Physics-Constrained Residual Learning for Refined Dynamic Identification and Robust Torque Estimation
Accurate dynamic modeling of industrial robots is essential for high-performance control and estimating torque. However, traditional physics-based models often fail to capture unmodeled dynamics such as complex friction, payload variations, and gearbox-induced distortions. This article refines a physics-based modeling framework with a data-driven residual learning policy to compensate for unmodeled dynamics. We first employ a nested optimization strategy using multistart sequential quadratic programming (MS-SQP) and QR-based base parameter extraction to identify identifiable inertial and Stribeck friction parameters. To compensate for remaining systematic errors, we integrate the residual error policy model using physics-aware feature engineering. The proposed method is validated on both synthetic datasets and a real-world six-DOF industrial manipulator across various trajectories (including Fourier, chirp, and trapezoidal excitations) and payload conditions. A friction modeling ablation study confirms that richer friction representations progressively reduce the residual space, with the Stribeck backbone achieving 2.32-Nm root-mean-square error (RMSE) compared to 3.89 Nm for the rigid-body-only baseline. Experimental results demonstrate that the proposed physics-imbued residual framework improves torque prediction RMSE 31.5 % in real-world trajectories and 31.7 % in unseen synthetic payload testing. The results confirm that the framework effectively captures complex unmodeled dynamics while maintaining physical interpretability and generalization capabilities essential for industrial instrumentation and measurement applications.