## 7 Simulations and Results

\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 \endThe above-illustrated parameters have been employed in order to obtain the linear DME and angular DME, described in Equations (44) and (45), and the maneuverability indices defined in Equations (46)-(49) in Section 6, for both the configurations of the UNIFI DIEF AURV. Figure 5, illustrates the angular and linear ellipsoids for the survey shape of the vehicle. In particular, it is worth noticing how the linear DME turns to a circle, since the singular value related to the sway direction is equal to zero, as observed in the Table 5; thus, [PERSON]'s index \(W_{1}(\mathbf{q}_{1})\) and \(W_{2}(\mathbf{q}_{1})\) are also a zero value. If these results define the survey configuration as a singular one (i.e., the motion on the sway axis of the body-fixed frame is not taken into account), it should be considered as the index \({}^{x}W_{3}(\mathbf{q}_{1})\), defined as the maximum values of the AURV body accelerations \(\dot{\mathbf{v}}\), along the surge \(x\) direction, given the quasimaximum value of the thruster rotational speeds as input, is much larger than the same index for the hovering configuration. Conversely, the hovering configuration has the property of a omnidirectional motion in all the six degrees of freedom, as shown in Figure 6, and, as a consequence, [PERSON]'s index \(W_{1}(\mathbf{q}_{2})\) is different from zero. Additionally, it is interesting to notice that the index \(W_{2}(\mathbf{q}_{2})\) is closer to the unit value in both linear DME and angular DME, which implies that the hovering configuration is accurately controllable in every direction of space and can find a realistic application in complex tasks, as, for instance, working on an offshore structure or recovering samples from a shipw. Furthermore, Figure 7 illustrates the linear DME for the survey configuration in two different situations: firstly, when the ellipsoid is calculated considering to be in the absence of accelerations due to nonlinear terms (i.e., \(\dot{\mathbf{v}}_{\Gamma}(\mathbf{v}_{r},\mathbf{q},\mathbf{\eta})=\mathbf{0}_{6\times 1}\)), then with the assumptions explained at the beginning of this Section. As proposed in Section 5, the nonlinear accelerations \(\dot{\mathbf{v}}_{\Gamma}(\mathbf{v}_{r},\mathbf{q},\mathbf{\eta})\) result in a translation of the linear DME center, while the shape of the linear DME is not affected, since it is only related to the singular values \(\sigma(\mathbf{q})\). These considerations can also be applied in the case of the angular DME indeed. In conclusion, this section showed the results of the innovative dynamic maneuverability analysis on the UNIFI DIEF AURV obtained by means of dynamic simulations. From a qualitative point of view, linear and angular DMEs have been estimated for both the extreme configurations of the vehicle. As a first observation, it can be noted that such strategy allows immediately to distinguish if a vehicle is omnidirectional or if it is singular along a direction of motion. Additionally, several indices have been supplied as quantitative measurements of the AURV maneuverability. More specifically, the index proposed by the authors in Equation (49) represents the maximum value of the AURV body accelerations given the quasi-maximum value of the thruster rotational speeds. Therefore, this index can be used as a relevant absolute value of maneuverability for the different AURV configurations.