Semi-centralized reconstruction of robot swarm topologies: The largest laplacian eigenvalue and high frequency noise are used to calculate the adjacency matrix of an underwater swarm from time-series

An important task in underwater autonomous vehicle swarm management is the knowledge of the graph topology, to be obtained with the minimum possible communication exchanges and amid heavy interferences and background noises. Despite the importance of the task, this problem is still partially unsolved. Recently, the Fast Fourier Transform and the addition of white noise to consensus signals have been proposed independently to determine respectively the laplacian spectrum and the adjacency matrix of the graph of interacting agents from consensus time series, but both methodologies suffer technical difficulties. In this paper, we combine them in order to simplify calculations, save energy and avoid topological reconstruction errors using only the largest eigenvalue of the spectrum and instead of white noise, a high frequency, low amplitude noise. Numerical simulations of several swarms (random, small-world, pipeline, grid) show an exact reconstruction of the configuration topologies.