On distributed maximization of algebraic connectivity in robotic networks

We consider the problem of maximizing the algebraic connectivity of the communication graph in a network of mobile robots by moving them into appropriate positions. We describe the Laplacian of the graph as dependent on the pairwise distance between the robots and formulate an approximate problem as a Semi-Definite Program (SDP). We propose a consistent, non-iterative distributed solution by solving local SDP´s which use information only from nearby neighboring robots. Numerical simulations show the performance of the algorithm with respect to the centralized solution.