Cooperatively controlled robotic assistants can be used in surgery for the repetitive execution of targeting/reaching tasks, which require smooth motions and accurate placement of a tool inside a working area. A variable damping controller, based on a priori knowledge of the location of the surgical site, is proposed to enhance the physical human-robot interaction experience. The performance of this and of typical constant damping controllers is comparatively assessed using a redundant light-weight robot. Results show that it combines the positive features of both null (acceleration capabilities > 0.8m/s2) and optimal (mean pointing error < 1.5mm) constant damping controllers, coupled with smooth and intuitive convergence to the target (direction changes reduced by 30%), which ensures that assisted tool trajectories feel natural to the user. An application scenario is proposed for brain cortex stimulation procedures, where the surgeon’s intentions of motion are explicitly defined intra-operatively through an image-guided navigational system.