Distributed observer-based coordination for multiple Lagrangian systems using only position measurements

This study addresses the distributed coordination problem for multiple Lagrangian systems under a directed graph. Two cases are considered, namely, the distributed tracking control problem with a dynamic leader and the leaderless synchronisation problem. To overcome the difficulty that only positions are measured, a kind of new distributed observer is designed to estimate the velocity for each follower. The velocity observer is updated using only position information from the agent itself and from its neighbours. Based on the outputs of the observer, the distributed control protocols are proposed, respectively, such that the tracking errors locally exponentially converge to zero in the tracking scenario and the agents synchronise in the leaderless synchronisation scenario. Furthermore, the stability of the overall scheme is discussed under the directed interaction graphs that contain a directed spanning tree. Finally, cooperative simulations are provided to show the effectiveness of the proposed observer and control algorithms.