Kinematic Calibration of a Novel Two-Axis Solar Tracker

Abstract

This paper deals with the kinematic calibration of a two-axis over-constrained solar tracker. In an over-constrained mechanism, it is difficult to derive the constraint among geometric errors and then the accurate error model can not be achieved. This paper presents a new error modeling method with considering constraints among geometric errors to derive a complete, continuous and minimal model. The constraint among geometric errors are derived from an algebraic approach with strict theoretical proof. Furthermore, an iterative Tikhonov regularization method is presented for parameter identification and the iteration termination condition is related to the measurement noise. The traditional Tikhonov regularization method is a posterior method that depends on the measurement data in calibration, while the proposed regularization method is a prior method with clear physical meaning. The kinematic calibration of the two-axis solar tracker is used to validate the proposed methods. The orientation error of the solar tracker is reduced by more than 95% after kinematic calibration. Note to Practitioners—The geometric error constraints are proven in the article to exist in an over-constrained two-axis solar tracker, which leads to the unsuitability of previous calibration methods. With our proposed method, the accuracy of the solar tracker has been improved by 95% after calibration. In our calibration, the error modeling method can be extended to other over-constrained robots, and the Tikhonov regularization method has good stability and accuracy in error identification. In future research, we will address the problem of deformation and joint clearance in kinematic calibration.