Fluoroscopy-Constrained Magnetic Robot Control via Zernike-Based Field Modeling and Nonlinear MPC

Magnetic actuation enables surgical robots to navigate complex anatomical pathways while reducing tissue trauma and improving surgical precision. However, clinical deployment is limited by the challenges of controlling such systems under fluoroscopic imaging, which provides low frame rate and noisy pose feedback. This paper presents a control framework that remains accurate and stable under such conditions by combining a nonlinear model predictive control (NMPC) framework that directly outputs coil currents, an analytically differentiable magnetic field model based on Zernike polynomials, and a Kalman filter to estimate the robot state. Experimental validation is conducted with two magnetic robots in a 3D-printed fluid workspace and a spine phantom replicating drug delivery in the epidural space. Results show the proposed control method remains highly accurate when feedback is downsampled to 3 Hz with added Gaussian noise (sigma = 2 mm), mimicking clinical fluoroscopy. In the spine phantom experiments, the proposed method successfully executed a drug delivery trajectory with a root mean square (RMS) position error of 1.18 mm while maintaining safe clearance from critical anatomical boundaries.