Optimal Generalized Linear Bias Compensation Method and Implementation for Nongeometric Errors in Multiaxis Motion Mechanisms

Error compensation is an effective approach for improving the positioning accuracy of multiaxis motion mechanisms. Existing kinematics-based compensation method usually neglects some nongeometric factors in modeling process and affects the mechanism’s accuracy. Numerical fitting is a common method for nongeometric error compensation, but there still exists certain fitting error and degrades the error compensation effect. To achieve an optimal error compensation effectiveness, this article proposes a generalized linear bias compensation method for multiaxis mechanisms. In this method, we analyze the error formation mechanism of the numerical fitting method, and establish a generalized linear bias error model on basis of geometric error model. With the generalized model, two bias factor expressions corresponding to the existing direct and hybrid methods are presented and their fitting error differences and compensation effects are compared. To further improve the fitting accuracy, we define a new bias factor expression for the generalized model by expanding the training network with the geometric error compensated data. Through theoretical analysis, we deduce that the newly defined bias factor can represent the nongeometric errors closely, and the nongeometric errors can therefore be compensated accurately. The proposed compensation method is verified on a 3PPR&PR hybrid five-axis mechanism. Simulation and experimental results show that compared to the existing methods, the proposed optimal bias factor compensation method can effectively compensate for the residual nongeometric errors, and significantly enhance the motion and positioning accuracy of the multiaxis mechanism.