Cluster Consensus in Multiple Lagrangian Systems Under Pinning Control

This paper is mainly concerned with cluster tracking control for robotic networks whose dynamics are modeled by a Lagrangian equation with multiple leaders. An adaptive distributed pinning tracking control protocol is presented to realize cluster consensus, and the corresponding convergence analysis is given by utilizing the property of directed acyclic networks topology. Furthermore, by developing a recursive analysis method, a criterion that ensures the convergence for proposed algorithm is given. Subsequently, simulations conducted on the seven two-link revolute arms are presented to illustrate the effectiveness of the theoretical results.