This paper proposes a position control strategy for a variable shared autonomy robotic platform for intra-procedural support in Structural Heart Disease treatment. The platform is created by robotizing the commercial MitraClipTM System (MCS), which treats mitral regurgitation by implanting a clip that grasps the valve leaflets. The paper introduces a Neural Network-based Inverse Kinematic Controller (IKC) that guarantees good trajectory tracking. The data set used for training the IKC was generated by exploring the whole workspace of the catheter. The control model proposed is tested for robustness at different motors' velocities, and its performance is compared to a state-of-the-art PID controller.