Abstract
Most current magnetic localization and orientation systems use single magnetic dipole (MD) models to calculate magnetic field, which, due to the fundamental limitation of the dipole, becomes inaccurate near the source as the MD model is unable to compensate for geometry and physical imperfections. The novel approach undertaken here retains the parametric nature of the MD to model fields far from the source and simultaneously harnesses artificial neural networks (ANNs) to characterize the magnetic field close to the source with high accuracy. This hybrid ANN-MD (HAM) model segregates the space around the magnet along magnetic equipotential lines via the Levenberg-Marquardt algorithm, and a sigmoid function provides a smooth transition between the two regions. The HAM model was evaluated with experimental field data, and it yielded better performance than the other models. More specifically, for a solid axisymmetric permanent magnet, the HAM modeling error (RMSE) was on average over one order of magnitude smaller than that of the dipole-based model and two times smaller compared to the ANN-only model. Using model-based localization, tracking results from following a predetermined conical-helix path were promising, with an average error of 0.46 mm from only three sensor inputs. The HAM model was also tested in the closed-loop position control of a linear actuator, which was commanded to follow a sinusoid signal, and the root mean square error was 0.385 mm.