Abstract: Kinematic calibration plays a crucial role in ensuring the accuracy of parallel robots. However, it solely compensates for geometric errors or non-geometric errors without considering the impact of unidentifiable geometric errors caused by the limitations of traditional error models. To address these issues, an error compensation method that combines error model and machine learning for parallel robots is proposed, and it is applied to a 2PRU-PSR parallel robot (where P denotes a prismatic joint, R denotes a revolute joint, U denotes a universal joint, and S denotes a spherical joint). Firstly, the kinematic model of the 2PRU-PSR parallel robot is established based on the closed-loop vector method. The geometric error model is established by the vector differential method. Secondly, the least square optimization function lsqnonlin method is employed to identify the geometric parameters and accomplished some parts of geometric errors compensation. Then, a back propagation (BP) neural network and Gaussian process regression (GPR) model is utilized to predict and compensate for the rest of unidentifiable geometric errors and non-geometric errors. Finally, the proposed method is validated correct and effective through simulation and experimentation. The experimental results indicate that after applying kinematic calibration combined with BP neural network for error compensation, the average position error of the end pose of 2PRU-PSR parallel robot decreases from 5.121 4 mm to 0.105 0 mm, the average orientation error reduces from 0.027 6 rad to 0.003 80 rad; When it combined with the GPR model, the average position error decreases from 5.121 4 mm to 0.0918 mm, the average orientation error reduces from 0.027 6 rad to 0.005 68 rad. This method is also suitable for error compensation of other parallel robots to improve the precision of end effectors.

Key words: parallel robot, geometric error, kinematic calibration, non-geometric error, machine learning