Kinematic Calibration of a 5-DoF Parallel Machining Robot with a Novel Adaptive and Weighted Identification Method Based on Generalized Cross Validation

Abstract Accurate kinematic calibration is the very foundation for robots’ application in industry demanding high precision such as machining. Considering the complex error characteristic and severe ill-posed identification issues of a 5-DoF parallel machining robot, this paper proposes an adaptive and weighted identification method to achieve high-precision kinematic calibration while maintaining reliable stability. First, a kinematic error propagation mechanism model considering the non-ideal constraints and the screw self-rotation is formulated by incorporating the intricate structure of multiple chains and a unique driven screw arrangement of the robot. To address the challenge of accurately identifying such a sophisticated error model, a novel adaptive and weighted identification method based on generalized cross validation (GCV) is proposed. Specifically, this approach innovatively introduces Gauss-Markov estimation into the GCV algorithm and utilizes prior physical information to construct both a weighted identification model and a weighted cross-validation function, thus eliminating the inaccuracy caused by significant differences in dimensional magnitudes of pose errors and achieving accurate identification with flexible numerical stability. Finally, the kinematic calibration experiment is conducted. The comparative experimental results demonstrate that the presented approach is effective and has enhanced accuracy performance over typical least squares methods, with maximum position and orientation errors reduced from 2.279 mm to 0.028 mm and from 0.206° to 0.017°, respectively.