Characterizing robust coordination algorithms via proximity graphs and set-valued maps

This paper studies correctness and robustness properties of motion coordination algorithms with respect to link failures in the network topology. The technical approach relies on computational geometric tools such as proximity graphs, nondeterministic systems defined via set-valued maps and Lyapunov stability analysis. The manuscript provides two general results to help characterize the asymptotic behavior of spatially distributed coordination algorithms. These results are illustrated in rendezvous and flocking coordination algorithms