## 5 Results Discussion and Comparative Analysis  
The formation of heterogeneous AUVs-UAVs without disturbance and uncertain parameters (water density and the inertia matrix) based on the modified \(L_{1}\) controller in 2D space and 3D space is shown in Figures 2 and 3, respectively. All the AUVs are following their UAV leader and maintaining their triangle formation during tracking. Information is exchanged between all the AUVs and their UAVs leader through the DDS middleware as in Figure 1.  
The formation of heterogeneous AUVs-UAVs with disturbance and uncertain parameters (water density and the inertia matrix) based on the modified L1 controller in 2D space and 3D space as shown in Figures 4 and 5, respectively. In the presence of these disturbances, the fleet of AUVs maintain their triangle formation with the leader in the center. The performance of the system is not influenced by these disturbances and the large  
Figure 14: The containment maintenance of five AUVs in star formation within their four UAVs leaders in square formation during obstacles avoidance in 3D space.  
Figure 13: The containment maintenance of five AUVs in star formation within their four UAVs leaders in square formation during obstacles avoidance in 2D space.  
variation in the water density. The communication between all the AUVs and their leader is achieved through the DDS middleware as in Figure 1.  
Figures 6 and 7 show how the three AUVs and one UAV avoided obstacles during their movement. The formation of the AUVs in triangle form with the leader at the center has been maintained during obstacle avoidance in both 2D and 3D space.  
The containment of heterogeneous AUVs-UAVs without disturbance and uncertain parameters (water density and the inertia matrix) based on the modified L1 controller in 2D space and 3D space is illustrated in Figures 9 and 10, respectively. All the AUVs have been localized in formation inside the space delimited by the four UAVs leaders. The exchange of information between all of the AUVs and their UAVs leaders has been conducted through the DDS middleware.  
The containment of heterogeneous AUVs-UAVs with disturbance and uncertain parameters (water density and the inertia matrix) based on the modified L1 controller in 2D space and 3D space is shown in Figures 11 and 12, respectively. The followers are tracking the leaders and are remaining within the space delimited by these leaders. The performance of the system has not been influenced by these disturbances and the large variation in the water density. The star formation of the followers and their containment within the four leaders has been maintained. The communication between all of the AUVs themselves and their UAVs leaders has been done through the DDS middleware with QoS adapted to the leaders and followers as in Figure 8. Figures 13 and 14 show how the five AUVs and four UAVs avoided the obstacles during their movement while maintaining their containment in 2D and 3D space. The obstacle has been avoided by the fleet following their leaders.  
The navigation and control approach provided an excellent robustness to disturbances and also avoided obstacles while maintaining the formation or the containment. The DDS middleware provided the right environment for communication and data exchange with the appropriate QoS.