# Analysis of a New Twin Hybrid Autonomous Underwater Vehicle
## 2 Structure of THAUV  
The twin hybrid autonomous underwater vehicle (THAUV) is a new type of underwater monitoring platform with two buoyant bodies, which allows it to carry more energy and a variety of measurement equipment. The two buoyant bodies are connected by an aluminum plate, which can also be considered as a fixed wing of the THAUV. In order to reduce the resistance to underwater movement, the main body of the THAUV is a torpedo-shaped rotating body. The rotating body is modeled using the MYRING hull profile equations [11], and the overall structural diagram of the THAUV is shown in Figure 1.  
The mass of the entire THAUV system consists of two parts: the dynamic mass, including the mass of the piston (\(m_{p}=1.022\)), the mass of the ballast water (\(m_{b}\)), and the static mass (\(m_{s}=65.33\)), which is the sum of the mass of the roller (\(m_{r}=1.04\)), and the mass of the remaining static accessories (\(m_{sb}=64.29\)). Due to the limited rotation range of the elevator, the effect of the elevator on the floating center and center of gravity is negligible. The mass distribution is illustrated in Figure 2.  
The total mass of the THAUV is expressed in Equation (1):  
\[m=m_{p}+m_{s}=m_{pr}+m_{pl}+m_{r}+m_{sb} \tag{1}\]  
The derived equation for the center of gravity is shown in Equation (2):  
\[\mathbf{r}_{\rm CG}=\big{[}m_{pr}\mathbf{r}_{pr}+m_{pl}\mathbf{r}_{pl}+m_{r}\mathbf{r}_{pl}\big{]} /m \tag{2}\]  
\[\mathbf{r}_{\rm s}=(m_{t}\mathbf{r}_{pr}+m_{ab}\mathbf{r}_{ab})/m_{a} \tag{3}\]  
Here \(\mathbf{r}_{pr}\) and \(\mathbf{r}_{pl}\) are the positions of the right and left pistons in the body coordinates, respectively; \(\mathbf{r}_{s}\) is the position of static mass (including roller); \(\mathbf{r}_{r}\) is the position of the roller in the body coordinates; and \(\mathbf{r}_{sb}\) is the equivalent position of the remaining static accessories in the body coordinates (it is a fixed value). Figure 1: The structure of the THAUV. Figure 2: Mass distribution and descriptions. Since the roller only rotates around the axis of the right body shown in Figure 2 and there is no displacement change in the x-axis direction, the position in the x-axis direction is fixed. Figure 3 shows the schematic diagram after the roller rotation angle \(\gamma\). At this time, the center of gravity is shifted in the y-axis direction, resulting in the tilting of the body in the y-axis, and the THAUV will produce a rotary hovering motion around a certain point due to the action of hydrodynamic lift. When the rotation angle of the roller is \(\gamma\), the position coordinates of the roller can be expressed as:  
\[r_{r}=r_{rxi} \begin{bmatrix}1\\ 0\\ 0\end{bmatrix} +\left(r_{ryi}+R_{r}sin\gamma\right) \begin{bmatrix}0\\ 1\\ 0\end{bmatrix} +\left[r_{rzi}-\left(R_{r}-R_{r}cos\gamma\right)\right] \begin{bmatrix} 0\\ 0\\ 1\end{bmatrix}  \tag{4}\]  
Here, \(R_{r}\) is the radius of rotation of the roller center of mass and \(r_{rxi}\), \(r_{ryi}\), and \(r_{rzi}\) are the initial coordinates of the roller in the body coordinates along the x,y,z axis, respectively, when the roller does not rotate. In this design, the buoyancy engine adopts the structure of piston, which changes the magnitude and direction of the net buoyancy of the THAUV through the movement of the piston to absorb or drain water. When the piston absorbs water inward, the gravity is greater than the buoyancy, and the THAUV is diving; when the piston drains water outward, the buoyancy is greater than the gravity, and the THAUV is surfacing. In order to keep the glider balanced and stable, the ballast water in the two buoyancy engines is always equal in the absence of special requirements. The ballast water is expressed with Equation (5):  
\[m_{b}=\rho\pi r^{2}d_{p}, \tag{5}\]  
Here, \(\rho\) is the density of the water, \(r\) is the radius of the piston (\(r=0.05\) m), and \(d_{p}\) is the displacement of the piston along the x-axis.