Analysis of the influence of passive joints on kinematic calibration of parallel manipulators based on complete error model

A complete kinematic error model that contains all potential error sources, is one of the fundamentals to ensure the best result of kinematic calibration. In the case of parallel manipulators, the complete error model includes items of passive joint motions. These motions usually cannot be accurately observed during the identification process but can be derived through kinematic analysis. However, due to kinematic errors, the obtained passive joint motions deviate from their actual values, causing motion errors of passive joints. In other words, the passive joints introduce input errors to the error model, which are of the same order of magnitude as kinematic errors and much larger than other measurement and random noises. This issue can significantly affect the stability and accuracy of parameter identification, but it has not been clearly recognized in the literature. To address this problem, this paper systematically analyzes the influence of passive joints’ motion errors on the kinematic calibration of parallel manipulators. It is found that when the complete error model including the passive joints’ motion errors is used for kinematic calibration of parallel manipulators, the variance of kinematic error parameters solved by the least squares (LS) method greatly increases, leading to iterative divergence even when the identification matrix is column full rank. To improve the stability and accuracy of parameter identification, this study employs the total least squares (TLS) method, which is a dedicated approach for handling input errors, in the identification process. Numerical simulations and experiments of kinematic calibration are conducted on several parallel manipulators. The results validate the correctness and effectiveness of the analysis of the influence of passive joints’ motion errors on the kinematic calibration of parallel manipulators. Furthermore, the results indicate that the TLS method can efficiently and accurately accomplish the identification of kinematic parameters.