2-D Magnetic Localization Newton–Raphson-Based Method Considering Measurement Uncertainties for Smart Surface Applications

Magnetic localization techniques present some interests for micro robotics applications using smart surfaces due to their inherent advantages, such as integration ability or low cost. However, at microscale, these methods often encounter challenges to perform with high precision in real scenario, because of the limitation of calculation algorithms (numerical stability, convergence, approximation methods) and the impact of measurement uncertainties (misalignment, sensor performance, etc.). This paper presents a new 2D magnetic localization method based on a 3D Hall effect sensor array system, in order to localize a cubic magnet. The proposed approach combines an efficient numerical resolution algorithm (Newton-Raphson) with precise analytical models of the magnetic field of the magnet to brave these measurement uncertainties and to achieve high-resolution 2D magnetic localization. Through performance assessments from simulation calculations and experimentations, the operation and efficiency of the proposed method is demonstrated. Results indicate good performance of the Newton-Raphson method with micrometric accuracy, even when there are measurement uncertainties in real scenario. Experimental test realized with a prototype of 3D Hall effect sensor array confirms the efficiency of the 2D magnetic localization with an averaged 12.73 μm localization error. A comparative analysis shows that this new magnetic localization method is well placed in the hierarchy of existing methods, that estimate the 2D position of a magnet by using a Hall effect sensor array system.