This work presents the control system strategy implemented in a new cooperative human-robot system for transpedicular fixation, a type of spine surgery consisting in the immobilization of two or more vertebrae by means of screws and metal bars. The prototype uses a PA-10 robotic arm. The main parts of the control strategy are the admittance module and the generation of virtual fixtures (active constraints) that assist the surgeon and prevent contact with surrounding critical areas. The virtual fixtures are obtained directly from the surgical planner with the purpose of increasing the precision in screw insertion and having safer interventions, reducing radiation doses, invasiveness and the probability of error. Differing from other surgery robotic assistants, the one proposed in this work oilers a larger workspace and a degree of versatility that permits its adaptation to different types of surgeries.