Abstract: The surgery assisted robotic tool helps the surgeon to cancel the relative motion between the beating heart and robotic tool, keeping the heart beating during the surgery, which will lessen post surgery complications for patients. Due to the highly irregular and non-stationary nature of heart motion, the robot is hard to track the beating heart motion. To solve this problem, a characteristic analysis of 3D heart motion data through Bi-spectral tool is used to demonstrate the nonlinearity of coupling between respiration and heartbeat in heart motion. Then an nonlinear Second order Volterra Series (SVS) based fast least square prediction algorithm is proposed to provide the future reference to the controller. The nonlinear model would accurately describe the heart motion and the fast least square algorithm would satisfy the real time needs. The comparative experiment results indicate that the proposed adaptive nonlinear heart motion prediction algorithm outperforms the former algorithms in the term of prediction accuracy. The relative motion cancellation ability of the robot is enhanced and prediction error is largely reduced.