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.

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