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On synchronous robotic networks - Part II: Time complexity of rendezvous and deployment algorithms
S. Martínez, F. Bullo, J. Cortés, E. Frazzoli
IEEE Transactions on Automatic Control, 52 (12) (2007), 2214-2226

Abstract

This paper analyzes a number of basic coordination algorithms running on synchronous robotic networks. We provide upper and lower bounds on the time complexity of the move-toward average and circumcenter laws, both achieving rendezvous, and of the centroid law, achieving deployment over a region of interest. The results are derived via novel analysis methods, including a set of results on the convergence rates of linear dynamical systems defined by tridiagonal Toeplitz and circulant matrices.

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