A Simple P+d Controller for Consensus of Euler-Lagrange Systems Over Directed Graphs

The state of the art in consensus control for multi-agent Euler-Lagrange (EL) systems relies on one or several of the following assumptions: the graph is undirected or directed and strongly connected, the controller is centralized, knowledge of the inertia and Coriolis matrices is needed, the systems’ trajectories are bounded. In this letter we show that a simple Proportional Derivative controller with gravity compensation, which does not rely on any of the previous hypotheses, achieves consensus for EL systems over connected acyclic directed graphs. The proof follows a cascaded-systems argument. Also, we provide some numerical simulations to illustrate the performance of the controller.