Passivity-based position consensus of multiple mechanical integrators with communication delay

We present a consensus framework for multiple variable-rate heterogeneous mechanical integrators (i.e. multidimensional integrators with mass, damping and spring matrices) on undirected graph with constant, yet, non-uniform communication delay. By connecting multiple mechanical integrators via (discrete-time) spring connections over delayed links with some damping injection, our proposed framework not only achieves position consensus, but also enforces closed-loop discrete-time passivity. Moreover, it allows arbitrary control gains regardless of integration steps, if there is no delay. Simulation result is also given to support the theory.