Kinematic Recurrent Neural Network-Based Hybrid Calibration for Serial Manipulators

This paper proposes a hybrid kinematic calibration framework for serial robotic manipulators that integrates analytical parameter identification with data-driven residual learning. First, the Levenberg–Marquardt (LM) algorithm is employed to calibrate the geometric parameters of the conventional D-H model. Although this calibration improves accuracy, residual errors remain due to unmodeled effects and measurement uncertainties. To compensate for these errors, we introduce a Kinematic Recurrent Neural Network (KRNN), which leverages a topology-aligned recurrent structure that explicitly matches the manipulator’s kinematic chain. Unlike conventional feedforward and residual networks, KRNN captures serial dependencies more effectively, thereby providing higher accuracy in residual modeling. Experimental validation on a 6-DOF industrial manipulator demonstrates that the proposed LM-KRNN framework achieves sub-millimeter calibration accuracy and significantly outperforms existing baseline methods. Moreover, KRNN also functions as a standalone kinematic model, consistently surpassing ANN, ResNN, other RNN variants, and even the LM-calibrated D-H model, confirming its strong generalization capability and practical potential for high-precision robotic applications. In addition, the results reveal that RNN-type architectures are inherently more suitable than feedforward networks for both kinematic modeling and residual-error learning in serial manipulators, as their recursive structure naturally aligns with the manipulator’s physical chain topology.