Dynamics Commons^™

Decentralized Control Of Vehicle Formations, Gerardo Lafferriere, Anca Williams, John S. Caughman Iv, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

This paper investigates a method for decentralized stabilization of vehicle formations using techniques from algebraic graph theory. The vehicles exchange information according to a pre-specified communication digraph, G. A feedback control is designed using relative information between a vehicle and its in-neighbors in G. We prove that a necessary and sufficient condition for an appropriate decentralized linear stabilizing feedback to exist is that G has a rooted directed spanning tree. We show the direct relationship between the rate of convergence to formation and the eigenvalues of the (directed) Laplacian of G. Various special situations are discussed, including …