Magnetic Model Calibration for Tetherless Surgical Needle Manipulation using Zernike Polynomial Fitting

Exerting forces and torques instantaneously on rigid magnetic bodies with no physical connection is an attractive feature of magnetic robotics. This demonstrates great potential for manipulating tools that are externally controlled through the use of magnetic fields in minimally invasive surgeries. The magnetic field can be controlled by the application of currents to electromagnets positioned around the surgical site, and the necessary currents for a specific desired manipulation can be derived from magnetic field models. However, the magnetic field generated by electromagnetic coils are highly nonlinear, especially in the vicinity of the magnetic field sources, which complicates the modeling process. While simple dipole models provide a good approximation for these fields far away from the electromagnets, these models tend to be highly inaccurate near the sources. Magnetic surgical applications benefit from models which accurately describe fields and gradients both near and far from the field source. Particularly, since forces and torques decay inversely proportionally with the cube of the distance to the coil, inaccurate modeling near the coil makes large regions near the coil unfit for applications requiring precisely predicted motion. Estimation errors near coils generate inaccuracies in field models that significantly reduce control performance for rigid magnetic bodies. In order to tackle this problem, we utilize Zernike basis functions to analytically represent the nonlinear magnetic field distribution more accurately. The accuracy of the controller is tested experimentally by driving a magnetic surgical suture needle with a length of 22 mm in the MagnetoSuture™ system along a lemniscate trajectory. The magnetic needle's tip position and the needle orientation, autonomously controlled by the proposed controller, shows RMS tracking error of 2.35 mm using typical dipole models and 1.71 mm for the Zernike fitting approach, a 27% improvement in tracking error. This suggests that the use of Zernike basis functions to capture the nonlinearities of the magnetic field may assist in implementing fast and precise autonomous control strategies for magnetic suture needles.