The undesired equilibria of formation control with ring graphs
He Bai · 2010
We consider the formation control problem with the ring graph. Because the graph is cyclic, undesired equilibria arise. We investigate the structures of the undesired equilibria and develop conditions that describe the undesired formations. When the desired formation is an equilateral polygon, we prove by linearization that the undesired equilibria are unstable. We also discuss the interpretation for the unstable eigenvector.