Inverse kinematic analysis and agile control of a magnetically actuated catheter

In recent years, there has been a growing application of robotic-assisted magnetic actuation systems in the treatment of cardiovascular diseases because of the fast response and the miniaturization of medical tools. However, inverse kinematic (IK) modeling in permanent magnet systems is still a challenging task due to the complexity of the magneto-solid strong coupling field. In this paper, we present a magnetic actuation system that uses the rotation of a single permanent magnet to steer the intravascular catheter. The main contribution is the proposal of an IK modeling method that establishes a relationship between the catheter's deflection angle and the rotation angle of the driving magnet (DM). Our proposed method uses the constant curvature model (CCM) to decouple the catheter's deformation and the magnetic loads, thus enabling the efficient estimation of the position of the catheter's tip based on the desired deflection angle. After establishing the equilibrium equation, we employ a numerical computation method to optimize the rotation angle of the DM. To facilitate fast convergence, we propose an analytical solution to determine the optimal initial value. Our proposed IK modeling method has been proven to be effective in the model validation experiment, which achieves a good balance between accuracy and efficiency. The difference between the planned and actual deflection angle is 4.55 +/- 3.44 degrees and the distal position error is 1.26 +/- 0.74 mm. The completion time of our IK method is 1-4 ms. The performance of our magnetic actuation system has been evaluated in the phantom experiment, in which the catheter can pass sequentially through the planned bifurcations and finally reach all the goals under the magnetic guidance.