Objective Hybrid crawling-swimming Autonomous Underwater Vehicles (AUVs) possess the unique capability to traverse both the water column and the seabed, yet their operation is severely challenged by drastic, nonlinear dynamic changes during configuration shifting (morphing), posing significant challenges for 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 DSAC architecture consists of 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 meaning of limb configuration changes, it automatically generates structural priors containing search spaces, required terms, and forbidden terms, compressing the blind symbolic regression (SR) search space from approximately 43,200 combinations to about 256 (a 169-fold reduction) and accelerating convergence by a factor of 2.1, thereby guiding the SR engine to rapidly discover drag laws in explicit analytical form from residual data. In the fast control loop (100 Hz), a Lyapunov-based safety filter verifies the stability of the generated model before updating the controller. is designed to verify the dissipativity of the generated model in real time before control law updates, ensuring theoretical stability of the system under dynamic transitions.

Results High-fidelity simulations under three morphing scenarios (gradual, step, and sinusoidal) demonstrate that the DSAC framework accurately identifies hydrodynamic structures during the deformation process, achieving a reduction in tracking error root-mean-square error (RMSE) by approximately 25% compared to conventional PID and robust MRAC, with the RMSE dropping to 0.054 m/s. This improvement is most evident during abrupt configuration shifts where traditional controllers struggle to maintain stability. The safety filter processed 47 candidate models during morphing phases and successfully intercepted 3 physically implausible “hallucinated” models (including one with negative damping terms). In adversarial stress tests where 30% of candidates were intentionally corrupted with non-physical terms, it maintained a 100% safety compliance rate, validating the effectiveness of the “LLM hypothesis generation—physical constraint verification” paradigm. Calibration simulations based on lake trial data further demonstrate that DSAC predictions are consistent with real nonlinear characteristics. These findings confirm the framework’s robustness against model misspecification and environmental disturbances.

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