Compliant and flexible cardiac catheters provide direct access to the inside of the heart via the vascular system without requiring clinicians to stop the heart or open the chest. However, the fast motion of the intracardiac structures makes it difficult to modify and repair the cardiac tissue in a controlled and safe manner. In addition, rigid robotic tools for beating heart surgery require the chest to be opened and the heart exposed, making the procedures highly invasive. The novel robotic catheter system presented here enables minimally invasive repair on the fast-moving structures inside the heart, like the mitral valve annulus, without the invasiveness or risks of stopped heart procedures.