Real-Time Forward Kinematics and Jacobians for Control of an MRI-Guided Magnetically Actuated Robotic Catheter

Abstract: This paper presents a forward kinematics and analytical Jacobian computation approach for real-time control of a novel magnetic resonance imaging (MRI)-actuated robotic catheter. The MRI-actuated robotic catheter is modeled as a series of rigid and flexible segments and actuated by magnetic torques generated on a set of current-carrying microcoils embedded on the catheter body by the magnetic field of the MRI scanner. First, a real-time forward kinematic modeling approach of the robotic catheter employing the static Cosserat-rod theory is presented. Second, the analytical calculation approach of the forward kinematic Jacobians of the proposed forward kinematic model is presented. The accuracy, reproducibility, and computational efficiency of the proposed methods are evaluated using a robotic catheter prototype with a single coil set, where catheter tip trajectories collected by a catadioptric stereo camera tracking system are validated using the desired tip trajectories. Experimental results demonstrate that the proposed method can successfully control the catheter in an open loop to perform complex trajectories with real-time computational efficiency, paving the way for accurate closed-loop control with real-time MR-imaging feedback.