Robotic catheters have the potential to revolutionize cardiac surgery by enabling minimally invasive structural repairs within the beating heart. This paper presents an actuated catheter system that compensates for the fast motion of cardiac tissue using 3D ultrasound image guidance. We describe the design and operation of the mechanical drive system and catheter module and analyze the catheter performance limitations of friction and backlash in detail. To mitigate these limitations, we propose and evaluate mechanical and control system compensation methods, including inverse and model-based backlash compensation, to improve the system performance. Finally, in vivo results are presented that demonstrate that the catheter can track the cardiac tissue motion with less than 1 mm RMS error. The ultimate goal of this research is to create a fast and dexterous robotic catheter system that can perform surgery on the delicate structures inside of the beating heart.