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In the CABG surgery the robot dynamically cancels the relative motion between the point of interest (POI) on the beating heart and robotic instruments, such that the surgeon can operate as if the heart is stationary. Due to high bandwidth of the POI motion, the quick and precise tracking ability of the robot system is necessary. Different from other heart motion tracking system with only position measurement, our system had both position and acceleration measurement to achieve better tracking performance. The state analysis of the physical model of surgical robotic system offered us the possibility to decrease the tracking error by adding accelerometer. The control algorithm based on the adaptive heart motion model employed the optimal tracking theory with Kalman Filter state estimation is proposed. The result showing better tracking performance is achieved by the added acceleration measurement which provided pre-lead phase over position and more dynamics. The comparison tracking results with and without acceleration measurement which was experimented on 3D test bed Phantom robotics are reported.