An Interpretable Nonlinear Decoupling and Calibration Approach to Wheel Force Transducers

The multi-dimensional force/torque decoupling and calibration is extremely crucial to increase the accuracy of the Wheel Force Transducer/Sensor (WFT). A novel interpretable nonlinear decoupling and calibration approach to WFT is presented. A physical interpretable prime-error framework is developed such that the linear prime part accounts for most force-voltage responses while the nonlinear error part accounts for the gross error deviation. The conventional least-square decoupling is improved with the delicate nonlinear error modeling using a polynomial base module and a hyperbolic activation function. The developed framework is proved to be mathematically solvable and physically feasible by a two-step calibration scheme. A two-axis WFT is tested and compared with the proposed interpretable nonlinear decoupling model (IND), the least-square-based method (LSM), and the error-based neural network model (eNN). Results demonstrate that the proposed IND provides an accurate, practical, and effective scheme for modeling and calibrating WFTs and maintains a good balance among accuracy, generalization ability, and computational efficiency for real applications.