Abstract
Model-based calibration of a magnetic workspace not only provides a smooth representation of the field and its gradient matrix, but also uses physical constraints to smooth the calibration measurements. This paper presents the first model-based technique to calibrate a magnetic manipulation system by using nonlinear least squares to solve for a scalar potential for each source. The performance of the method is verified by comparison to numerical finite element simulation and a case study calibration of a real system, where it is able to achieve an $R^{2}$ value of 0.9997. Furthermore, the analytical representations for the first three spatial derivatives of a spherical multipole expansion are provided for convenience, which correspond to the torque, force, and force-spatial-rate-of-change on a magnetic dipole in the workspace.
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