Electromagnetic Displacement Sensor and Docking Method Based on Elliptic Integral Series Expansion

Automatic charging can improve the endurance of unmanned work platforms, but the docking accuracy limits its success rate and charging efficiency. In order to solve this problem, an accurate docking method based on elliptic integral series expansion is proposed. The relationship between load voltage and coil transverse offset distance is constructed by establishing a coil mutual inductance circuit, a coil center points transverse offset mutual inductance coefficient calculation model, and a triangular positioning geometry structure. Numerical integration and elliptic integration series expansion are used to solve the exact correspondence between the coil mutual inductance coefficient and the coil transverse offset distance. Finally, the relationship between the load voltage and the lateral offset distance from the center of the coil is obtained. The method does not require the arrangement of additional sensors and coils, nor does it require extensive prior data collection for unique coil configurations. The system can be used for energy transmission and as a displacement sensor. It has been verified by COMSOL Multiphysics simulations that the maximum relative error in the coefficient of mutual inductance is 6.507% for the numerical integration method and 9.022% for the elliptic integration series expansion approach. After experimental verification, the maximum average relative error of the load voltage is 4.048% for the numerical integration method and 11.89% for the elliptic integration series expansion approach. This method achieved high accuracy positioning measurement with the error range at the centimeter level. The method contributes to the long-term application of unmanned operating platforms.