In this paper, we develop a novel control strategy to constrain the internal motion of a robotic platform intended to assist surgeons in spine surgery. The targeted task consists in drilling into a specific region of vertebrae in order to position spinal implants and thus re-ensure the spine stability. The present platform includes a redundant robotic arm with 7 degrees of freedom (DoF) directly manipulated by the surgeon in a comanipulation scheme. A torque-based impedance control has been chosen to generate a compliant behavior on the whole body of the robot and thus increase the degree of safety of the robotic device. In this regard, a new control law was implemented to constrain the internal motion of the robot, i.e. the movements of its elbow, allowed by its degree of redundancy. Unlike the classical control approaches, the proposed control law implements a non-linear response of the stiffness in the null-space to better comply with the motion constraints. In order to validate the behavior of the robot using this new control law, experimental tests have been carried out and their results were compared with those obtained with a classic null-space compliance law defined in joint coordinates.