Objective Hybrid crawling-swimming autonomous underwater vehicles (AUVs) possess the unique capability to operate both in the water column and along the seabed. However, their operation is severely challenged by abrupt and highly nonlinear variations in system dynamics during configuration transitions (morphing), which pose significant challenges for ensuring safe and stable control. This paper proposes a dual-loop symbolic adaptive control (DSAC) framework driven by large language model (LLM)-guided symbolic regression.

Method The proposed DSAC architecture comprises a slow adaptation loop (~0.1 Hz) and a fast control loop (100 Hz). In the slow adaptation loop, an LLM is innovatively employed as a "physics reasoner". By interpreting the semantic implications of limb configuration changes, the LLM automatically generates structural priors—namely, the search space, required terms, and forbidden terms—thereby reducing the blind symbolic regression (SR) search space from approximately 43 200 combinations to about 256 (a 169-fold reduction) and improving convergence speed by a factor of 2.1. Guided by these priors, the SR engine efficiently identifies drag laws in explicit analytical form from residual data. In the fast control loop (100 Hz), a Lyapunov-based safety filter is designed to verify the dissipativity of the identified model in real time before updating the control law. This mechanism ensures the theoretical stability of the system during dynamic transitions.

Results High-fidelity simulations under three morphing scenarios (gradual, step, and sinusoidal) demonstrate that the proposed DSAC framework can accurately identify hydrodynamic structures during the deformation process. Compared with conventional PID control and robust MRAC, the DSAC framework reduces the tracking error root-mean-square error (RMSE) by approximately 25%, with the RMSE decreasing to 0.054 m/s. This performance gain is particularly pronounced during abrupt configuration transitions, where traditional controllers often struggle to maintain stability. During the morphing phases, the safety filter evaluated 47 candidate models and successfully rejected 3 physically implausible "hallucinated" models, including one containing negative damping terms. In adversarial stress tests, where 30% of the candidate models were intentionally corrupted with non physical terms, the framework maintained a 100% safety compliance rate, thereby validating the effectiveness of the "LLM-driven hypothesis generation—physical constraint verification" paradigm. Calibration simulations based on lake trial data further demonstrate that the DSAC predictions are consistent with real-world nonlinear characteristics. These findings confirm the robustness of the proposed framework against model misspecification and environmental disturbances.

Conclusion The proposed DSAC framework effectively addresses three fundamental challenges in morphing AUV dynamics modeling: unknown model structures, inefficient search processes, and poor physical plausibility. By integrating LLM-based semantic guidance with Lyapunov-based stability verification, it achieves a unified balance between adaptability and stability. This methodology can be extended to other robotic systems with configuration-dependent dynamics.