IEEE Transactions on Automatic Control, Vol.52, No.12, 2214-2226, 2007
On synchronous robotic networks - Part II: Time complexity of rendezvous and deployment algorithms
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.
Keywords:circumcenter and centroid laws;coordination algorithms;deployment;rendezvous;robotic networks;time complexity