This paper outlines a method for applying a kinematic path following control of a mobile robot without any regard for surface structure. Background. A great deal of mobile robotics kinematics analysis is based on the movement of the robot on a two dimensional flat surface. Our application for precision surgery required a new approach to a system that would operate on a highly non-linear surface; this specific system was a surgical robot that would conduct craniotomies while moving over highly irregular and often deformed skulls. Methods. The approach used an abstract view of the operating environment that would totally ignore the surface, instead determining the control parameters based only on the robot and the desired cutting trajectory. The approach was then evaluated in a 3D environment using a series of predefined surfaces to determine bounding limits in the control theory. These limits were then tested in a second series of tests using real data from the CT preoperative imagery of previous patients and phantoms. The simulation results were then compared with the actual performance of the robot on phantoms and cadavers. Results. The approach has been successfully implemented on the first medical robot to position itself through spiked wheels on the surface of the skull. Testing has to date been successful in both a simulation environment, and on initial phantom and cadiever trials, with accuracies equal to that of the larger industrial modified surgical robots.