This work is dedicated to position control of redundant robots, realized with the help of the sensibility theory. The control method allows controlling the robot position following some working trajectory, and at the same time maintaining its orientation state unchanged or vice-versa. The latter is achieved by using the features of the four robot configuration space orthogonal fibrations. Their characteristics and role are clarified. A concept of robot image trajectories is formulated and its application is analyzed. The proposed method is going to be applied for a real-time control to a 7 d.o.f. robot, based on Puma type construction. Simulations have been done for it, taking into account its dynamics and sensibility models and also by applying the position control method. The results and conclusions are presented.