## 7 Simulations and Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline Mass matrix: & \(M(\mathbf{q}_{1})=\left[\begin{array}{cccccc}250.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&250.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&250.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&10.7&0.0&0.0\\ 0.0&0.0&0.0&0.0&58.2&0.0\\ 0.0&0.0&0.0&0.0&0.0&65.3\end{array}\right]\) \\ Coriolis matrix: & \(C(\mathbf{v}_{r},\mathbf{q}_{1})=\left[\begin{array}{cccccc}0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&100.0\\ 0.0&0.0&0.0&0.0&-100.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&100.0&0.0&0.0&0.0\\ 0.0&-100.0&0.0&0.0&0.0&0.0\end{array}\right]\) \\ \multirow{2}{*}{Damping matrix:} & \(D(\mathbf{v}_{r},\mathbf{q}_{1})=\left[\begin{array}{cccccc}-21.5&0.0&0.0&0.0&0.0&0.0 \\ 0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&0.0\end{array}\right]\) \\ \multirow{2}{*}{Gravity and Buoyancy vector:} & \(\mathbf{g}(\mathbf{\eta})=\left[0.0,0.0,-12.2,0.0,0.0,0.0\right]^{\mathrm{T}}\) \\ \hline Mass matrix: & \(M(\mathbf{q}_{2})=\left[\begin{array}{cccccc}250.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&250.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&250.0&0.0&0.0&0.0\\ 0.0&0.0&250.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&49.2&0.0&0.0\\ 0.0&0.0&0.0&0.0&31.6&0.0\\ 0.0&0.0&0.0&0.0&0.0&77.2\end{array}\right]\) \\ \multirow{2}{*}{Coriolis matrix:} & \(C(\mathbf{v}_{r},\mathbf{q}_{2})=\left[\begin{array}{cccccc}0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&100.0\\ 0.0&0.0&0.0&0.0&-100.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&100.0&0.0&0.0&0.0\\ 0.0&-100.0&0.0&0.0&0.0&0.0\end{array}\right]\) \\ \multirow{2}{*}{Damping matrix:} & \(D(\mathbf{v}_{r},\mathbf{q}_{2})=\left[\begin{array}{cccccc}-41.2&0.0&0.0&0.0&0.0&0.0 \\ 0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&0.0\end{array}\right]\) \\ \multirow{2}{*}{Gravity and buoyancy vector:} & \(\mathbf{g}(\mathbf{\eta})=\left[0.0,0.0,-12.2,0.0,0.0,0.0\right]^{\mathrm{T}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: UNIFI DIEF AURV dynamic parameters. \begin{table} \begin{tabular}{l c} \hline \hline  & \(\mathbf{r_{1}}=[0.7,-0.4,0.0]\) \\  & \(\mathbf{r_{2}}=[0.7,0.4,0.0]\) \\  & \(\mathbf{r_{3}}=[-0.7,-0.4,0.0]\) \\ Thruster positions \((\mathbf{q_{1}})\) \([m]\): & \(\mathbf{r_{4}}=[-0.7,0.4,0.0]\) \\  & \(\mathbf{r_{5}}=[0.0,-0.3,0.0]\) \\  & \(\mathbf{r_{6}}=[0.0,0.3,0.0]\) \\  & \(\mathbf{r_{7}}=[0.8,0.0,0.0]\) \\  & \(\mathbf{r_{8}}=[-0.8,0.0,0.0]\) \\  & \(\theta_{1}=\frac{\pi}{2}\), \(\varphi_{1}=0.0\) \\  & \(\theta_{2}=\frac{\pi}{2}\), \(\varphi_{2}=0.0\) \\  & \(\theta_{3}=\frac{\pi}{2}\), \(\varphi_{3}=0.0\) \\ Thruster longitudinal axis \((\mathbf{q_{1}})\) \([rad]\): & \(\theta_{4}=\frac{\pi}{2}\), \(\varphi_{4}=0.0\) \\  & \(\theta_{5}=0.0\), \(\varphi_{5}=0.0\) \\  & \(\theta_{6}=0.0\), \(\varphi_{6}=0.0\) \\  & \(\theta_{7}=0.0\), \(\varphi_{7}=0.0\) \\  & \(\theta_{8}=0.0\), \(\varphi_{8}=0.0\) \\ \hline TAM: & \(B(\mathbf{q_{1}})=\left[\begin{array}{cccccccc}1.0&1.0&1.0&1.0&0.0&0.0&0.0&0.0 \\ 0.0&0.0&0.0&0.0&0.0&0.0&0.0\\ 0.0&0.0&0.0&0.0&1.0&1.0&1.0\\ 0.0&0.0&0.0&0.0&-0.3&0.3&0.0&0.0\\ 0.0&0.0&0.0&0.0&0.0&-0.8&0.8\\ 0.4&-0.4&0.4&-0.4&0.0&0.0&0.0&0.0\\ \hline \hline \end{tabular} \begin{tabular}{l c} \hline \hline  & \(\mathbf{r_{1}}=[0.6,-0.5,0.0]\) \\  & \(\mathbf{r_{2}}=[0.6,0.5,0.0]\) \\  & \(\mathbf{r_{3}}=[-0.6,-0.5,0.0]\) \\  & \(\mathbf{r_{4}}=[-0.6,-0.5,0.0]\) \\  & \(\mathbf{r_{5}}=[0.0,-1.0,0.0]\) \\  & \(\mathbf{r_{6}}=[0.0,1.0,0.0]\) \\  & \(\mathbf{r_{7}}=[0.6,-0.0,0.0]\) \\  & \(\mathbf{r_{8}}=[-0.6,-0.0,0.0]\) \\ \hline \hline \end{tabular}  \ \begin{tabular}{l c} \hline \hline  & \(\mathbf{r_{1}}=[0.6,-0.5,0.0]\) \\  & \(\mathbf{r_{2}}=[0.6,-0.5,0.0]\) \\  & \(\mathbf{r_{3}}=[-0.6,-0.5,0.0]\) \\  & \(\mathbf{r_{4}}=[-0.6,0.5,0.0]\) \\  & \(\mathbf{r_{5}}=[0.0,-1.0,0.0]\) \\  & \(\mathbf{r_{6}}=[0.0,1.0,0.0]\) \\  & \(\mathbf{r_{7}}=[0.6,-0.0,0.0]\) \\  & \(\mathbf{r_{8}}=[-0.6,-0.0,0.0]\) \\ \hline \hline \end{tabular}