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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