# Cooperative Standoff Tracking of Moving Targets Using Modified Lyapunov Vector Field Guidance
## 5 Experiments and Results
### Hardware-in-the-Loop Simulation
#### 5.2.2 HIL Simulation Results  
As shown in Figure 20, three UAVs cooperatively track the target moving on ground of which the trajectories are described in Figure 19. In Figure 20a, UAVs clump around the start point after receiving \"tracking\" command at the standby point. UAVs are distributed evenly around the standoff circle by adjusting speed in Figure 20b. Figure 20c illustrates the cooperative tracking of the target moving at a constant velocity, while the trajectories of UAVs tracking accelerating targets are shown in Figure 20d. We can intuitively see that the team of three UAVs can cooperatively track the target moving on ground, distributed in a circle with a suitable angular difference. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Description** & **Value** \\ \hline \(R\) & standoff distance & 90 m \\ \(s\) & cruising speed of the UAV & 14 m/s \\ \(s_{\text{min}}\) & minimum speed of the UAV & 10 m/s \\ \(s_{\text{max}}\) & maximum speed of the UAV & 18 m/s \\ \(a_{\text{min}}\) & minimum acceleration of the UAV & \(-2\) m/s\({}^{2}\) \\ \(a_{\text{max}}\) & maximum acceleration of the UAV & 2 m/s\({}^{2}\) \\ \(\dot{\psi}_{\text{max}}\) & maximum course rate & 0.2 rad/s \\ \(v_{tl}\) & low constant speed of the target & 3 m/s \\ \(v_{th}\) & high constant speed of the target & 7 m/s \\ \(a_{t}\) & constant acceleration of the target & 1.5 m/s\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Key parameters in the HIL simulation. Figure 19: The target trajectories and moving speed in the simulation environment. Figure 20: _Cont._  
The details of tracking performance are listed in Figures 21 and 22. In the 'gathering' stage shown in Figures 21a and 22a, the distance error deceases rapidly to zero as UAVs fly toward the start point at the maximum speed. In the early stage, such as interval (I) in Figures 21a and 22a, UAVs hover over the standby point, which is far away from the start point, so the phase difference relative to the target undergoes drastic changes. In the phase adjusting stage, UAVs mainly adjust the phase difference between neighboring UAVs. In interval (II) as shown in Figure 21b, the distance errors of three UAVs gradually converge to zero, but there is a slight shock around zero in interval (III), owing to the unstable UAV model in the Xplane simulator. In interval (II) as shown in Figure 22b, the phase difference converges to the desired phase (\(120^{\circ}\)) while the UAVs speed varies, which is controlled by the policies generated by Equation (28). In interval (III) as shown in Figure 22b, the phase difference between neighboring UAVs is stably near the desired value. When the ground target is moving, the tracking performance is closely related to the target speed. Tracking the low-speed targets is relatively easier than tracking high-speed and accelerating targets, and tracking the accelerating target is the hardest task, which is obviously shown in the distance error fluctuation (Figure 21c-e). The main reason may be that the estimation of the state of low-speed targets is relatively easier, while for accelerating targets, the estimation is the most inaccurate. Furthermore, the estimation results are utilized to modify the guidance laws, so tracking performance is impacted. Correspondingly, the phase difference error shows a similar trend (Figure 22c-e) as distance error, which complies with the fact that performance in distance keeping influences phase keeping a great deal. Figure 20: The snapshots of cooperative standoff tracking shown on the Ground Control Station in the HIL simulation. (**a**) Gather around the target; (**b**) Adjust phase difference; (**c**) Track the constant-speed target; (**d**) Track the accelerating target. Figure 21: _Cont._  
Figure 21: The standoff tracking distance error.