## 4 Results
### Experiments in the Simulated Environment
#### 4.2.3 Experiments to Test the Life-Long Operation Capabilities of the System  
To further demonstrate the robustness of our algorithm and its life-long operation capability, we carried out the following experiment: we launched the system once and let the UAV perform up to a maximum of 50 takeoff-tracking-landing maneuvers continuously. For every iteration, 10 s pass from the moment of takeoff before an automated landing signal is sent. Once the UAV lands, it rests for 1 s on top of the landing platform before taking off again to complete a new takeoff-tracking-landing maneuver. This test was carried out for a circular trajectory and for two different velocity conditions of the landing platform, resulting in a total of 100 attempted maneuvers: on the one hand, nominal conditions (\(v_{x}=0.5\,\mathrm{m\,s^{-1}},w_{z}=0.05\,\mathrm{rad\,s^{-1}}\)); and, on the other hand, more demanding conditions (\(v_{x}=0.7\,\mathrm{m\,s^{-1}},w_{z}=0.07\,\mathrm{rad\,s^{-1}}\)). Note that, in practice, the UGV model, i.e., the Summit XL, rarely reaches linear speeds higher than \(v_{x}=0.7\,\mathrm{m\,s^{-1}}\), commonly operating at a nominal speed of \(0.5\,\mathrm{m\,s^{-1}}\) along its x axis. However, we wanted to evaluate our re-localization module thoroughly under more challenging conditions. We used our best-performing system, namely our system based on a predictive, height-adaptive PID controller. Figure 11 visualizes the trajectories described by both the UAV and the UGV for the two speed conditions mentioned above. Note that, in practice, the trajectory followed by the UGV is never exactly a circle due to the wheels' friction coefficients. Moreover, the UGV also drifted in time, thus resulting in various circles centered in different locations, as can be seen in Figure 11.  
As gathered in Table 2, for a velocity of (\(v_{x}=0.5\,\mathrm{m\,s^{-1}}\), \(w_{z}=0.05\,\mathrm{rad\,s^{-1}}\)) the system managed to land the aerial vehicle successfully in all 50 consecutive maneuvers with a Mean Absolute Error (MAE) along the UAV's x axis of 0.127 m and 0.245 m along its y axis. Moreover, the maximum absolute error along the x and y axes was 0.734 m and 0.653 m, respectively. When operating at a higher velocity (\(v_{x}=0.7\,\mathrm{m\,s^{-1}}\), \(w_{z}=0.07\,\mathrm{rad\,s^{-1}}\)), the re-localization module had to be launched 16 times, leaving a total of 34 successful landings. In this case, the MAE along the UAV's x axis was 0.245 m and 0.232 m along the y axis, and the maximum absolute errors were 1.526 m and 1.441 m for the x and y axes, respectively. Figure 11: _Cont._  
Note that all 16 recovery maneuvers under the more challenging conditions were triggered not because the UAV lost sight of the landing platform, but due to a too large error--greater than 0.25 m in our experiments--in the moments before landing. Such an early detection of potential failed landings allows the system to avoid accidents and flawlessly continue functioning even under challenging velocity conditions of the landing platform. An example of a relocalization maneuver can be viewed in Figure 12. Moreover, Figure 13 shows the error along the UAV's z axis during the first 200 s of the experiment for both velocity conditions studied. Overall, the rate of successful landings was 100% for the nominal velocity of the UGV and 68% in the case of more challenging (and rather unusual) conditions. In this subsection, we demonstrated how our system performs flawlessly at the nominal speed of the UGV. More importantly, we have shown that by leveraging our novel recovery module, potential failed landing maneuvers can be detected and avoided, thus demonstrating the great benefits that such a system brings about, both in terms of robustness and reliability.