For the orientation control system of the manipulator’s end effector with electrical actuators, we develop a decomposition procedure of feedback law design to track given trajectories in the end effector’s coordinate system. Owing to the S-shaped smooth sigma-functions used as the local feedback laws and corrections of the state observer, the tracking system is invariant with a given accuracy with respect to existing uncertainties under constraints imposed on the variables of the mechanical subsystem. The suggested approach does not involve the solution of the inverse kinematics and dynamics problems and also relaxes the requirements to the volume of a priori information about the plant and external perturbation.