Adaptive Tracking Control of a Class of Constrained Euler–Lagrange Systems by Factorization of Dynamic Mass Matrix

Due to the uncertain parameters and/or the coupled matrices in a majority of Euler-Lagrange (EL) systems among multiple inputs and outputs, the controller designs for the constrained robots with unknown nonlinearities and disturbances are still challenging and difficult. In this paper, a new adaptive motion tracking control method for a class of constrained EL systems is presented. The main feature of the presented control is that high-dimensional vector-based integral Lyapunov function combined with a disturbance observer is presented for a class of EL systems with the nonsymmetric nonlinearity of input of the actuators. As long as the error trajectories deviate from or approach the sliding surface, it allows the disturbance estimation to adjust its value. The errors of tracking will converge to a small zone. Thus, stability of a closed-loop system can be ensured. When the designed parameters of the controller are chosen appropriately, the size of the tracking errors in stable state can be ensured. The applicability of this control method has been verified by the experiments with a planar robotic manipulator.