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The application of robots in high-precision automated machining is constrained by their limited multi-directional repeatability. In contrast, robots demonstrate superior levels of unidirectional repeatability, implying the potential for enhancing their precision. To further improve the positioning accuracy of robots, backlash error induced by rotating direction is considered, the concept of robot joint extended space is proposed, and the robot kinematic model is used to analyze the spatial similarity of robot error in the extended joint space. The dynamic Kriging method based on the optimization of basis functions is proposed to avoid overfitting of the surrogate model, and a model for estimating the robot&#x2019;s positioning error in the joint extended space is constructed. Based on the estimated positioning error, the proposed calibration method is finally experimentally validated by error feedforward compensation. The results indicate that after Kriging interpolation in the robot joint space and feedforward compensation, the maximum/average positioning error of the robot is improved from 1.5157 mm and 0.8562 mm before compensation to 0.3471 mm and 0.1856 mm after compensation, and then further improved to 0.1848 mm and 0.1197 mm after adopting joint expansion space and dynamic Kriging interpolation, which decreases by 46.7% and 33.5%, respectively. This method effectively compensates the multi-directional repeatability error introduced by the joint backlash and improves the robot&#x2019;s positioning accuracy.

Kinematic Calibration and Compensation of Industrial Robots based on Extended Joint Space