Stabilization of Symmetric Formations to Motion around Convex Loops

Derek A. Paley, Naomi Ehrich Leonard and Rodolphe Sepulchre

Systems and Control Letters, 57, 2008, pp. 209-215.
We provide a cooperative control algorithm to stabilize symmetric formations to motion around closed curves suitable for mobile sensor networks. This work extends previous results for stabilization of symmetric circular formations. We study a planar particle model with decentralized steering control subject to limited communication. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. We illustrate the result for a skewed superellipse, which is a type of curve that includes circles, ellipses, and rounded parallelograms.

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