Robotic manipulators are widely used in modern industry. In order for robot manipulators to achieve trajectory tracking control, the end-effectors must move precisely along the given trajectories. The nonlinearity, strong coupling, and uncertainty of the system make trajectory tracking very complicated and difficult. An approach for robust feedback control is presented in this paper as a solution to this problem. The design relies on active disturbance rejection control to estimate unknown disturbances affecting the plant. The controlled system is an uncertain two-link manipulator with elastic gear transmissions, described by nonlinear friction and elasticity. It is based on an industrial benchmark problem. The model has two significant uncertainties: parametric uncertainty as well as external disturbances that affect tools and motors. A simulation-based evaluation of the proposed control method and a comparison of its performance, considering specific robustness requirements and trajectory tracking, are presented. The comparison includes the baseline controller, the QFD (Quality Function Deployment) method, and PD-CNN (PD Control Compensation based on the Cascade Neural Network). Computer simulations of the proposed controller are carried out to validate the ABB (Asea Brown Boveri) industrial benchmark. The simulation results demonstrate superiority in meeting stability and target value requirements. The stability and ultimate boundedness of the tracking error of ADRC (Active Disturbance Rejection Control) are demonstrated.