A novel controller for solving the acceleration tracking of an end-effector of a multi-articulated robotic manipulator is proposed in this study, including the actuator dynamics as part of the control design. The controller possesses state dependent gains that include the presence of states restrictions in angular displacements and velocities for the robot joints. The design of the state-dependent gains is developed using a class of logarithmic barrier Lyapunov functions with time-varying parameters that are evolving using the state restrictions information. A back-stepping strategy leads to defining the design of the voltage that drives the actuators to complete the acceleration tracking when it is feasible considering the complementary joints restrictions. The proposed controller is numerically evaluated using a virtual representation of six degrees of freedom industrial robot. The obtained trajectories for acceleration of the end-effector show the effective tracking of the reference acceleration, while the joints position and velocities restrictions are satisfied. The second set of evaluations confirm that under some non-feasible reference accelerations, the joints restrictions are satisfied. The comparison with traditional non-restricted state feedback confirmed the superiority of the proposed controller, measured in terms of the mean square error of the acceleration tracking and the satisfaction of the joint restrictions.