A Hybrid Kinematic Calibration Framework for Serial Robots Using DH-POE and Baker–Campbell–Hausdorff Expansion

Abstract Kinematic calibration of serial robots remains a notable challenge for industrial deployment, particularly due to the complexity of existing mathematical models. Notably, the method based on the Product of Exponentials (POE) formulation, while grounded in a rigorous theoretical foundation, is often algebraically complex and lacks clear physical interpretability of the errors. Furthermore, acquiring end-effector pose data entails high cost. To address these limitations, this study proposes a new error modeling framework for open-chain serial robots, grounded in rigid-body motion error representation. Building upon this framework, a hybrid calibration model is developed by integrating the Denavit–Hartenberg (D–H) and Product of Exponentials representations. The proposed model explicitly decomposes the actual motion in 𝒮𝐸(3) into its nominal motion and error components. The error term is then linearized using the Baker–Campbell–Hausdorff (BCH) expansion in the 𝔰𝔢(3) space. This approach requires only point data for calibration, thereby reducing implementation costs in practical applications. Structural identifiability analysis is employed to optimize the model, leveraging both geometric features and algebraic properties of the Lie group to reduce the number of calibration parameters and to contribute to improving numerical stability. The proposed method is validated on SCARA (4-DOF) and PUMA 560 (6-DOF) robots. Comparative experiments demonstrate both fast convergence and improvement in end-effector positioning accuracy across the entire workspace, particularly under high measurement noise.