Precise Model-Free Spline-Based Approach for Magnetic Field Mapping

Untethered magnetic manipulation has found applications in a rapidly increasing number of fields, ranging from minimally invasive surgery to assembly of industrial microelectromechanical systems. Despite this relevance, present-day literature on precise magnetic mapping is sparse, especially for magnetic fields affected by external disturbances. In this letter, we address this deficiency by introducing a model-free mapping technique. Remarkably, the presented spline-based approach is capable of addressing the presence of inhomogeneous static disturbances and the mapping of nonazimuthally symmetric electromagnets. This work is validated with the mapping of nine metal-core electromagnets in the presence of inhomogeneous static disturbances. A grid of 5120 measurements is collected by a custom-programed robotic arm and used for mapping. The values predicted by the approach are compared against 3430 independent field measurements with an R² value of 0.9884 and maximum relative errors of 7%. Overall, this spline-based approach provides a flexible technique for the precise mapping of electromagnetic fields and gradients even when, for reasons regarding coil shape or disturbances, the electromagnetic field does not present any axial symmetry.