## 4 Simulation Results  
### Formation Control Based on L1 Adaptive Control with Actuator Time Delay  
The L1 controller with actuator time delay, DDS middleware, and flocking technique built above have been introduced. The underwater and quadrotor model parameters are selected as in [25,26]. Table 2 list the parameters for the quadrotor. Tables 3-5 list the MARES parameters, inertia and added masses respectively. \begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Value [\(kg\times m^{2}\)]** \\ \hline \(I_{xx}\) & \(1.55\times 10^{-1}\) \\ \(I_{yy}\) & \(4.73\) \\ \(I_{zz}\) & \(4.73\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: MARES inertia. \begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Unit** & **Value** \\ \hline Mass & m & 0.52 kg \\ Gravity Acceleration & g & 9.8 m/s\({}^{2}\) \\ Drag’s Translational & \(k_{t}\) & 0.95 \\ Drag’s Rotational & \(k_{r}\) & 0.105 \\ Ratio of Drag \& Thrust & \(d\) & \(7.5\times 10^{-7}\) kg \(\times\) m\({}^{2}\) \\ Inertia of \(x\)-axis & \(I_{x}\) & 0.0069 kg \(\times\) m\({}^{2}\) \\ Inertia of \(y\)-axis & \(I_{y}\) & 0.0069 kg \(\times\) m\({}^{2}\) \\ Inertia of \(z\)-axis & \(I_{z}\) & 0.0129 kg \(\times\) m\({}^{2}\) \\ Arm Length & \(L\) & 0.205 m \\ Propeller Inertia & \(I_{R}\) & \(3.36\times 10^{-5}\) kg \(\times\) m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The quadrotor model parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Value** \\ \hline Length & 1.5 m \\ Diameter & 20 cm \\ Weight in air & 32 kg \\ Depth rating & 100 m \\ Propulsion & 2 horizontal + 2 vertical thrusters \\ Horizontal velocity & 0–1.5 m/s, variable \\ Energy & Li-Ion batteries, 600 Wh \\ Autonomy/Range & about 10 h/40 km \\ \hline \hline \end{tabular}
\end{table} 
Table 3: MARES parameters. With the L1 control with actuator time delay parameters chosen as \(\gamma_{1}=10^{4},\ \ \gamma_{2}=10^{4},\ \ \gamma_{3}=10^{4},\ \ \ k=10^{3},\ \ \ k=10^{3},\) and \(\tau=0.1\). [PERSON] rules parameters chosen as \(k=k_{coh}=10,S=1,S_{o}=1,M=1,\) and \(C=5\). For formation control, the DDS middleware communication between the agents is shown in Figure 1 by considering some policies of QoS in Table 6 that must be fulfilled before the interaction between the subscribers and the publishers. The QoS illustrated in Figure 1 will be adopted during all the tests shown in Figures 2-7. Two cases have been included for the formation control results based on the modified L1 controller. * AUVs-UAVs formation control without disturbance and uncertain parameters. Figure 2 illustrates a group of AUVs in a triangular formation tracking their UAVs leader and coordinating themselves around it in 2D space. At the same time, Figure 3 depicts the 3D space of the set of three AUVs without disturbance and uncertainty in the inertia matrix. * Formation of AUVs-UAVs with disturbance and uncertainty in parameters. In Figures 2 and 3, the disturbance and parameter uncertainties (water density and the inertia matrix) were not taken into account. Figures 4 and 5 show the 2D space and the 3D space of the group of three AUVs with disturbance and uncertainty in water density and inertia matrix. Figures 6 and 7 illustrate the formation control of three AUVs in triangular form and one UAV avoiding some obstacles during their movement in 2D and 3D space. One can observe that during this maneuver, the controller still maintains the formation. Figure 1: The formation structure based on DDS middleware.