## 7 Simulations and Results  
The maneuverability simulation performed for both the extreme UNIFI DIEF configurations are presented in this Section. Within the context of this work, the following notation is employed: a generic property \(A(\mathbf{q}_{1})\) belongs to the \"survey\" AURV configuration, while \(A(\mathbf{q}_{2})\) relates to a feature of the \"hovering\" one. Furthermore, the results hereafter presented have been obtained by means of MATLAB-coded dynamic simulations. In particular, along with the assumptions proposed in Section 3, the following settings have been used:the AURV position \(\eta_{1}\) is the same in both the two configurations, and the vehicle orientation \(\eta_{2}\) will be expressed with respect to the NED frame. Additionally, it is assumed that the vehicle is in resting position (i.e., \(\
u=0_{6\times 1}\)) affected by the marine currents. Although this hypothesis may seem restrictive, it was decided, within this preliminary study, to consider the scenario in which the AURV, in both the configurations, is stationary; realistic cases of motion will be investigated in the future. The kinematic parameters are summarized in Table 1:  
* The dynamic terms in Equation (4) have been evaluated by exploiting several preliminary hydrodynamic simulations. More accurate identification strategies will be further analyzed in the future in order to provide an accurate estimate of the AURV dynamic parameters. Therefore, the dynamic features of survey \(q_{1}\) and hovering \(q_{2}\) configurations are respectively listed in Table 2.
* The two different thrust allocation matrices \(B(q)\) have been evaluated by using the body-fixed position \(r_{i}\) and longitudinal direction \(n_{i}\) of the \(i\)th thruster in both configurations, estimated in the design stage of the AURV. As a result, Table 3 shows the thruster configurations parameters, where the \(i\)th thruster longitudinal axis have been expressed in the terms of the inclination \(\theta_{i}\) and azimuth \(\varphi_{i}\) angle in spherical coordinates. It can be straightforwardly observed, as already described in the Section 2, how the first four thrusters are necessary for the linear motion of the vehicle along the horizontal plane, whereas the last four provide displacement along the vertical direction of the body-fixed frame. In particular, Table 3, shows how the first four thrusters are all aligned along the surge axis in the survey configuration, with the aim of improving the longitudinal navigation, whilst, at the same time, the AURV cannot move in the sway direction. * With regard to the propulsion system parameters, Table 4 outlines the estimated values for the BlueRobotics T200 propeller [20], the motor selected to be equipped in the UNIFI DIEF AURV; it is worth noticing how these values have been evaluated by exploiting the methodology described from the authors in [21]. As highlighted in Section 4, in this work, a preliminary assumption has been done by neglecting the dead-zone boundary values and the term depending upon the motor advance speed. Indeed, we approximate the relationship among the motor rotational speed and the longitudinal thrust with the forward bollard coefficient defined in Table 4. \begin{table}
\begin{tabular}{c c} NED position (m): & \(\eta_{1}=[0.0,0.0,1.0]^{T}\) \\ NED orientation (RPY) [_rad_]: & \(\eta_{2}=[0.0,0.0,0.0]^{T}\) \\ Linear relative body-fixed velocity (m/s): & \(\
u_{1r}=[-0.4,0.0,0.0]^{T}\) \\ Angular relative body-fixed velocity (rad/s): & \(\
u_{2r}=[0.0,0.0,0.0]^{T}\) \\ \end{tabular}
\end{table} 
Table 1: Main kinematic parameters.