Second-order consensus of networked mechanical systems with communication delays

In this paper, we address the second-order consensus problem for networked mechanical systems on a directed topology in the case of existence of nonuniform communication delays. To realize the goal of second-order consensus, we propose an adaptive consensus scheme that consists of an adaptive controller and a distributed velocity observer. It is demonstrated that the position and velocity consensus errors between the mechanical systems converge to zero, and that the velocities of the mechanical systems converge to the scaled weighted average of their initial values. We further demonstrate that the proposed consensus scheme can be used to solve the second-order consensus problem for multiple mechanical systems with a constant-velocity leader. The performance of the proposed consensus scheme is shown by a numerical simulation.