In this paper, the problems of system design, dynamic modeling, and trajectory tracking control of coaxial hybrid aerial underwater vehicles (HAUVs) with time-varying model parameters and composite marine environment disturbances are investigated. It is clear that a stable transition between different media remains a challenge in the practical implementation of amphibious tasks. For HAUVs, accurate dynamic modeling to describe complex dynamic variations during vehicle takeoff from underwater to air is a huge challenge. Meanwhile, due to the rapid changes in model parameters and the external environment, vehicles are likely to fall into the sea during the cross-domain process. An integrated continuous dynamic model considering hydrodynamic changes is established by introducing a linear switching coefficient during the process of trans-medium motion. A nonsingular fast terminal sliding-mode control (NFTSMC) algorithm combined with adaptive technology is used to design the position and attitude of the controller. With no previous knowledge of external interferences and lumped uncertainties of the HAUV, the adaptive NFTSMC (ANFTSMC) algorithm achieves the control objectives; at the same time, the inherent chattering problems of sliding mode control (SMC) are weakened. The finite-time stability of the global system is proven strictly using a series of mathematical derivations based on Lyapunov theory. The effect of the controller applied is analyzed through a series of simulations with representative working conditions. The results show that the proposed ANFTSMC can realize a “seamless” air–water trans-medium process, which proves the superiority and robustness of the proposed control algorithm.

The variation in aerodynamic parameters during the process of a variable sweepback hybrid aerial underwater vehicle (HAUV) affects flight stability. During the air–water trans-media locomotion, there are medium mutations and solid–liquid gas coupling phenomena, resulting in the complex dynamic process of HAUV. To ensure stable control during the trans-media process of a variable sweepback vehicle, this study proposes a neural-network-based adaptive dynamic surface control method for aircraft flight-path angle. This method aims to establish an effective control model for the entire process of air to media transition, in response to the characteristics of uncertainty and external disturbances in the process of variable backsweeping in the air and media transition. By utilizing the multibody dynamics method, the dynamic equations for variable-swept vehicles are established and transformed into a rigorous feedback system with model uncertainty. The adaptive dynamic surface method in this paper introduces a first-order filter, which overcomes the “differential explosion” problem in traditional backstepping control design through differential filtering; the unknown parameters present in the model are estimated online through adaptive laws, and the uncertain parts of the system are overcome through nonlinear damping items. By analyzing Lyapunov stability, the semi-global stability of the required closed-loop system can be obtained, and adjusting the controller parameters can make the tracking error infinitely small. Numerical simulations are conducted to illustrate the tracking control of flight-path angles for different plunge-diving angle rates and strategy of ingress. The results show that HAUV with variable-swept configuration with different strategy has a great effect on the stability of plunge-diving locomotion; the designed controller can effectively track the target trajectory and has a certain degree of robustness and adaptability.