## 4 Field Experiment Evaluations
### Formation Flight Experiment Evaluations  
To evaluate the formation flight capabilities of a UAV equipped with our developed AFCCS, we conducted field experiments including multiple UAVs with speed \(2\,\mathrm{m/s}\) and \(D=10\,\mathrm{m}\). In this experiment, a LoRa module with two transmissions per second is adopted in the Drone Mapper and a formation \(f_{n}\) for \(N=4\) UAVs is implemented, as shown in Figure 10b. In order to validate the effectiveness of the proposed method, a parameter named the deviation distance \(\xi_{n}\) is introduced. This parameter means the distance between the actual position of UAV\({}_{n}\) and the position where it should be during formation flight with the given formation \(f_{n}\). Mathematically, \(\xi_{n}\) can be expressed as  
\[\zeta_{n}=||(\hat{x}_{n},\hat{y}_{n},\hat{z}_{n})-(x_{n,n},y_{n,n},z_{n,n})||_{2}. \tag{12}\]  
Smaller deviation distances \(\zeta_{n}\) for all UAVs at any given time indicate better maintenance of the desired formation during their flight. Conversely, larger deviation distances \(\zeta_{n}\) suggest that the UAVs are not flying in the designed formation. Theoretically, perfect formation flight can be achieved under the condition that \(\zeta_{n}=0\) for all UAVs at all times. The experimental results of UAV formation flight under the aforementioned conditions are shown in Figure 16.  
The resultant longitude and latitude coordinates of all UAVs, as well as the flight path of the leader UAV, based on our experimental data are shown in Figure 17. The results include the theoretical flight formation data constructed by four UAVs, which are represented by dashed lines, and their actual positions, which are represented by solid lines. Additionally, in Figure 18, we provide information on the altitude and flight direction of the leader UAV. The altitude data of the leader UAV are utilized to determine the observation flight period of the experiment.  
In Figure 19, the deviation distances of the three follower UAVs throughout the entire flight process are provided. It can be observed that during the observation period from \(200\,\mathrm{s}\) to \(500\,\mathrm{s}\), the deviation distances of all follower UAVs remain less than \(5\,\mathrm{m}\). However, these distances increase significantly (more than \(10\,\mathrm{m}\)) when the flight direction of the leader UAV rotates 90 degrees to the right. One possible explanation is that a substantial change in the flight direction of the leader UAV results in a significant change in the flight formation. Compared to the case of flying along a straight line, the follower UAVs require additional time to adapt to such significant changes by adjusting their speed. This reveals a major challenge due to physical constraints of the UAV, such as flight torque and acceleration. Generally speaking, methods like increasing the frequency of information  
Figure 15: Intrusion distances for UAV collision-avoidance experiments based on an FSK module with \(N=2\) and \(r_{n,n}=15\,\mathrm{m}\)\(\forall n\in\{1,\cdots,N\}\).  
sharing by replacing the LoRa module with an FSK module may reduce the deviation distances and improve the performance, which needs further evaluation in future studies.  
Figure 16: An experiment of UAV formation flight based on a LoRa module with \(N=4\) and \(v_{u,n}=2\,\mathrm{m/s}\) for all \(n\in\{1,\cdots,N\}\).  
Figure 17: Longitude and latitude of all UAVs and the flight path of the leader UAV.  
Figure 18: Altitude and flight direction of leader UAV.