The hybrid aerial underwater vehicle (HAUV) of Xing, Wei, Lu and Liao (2023) crosses the air-water interface by plunge-diving with variable-swept wings, but its only demonstrated controller is an adaptive dynamic surface law that tracks a flight-path-angle command in the longitudinal plane during the oblique water-entry phase - proven semi-globally stable by Lyapunov analysis and validated solely in numerical simulation with idealized disturbances, on a model that excludes the morphing mechanism. The open problem, stated as future work in the source paper, is the complete motion of this water-air integrated vehicle: closed-loop control of the full three-dimensional (six-degree-of-freedom) dynamics during water entry and underwater cruise - including lateral-directional coupling and the time-varying inertia, buoyancy, and added mass produced by wing morphing and interface crossing - together with a control solution for the water-exit transition into aerodynamic flight.

Background

A hybrid aerial underwater vehicle (HAUV) is a crewless vehicle intended to fly in air, navigate underwater, and cross the air-water interface repeatedly, combining the reach and speed of an aircraft with the endurance and concealment of an underwater vehicle. Its full mission profile comprises four stages: cruise in the air, water entry, underwater cruise, and water exit. The interface crossings are the difficult part: water is roughly three orders of magnitude denser than air, so lift, drag, buoyancy, and added mass (the effective inertia a body acquires from the fluid it drags with it) change abruptly as the vehicle crosses the free surface, while wind and waves superimpose time-varying disturbances. Because a wing sized for efficient air cruise is oversized and vulnerable underwater, several prototypes adopt morphing configurations - wings that fold or sweep back before entry, imitating plunge-diving birds such as gannets and kingfishers, which fold their wings to reduce impact forces and stabilize the dive (Siddall, Ortega Ancel and Kovač, 2017, tested such a variable-sweep aquatic micro air vehicle in wind and water tunnels).

The source paper (Xing, Wei, Lu and Liao, 2023) studies a variable-swept HAUV with a blended-wing-body airframe (a configuration in which hull and wings form a single integrated lifting surface, chosen for its high lift-to-drag ratio and clean underwater shape). During wing-sweep morphing the vehicle is no longer a rigid body: its inertia tensor, center of mass, and aerodynamic coefficients vary with sweep angle, so the authors derive longitudinal-plane equations of motion from multibody dynamics, cast them as a strict-feedback nonlinear system (a cascade form in which each state appears as the virtual control of the next) with model uncertainty and external disturbance, and design an adaptive dynamic surface control (ADSC) law - a backstepping-style nonlinear technique in which first-order filters replace repeated differentiation of virtual control signals, avoiding the 'explosion of complexity' of classic backstepping, while adaptive laws estimate unknown parameters and a radial basis function (RBF) neural network, a standard function-approximation network, compensates unknown nonlinearities. A Lyapunov argument gives semi-global closed-loop stability (stability for initial states in an arbitrarily large compact set, with the tracking error converging to a residual bound set by design parameters), and simulations demonstrate flight-path-angle tracking during oblique plunge-diving entry for two sweepback schedules. A closely related ADSC controller for a non-morphing HAUV had been developed by Lu, Xiong, Zeng and Lian (2020).

The scope of that result is deliberately narrow. The model covers only longitudinal motion (pitch-plane flight-path angle γ\gamma, pitch attitude, and angle of attack); the morphing mechanism's structural design, material strength, and actuation are explicitly excluded; thrust is set to zero during entry; the disturbance profiles are idealized; and all evidence is numerical simulation. In its conclusions the paper defers to future work 'research on the complete motion of the water-air integrated HAUV' and 'possible solutions for HAUV's water-exit motion'.

Neighboring results delimit what is known. For water exit, Qi, Feng, Xu, Liu and Li (2017) built a water-exit dynamic model and a sliding-mode takeoff controller for a morphing cross-media vehicle (numerical simulation under a simplified environment); Han, Cao, Li et al. (2024) measured the hydrodynamics of foldable-wing vehicles during water exit experimentally (no control); and Li, Zhang, Huang et al. (2025) combined computational fluid dynamics (CFD) with Gaussian-process system identification (a non-parametric regression method for learning dynamics from data) for the water exit of a propeller-and-rotor HAUV. Autonomous water exit has been demonstrated in hardware only by vehicles that can hover on propeller thrust: the small delta-wing unmanned aerial-aquatic vehicle of Moore (2019) and the tail-sitting vertical-takeoff-and-landing (VTOL) fixed-wing HAUV Nezha-SeaDart of Jin, Zeng and Lian (2025). Full-mission demonstrations in the real ocean exist for multi-propeller HAUVs (Nezha-IV; Jin, Bi, Lyu, Bai, Zeng and Lian, 2024). For fixed-wing HAUVs, Li, Jin, Hu et al. (2024) studied trajectory-tracking control across the air/water transition under wind and wave disturbances in simulation, on a non-morphing platform (Wei, Teng, Meng, Yao and Lian, 2022). Reviews through 2026 (Ma, Chen, Li, Jing and Xiao, 2022; Yao, Li, Zhang et al., 2023; Liu, Xiao, Peng et al., 2026; Tu, Zhuang, Chen et al., 2026) consistently report that transition stability control and water-exit locomotion, especially for morphing vehicles, remain open challenges.

Problem Statement

For the variable-swept blended-wing-body HAUV of Xing, Wei, Lu and Liao (2023), extend controlled trans-media locomotion from the longitudinal, simulation-only plunge-diving water-entry phase to the complete motion of the vehicle across the full air-water mission profile. Concretely: (1) establish the three-dimensional dynamics of the vehicle during water entry and underwater cruise, including lateral-directional coupling and the time-varying inertia, center-of-mass, buoyancy, and added-mass effects induced by wing-sweep morphing and by crossing the air-water interface; (2) design a closed-loop control architecture with stability or bounded-tracking guarantees that carries the vehicle through controlled water entry and underwater cruise - not only the longitudinal flight-path-angle tracking already demonstrated; and (3) provide a control solution for the water-exit transition, in which the vehicle leaves the water and transitions to stable aerodynamic flight without falling back, which the source paper explicitly identifies as required by the complete mission profile and leaves untouched. Deliverables (1)-(3) serve one scientific objective - a single vehicle and control architecture operating across the entire mission profile - and are to be judged jointly rather than as independent papers.

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