On Synchronous Robotic Networks—Part II: Time Complexity of Rendezvous and Deployment Algorithms
Sonia Martı́nez, Francesco Bullo, Jorge Cortés, Emilio Frazzoli · IEEE Transactions on Automatic Control · 2007
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.