Distributed Tracking for Multiple Lagrangian Systems Using Only Position Measurements

This paper investigates the distributed tracking control problem for multiple Lagrangian systems under a general directed graph where only a portion of the agents have access to the desired time-varying trajectory. To overcome the problem that only positions are measured, a observer is designed to estimate the velocity for each follower. By employing the estimated states, the distributed observer-based controller is proposed using only position measurements. Furthermore, the condition for the distributed tracking problem on the directed graph is derived, such that the tracking errors and observer errors semi-globally converge to zero. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.