# Autonomous Target Tracking of UAV Using High-Speed Visual Feedback
## 6 Experimental Results
### Target Tracking
#### 6.3.2 Results  
The tracking trajectories were transformed to the world coordinate system (Figure 14) located on the robot arm, as shown in Figure 15, with the target moving at a linear velocity of 0.5 [m/s] and a linear acceleration of 0.1 [m/s\({}^{2}\)]. The setpoint position \({}^{o}x\) was set to \([0.6,0.1,0.1]^{T}\) [m], and the setpoint yaw angle \({}^{o}\psi_{sp}\) was set to 0 [deg] relative to the original point on the target.  
The experimental results showed that the positional tracking mean errors were \([41.4,51.2,34.5]\) [mm] with standard deviations \([1.2,1.3,1.0]\) [mm] in the \(x,y,\) and \(z\) directions, respectively. The angular tracking mean error was \(0.7006^{\circ}\) with a standard deviation \(0.0574^{\circ}\) in the yaw direction. Since the relative setpoint was \([0.6,0.1,0.1]^{T}\) [m] in the \(x,y,\) and \(z\) directions with respect to the object, we can see the position deviation between the UAV's trajectories and the robot end effector during the tracking.  
To test the performance of our direct visual servoing system while tracking a high-speed moving target, we repeated the above experiment with higher acceleration. Figure 16 shows the tracking results while the target was moving backward and forward with a linear velocity of 0.5 [m/s] and a linear acceleration of 1.0 [m/s\({}^{2}\)].  
Figure 14: Relationship between object coordinate system and world coordinate system.  
Figure 15: Trajectory of autonomous target tracking (Moving speed: v = 0.5 [m/s], a = 0.1 [m/s\({}^{2}\)], Target recognition rate: 350 Hz).  
The experimental results showed that the positional tracking mean errors were \([50.5,80.1,129.1]\) [mm] with standard deviations \([1.8,2.6,4.9]\) [mm] in the \(x\), \(y\), and \(z\) directions, respectively. The angular tracking mean error was \(1.0101^{\circ}\) with a standard deviation \(0.0019^{\circ}\) in the yaw direction. As shown in Figure 16, we found that there was an overshot phenomenon while the target was moved with a higher linear acceleration. This may have resulted from an excessively high mass of inertia of our flying platform, which was originally used for a racing drone.  
We also compared the tracking performance in the \(z\) direction and yaw angle estimation with different target recognition rates, as shown in Table 2. The experimental results showed that higher target recognition rates not only effectively improved the tracking performance but also allowed the accuracy of the attitude estimation to be evaluated. Figure 17 shows the tracking results with a 30 Hz target recognition rate. Compared with Figure 16, a tracking delay in the \(z\) direction was obvious due to the larger control latency resulting from insufficient position update rates.  
Figure 18 shows the experimental result of dynamic target tracking within 1.7 s.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Target Recognition Rates** & \(z\) **Mean Error** & \(z\) **Mean Error std.** & **Yaw Mean Error** & **Yaw Mean Error std.** \\ \hline
350 Hz & 0.1382 m & 0.0057 m & 1.0246\({}^{\circ}\) & 0.1255\({}^{\circ}\) \\
30 Hz & 0.1634 m & 0.0129 m & 1.4859\({}^{\circ}\) & 0.1939\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Tracking performance comparison with different target recognition rates.  
Figure 17: Trajectory of autonomous target tracking (Moving speed: v = 0.5 [m/s], a = 1.0 [m/s\({}^{2}\)], Target recognition rates: 30 Hz).