A Comparative Study on Kinematic Calibration for a 3-DOF Parallel Manipulator Using the Complete-Minimal, Inverse-Kinematic and Geometric-Constraint Error Models

Abstract Kinematic calibration is a reliable way to improve the accuracy of parallel manipulators, while the error model dramatically affects the accuracy, reliability, and stability of identification results. In this paper, a comparison study on kinematic calibration for a 3-DOF parallel manipulator with three error models is presented to investigate the relative merits of different error modeling methods. The study takes into consideration the inverse-kinematic error model, which ignores all passive joint errors, the geometric-constraint error model, which is derived by special geometric constraints of the studied RPR-equivalent parallel manipulator, and the complete-minimal error model, which meets the complete, minimal, and continuous criteria. This comparison focuses on aspects such as modeling complexity, identification accuracy, the impact of noise uncertainty, and parameter identifiability. To facilitate a more intuitive comparison, simulations are conducted to draw conclusions in certain aspects, including accuracy, the influence of the S joint, identification with noises, and sensitivity indices. The simulations indicate that the complete-minimal error model exhibits the lowest residual values, and all error models demonstrate stability considering noises. Hereafter, an experiment is conducted on a prototype using a laser tracker, providing further insights into the differences among the three error models. The results show that the residual errors of this machine tool are significantly improved according to the identified parameters, and the complete-minimal error model can approach the measurements by nearly 90% compared to the inverse-kinematic error model. The findings pertaining to the model process, complexity, and limitations are also instructive for other parallel manipulators.