Physics-Enhanced Hierarchical Dynamics Modeling at the Current Level for Underwater Manipulators

Underwater manipulators play a critical role in marine exploration and inspection tasks, where accurate dynamics modeling is essential for reliable control and interaction. However, conventional in-air manipulator dynamics models cannot be directly applied underwater due to environment-induced hydrodynamic effects. To address this challenge, this article proposes a hierarchical dynamic modeling framework for underwater manipulators that decomposes system dynamics into intrinsic and environment-induced components. Within this framework, an encoder-only Transformer is used to learn intrinsic dynamics, whereas a physics-enhanced residual learning strategy incorporates empirical hydrodynamic priors into the self-attention mechanism without modifying the Transformer backbone. Experimental results demonstrate that the proposed framework outperforms representative baselines, including nonhierarchical Transformer-based models and physics-free hierarchical variants in root mean square error (RMSE) and R². The model achieves an average inference latency of 6.051 ms, meeting real-time control requirements. Moreover, the hierarchical structure supports modular retraining, making it well-suited for practical underwater manipulation tasks.