A Newton method with characteristic value correction for geometric error calibration of parallel mechanism

Abstract

To address the ill-conditioning of the Jacobian matrix in the geometric error calibration of parallel mechanisms, a Newton method with characteristic value correction (NMCVC) is proposed. This method integrates and enhances the principles of the characteristic value correction iteration method (CVCIM), and Newton method, offering targeted improvements for more effective calibration. First, the damping coefficient is introduced into the CVCIM, and an adaptive strategy for determining the damping coefficient is developed with rigorous proof steps according to the relationship between the condition number and the singular value, which enhances computing efficiency while avoiding the ill-conditioning of the Jacobian matrix. Second, a dynamic adjustment strategy for the CVCIM’s termination condition is designed. This strategy initially estimates the descending direction roughly to approximate the actual descending direction, enhancing computing speed, and then estimates it more accurately at the end of the training stage to obtain precise geometric error values. Finally, by taking a 3RPS parallel mechanism as the instance, three sets of simulation experiments have been designed to test and verify the effectiveness of the algorithm.