This article investigates the leader–follower formation control problem for the multiple underactuated autonomous underwater vehicles with model uncertainties and external disturbances. Sliding mode control, multilayer neural network, and adaptive robust techniques are employed to design a formation controller for underwater vehicles. After that, a Lyapunov-based stability analysis is proposed to guarantee that all variables are uniformly ultimately bounded in the closed-loop control system. The following advantages of this approach are highlighted: 1) the proposed control strategy only depends on the measurements of line-of-sight and angle sensors; no other information about the leader vehicle is required; 2) a continuous function is designed to replace the signum term in the control system, which greatly reduces the inherent chattering of sliding mode controller; 3) the proposed controller does not rely on any prior knowledge about hydrodynamic damping and external disturbances, which is easily implemented in practice. Finally, the numerical simulations are provided to demonstrate the effectiveness of the proposed controller.

A semi-sealed cylindrical shell is a hollow cylinder in which one end is open and the other end is sealed. In order to systematically study the cavity evolution, the hydrodynamic characteristics, and corresponding structural response of the semi-sealed cylindrical shell during high-speed vertical water entry, a numerical simulation is carried out based on a Star-CCM+ and ABAQUS collaborative simulation method. The results show that a nested cavity is formed that presents three different morphologies as the semi-sealed cylindrical shell penetrates the water. Moreover, a jet is formed under the shell, which profoundly influences the hydrodynamic and structural characteristics. Compared with the completely sealed case, the velocity and displacement of the semi-sealed cylindrical shell are significantly changed upon water entry, and the deformation at the top wall is more prominent.

Despite cavity dynamics have been studied for more than a century, cavity formations during water entry of deformable spheres have rarely been studied. Series of interesting cavities arise during vertical water entry of deformable spheres. We study these phenomena experimentally and numerically. Experimental observations show that deformable spheres can produce three typical cavities: dumpy cavity, tight cavity, and nested cavity. Numerical modeling accounts for the effect of elasticity on the cavity dynamics. Our results show that the motion parameters used to characterize the three typical cavity walls present a hierarchical order. During the first cycle of cavity flows, the dependence of the dynamics of the deformed sphere on the dimensionless ratio of material shear modulus to impact hydrodynamic pressure is determined. Before the pinch-off of cavity, a density correction coefficient is proposed to characterize the linearization of wetted areas. Elasticity can alter the shape of the cavity, which requires sufficient impact conditions and material properties. Within this range, the formation time and number of the nested cavity are analyzed. On this basis, the minimum velocity required to form the nested cavity is theoretically predicted and identified by experimental and numerical techniques.

In the successive underwater launch of two projectiles, wake vortices shed from the leading projectile have significant effects on the subsequent projectile's hydrodynamic forces, attitude, and trajectory. Herein, experimental research is conducted by successively launching two underwater projectiles at prescribed transport velocities using embedded inertial measurement units to record acceleration data simultaneous with a high-speed camera to visualize the cavity behaviors. After a trial error evaluation, the interference between two conical-nosed projectiles is shown to increase as wake vortices develop from dispersed vortex rings at low transport velocities into continuous counterrotating vortex pairs at high transport velocities. Thus, the second projectile experiences less lateral movement and rotation than the first projectile at u > 0.1 m s⁻¹. The effect of the nose shape is also studied by conducting experiments on ellipsoidal-nosed projectiles, whose trends are similar to those of the conical-nosed projectiles. A quantitative comparison of the interference shows that the ellipsoidal-nosed projectiles experience more interference than the conical-nosed projectiles due to the absence of the shoulder cavity.