A Modeling and Identification Method for Industrial Robot Positioning Accuracy Based on Parameter and Error Separation

Kinematic modeling and parameter identification are essential for achieving high-precision robot calibration. A widely used strategy involves utilizing the end-effector position error for parameter identification. However, the strong coupling between length and angular parameters often impedes calibration accuracy. In addition, substantial differences in their scales further exacerbate this issue. To overcome these limitations, following the variable projection method, this paper reformulates the conventional Modified Denavit–Hartenberg (MDH) model into a separable nonlinear structure. This allows independent identification of the two parameter types. Non-geometric errors such as joint compliance and backlash are also explicitly taken into account. The backlash errors are separated from the angular positions of each joint by modeling their bidirectional positioning errors with Chebyshev polynomials. This method enables the establishment of a comprehensive positioning error model to mitigate the influence of backlash errors. Based on the variable projection method, an improved variable projection with modified Gram–Schmidt (IVPMGS) identification method is proposed, which also eliminates redundant parameters that hinder identification robustness. Simulations indicate that the proposed method achieves faster convergence and higher identification accuracy. Compensation experiments demonstrate that the average absolute positioning error is reduced from 0.1804 mm to 0.0917 mm compared with the traditional MDH model, corresponding to a 49.17% improvement in positioning accuracy. These findings confirm the accuracy and effectiveness of the proposed approach.