Time-Varying Formation Tracking Control for Multiple Euler–Lagrange Systems With an Uncertain Leader: Theory and Experiment

Time-varying formation tracking (TVFT) control problem for multiple Euler–Lagrange (EL) systems with an uncertain leader is investigated in this article. The objective of this problem is for the followers' states to track the uncertain leader's output and achieve the desired formation. One of the major challenges in solving such a problem lies in estimating the information of the leader. In this article, an observer-based TVFT control framework is presented in this article, which does not require all or part of the follower agents to know the system dynamic knowledge of the leader agent directly in advance. First, two fully distributed adaptive observers are presented for estimating the uncertain leader's state, output, and the unknown system matrices under an IE condition, which relaxes the existing restrictive persistently exciting or cooperative finite-time excitation condition. Then, on the basis of the constructed adaptive observers, state and output variables of the leader, a fully distributed TVFT for EL systems with an uncertain leader is developed, which means the proposed formation tracking controller operates independently of the system dynamic knowledge of the leader agent; with the help of the Lyapunov stability theory, the TVFT criterion for the considered system is derived. Finally, in order to demonstrate the theoretical results derived in this article, a practical air–ground formation tracking platform, which consists of an unmanned aerial vehicle and four unmanned ground vehicles, is introduced, and physical experimental results are obtained.