Stabilization of Planar Collective Motion: All-to-all Communication
Rodolphe Sepulchre, Derek Paley, Naomi Ehrich Leonard
IEEE Transactions on Automatic Control, Vol. 52, No. 5, pages 811-824, 2007.
This paper proposes a design methodology to stabilize isolated relative
equilibria in a model of
all-to-all coupled identical particles moving in the plane at unit speed. Isolated
relative equilibria correspond to either parallel motion of all particles with fixed
relative spacing or circular motion of all
particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov
functions that prove
exponential stability and suggest almost global convergence properties. The results of
the paper provide a low-order parametric family of stabilizable collectives that
offer a set of primitives for the design of
higher-level tasks at the group level.