Geometric motion estimation and control for robotic-assisted beating-heart surgery

One of the potential benefits of robotic systems in cardiac surgery is that their use can increase the number of possible off-pump (beating heart) coronary artery bypass grafting procedures. Robotic systems can actively synchronize the motion of surgical tools to the motion of the surface of the heart, with the surgeon specifying only the relative motion of the tool with respect to the heart. Accurate prediction of the motion of the heart surface is obviously of crucial importance for the safety and robustness of such a system. This paper presents a novel approach to predict the motion of the surface of a beating heart. We show how ECG and respiratory information can be used to extract two periodic components from the quasi-periodic motion of the heart surface. Contrary to most existing literature, we consider the full geometric motion, including rotation due to respiration. We then show how to combine the periodic components to accurately predict future motion of the heart surface, and how this information can be used to design an explicit controller that asymptotically stabilizes the relative motion of the surgical tool to a desired relative distance and orientation.