## 4 Results
### Experiments in the Simulated Environment
#### 4.2.1 Experiments under the Same Initial Conditions  
In this set of experiments, the system was re-launched every time so as to have the same initial conditions for every try. Moreover, the landing platform followed two different trajectories, namely linear and circular. A total of 20 takeoff-tracking-landing maneuvers were executed, 10 for each trajectory type, always re-initiating the whole system for every new test. Within a trajectory type, we tested the two variants of our tracking algorithm, i.e., w/ and w/o prediction. In all experiments, we computed the Euclidean distance between the landing platform's centroid and the UAV's body frame with respect to the latter. In the following, we will denote this as the _error_. Note that this error only coincides with the error fed to our height-adaptive PID controller in the mode w/o prediction. The details of the two types of trajectories together with the results obtained in each case are described next. **Linear trajectory. ** The UGV (and thus the landing platform) describes a linear trajectory at a speed of 0.5 m s\({}^{-1}\) along its x axis. Initially, both the UGV and the UAV are at rest, with the latter lying on the landing platform. After a takeoff signal, the aerial vehicle begins its ascent phase to a pre-defined height of 4 m, and the UGV starts moving along a linear trajectory. Upon detection of the landing platform, the UAV automatically begins to follow the UGV by reducing its distance to the latter in the xy-plane, as explained in previous sections. After 30 s in tracking mode, a landing signal is sent automatically to the drone, which begins its descent towards the UGV. Figure 6 shows the trajectory described by the UAV and the UGV for a single experiment of the linear trajectory. Results for both the non-predictive and predictive modes of the controller are presented. At first glance, no notable differences can be appreciated. The system w/ prediction is, however, more stable than its non-predictive counterpart as can be noted by visualizing the slightly more smooth curves in Figure 6b compared to those in Figure 6a. Importantly, note the scale of the y axis in Figure 6a,b and how the trajectory of the UAV is bounded within roughly 3 cm after the first 5 m in both cases (w/ and w/o prediction), following almost perfectly the linear trajectory described by the landing platform. Figure 7 plots the error along both the x and y axis for a single experiment of the linear trajectory. As with the previous figures, results for both for the non-predictive and predictive variants are shown. Note that the error along the UAV's y axis is close to zero for both modes (w/ and w/o prediction), as was expected in the case of a linear trajectory. As for the error along the x axis, the general trend is similar in both modes, though more bounded for the algorithm w/ prediction. The big initial peak in Figure 7a is due to the fact that the UGV starts moving at the same time that the UAV takes off, thus generating a relatively large initial error along the x axis that is corrected after the first 10 s of simulation. Figure 6: Views of the movements of the UGV and the UAV during a linear trajectory experiment. Figure 7: Errors for a linear trajectory sequence. **Circular trajectory. ** In this experiment, the UGV describes circles with a forward speed along its x axis of 0.5 m s\({}^{-1}\) and an angular velocity along its z axis of 0.05 rad s\({}^{-1}\). In theory, this would result in a circular trajectory of radius 10 m. In practice, due to the friction coefficient of the UGV's wheels, it results in a circle of radius 12 m in this particular case. Note that the takeoff-tracking-landing procedure described for the linear trajectory is also followed here. Figure 8 shows the trajectory described by the UAV and the UGV for a single experiment of the circular trajectory. As with previous figures, results for both the non-predictive and predictive variants are presented for comparison.