## 6 Experiments  
We have carried out three computational simulation experiments that require a team of three quadrotors transporting a DLO attached to them in a follow-the-leader strategy, where followers try to mimic the motion of the leader, i.e., following parallel paths to the one of the leader trying to preserve the distance among quadrotors. In both experimental simulations, time is discretized in steps of 0.1 s, the DLO is modeled by the catenary-parabola approximation and we apply a fuzzy logic approach for the adaptive tuning of the PD controller. Both experiments feature sharp path changes that were unmanageable with previous versions of the controller [17].  
_Experiment 1:_ In this experiment, the nominal path set for the leader quadrotor has sudden changes of direction, as shown in Figure 5. The objective of the experiment is to check whether the drone team's formation remains stable and is able to cope with the different path corners, particularly with the sharp angle located at \(x=400\) cm. For the experiment, both with and without wind disturbance conditions in the X direction are used to model the following dynamic equation \(d(t)=5+5\sin(\frac{\pi}{2}t)\).  
_Experiment 2:_ In this experiment, the three quadrotors transport the DLO in a straight line path. When the leader drone has traversed a distance of \(x=350\) cm, it suffers a sudden lateral disturbance consisting of a push displacing it 80 cm in the Y positive direction, as shown in Figure 6. The experiment aims to observe how the leader and followers recover the nominal path after the disturbance.  
_Experiment 3:_ Now, the three quadrotors must follow a spiral 3D ascending path specified by \(x=100\sin(t)\), \(y=100\cos(t)\), \(z=5(t)\), with \(t=[0:3\pi]\), as seen in Figure 7.  
This test aims to check the capacity of the drones control system to cope with the three direction paths at the same time, with no-wind conditions, and considering only the hybrid DLO model of catenary and parabola. The leader drone's starting position is at \((0,0,0)\).  
In the three experiments, the initial distance in the horizontal axis between drones at the extremes and the central drone is the same and is set as \(\rho_{d}=70\) cm. Moreover, in order to ensure balanced energy consumption, the system is in equiload conditions [18; 45]. As a consequence, no further correction of altitude is applied, although the horizontal Euclidean distance between robots might change. In platoon formation, the maximum vertical thrust was limited for each quadrotor to 20 N following standard hardware specifications. The length of the catenaries was set to \(L_{0}=240\) cm; the mass density of the DLO was set to \(w=0.005\) [kg/cm]. For online fuzzy tuning of the PD controller, the adaptation factor was set to \(\alpha=0.5\). Dynamic parameters of each quadrotor appear in Table 2. We set the initial PD parameter values as follows: \(K_{px}=K_{py}=0.22\); \(K_{dx}=K_{dy}=0.76\).  
Figure 5: Nominal path for the drone leader in Experiment 1, featuring sharp changes in direction.  
Figure 6: Experiment 2. Nominal path followed by the leader drone suffering a sudden lateral disturbance.  
Figure 7: Spiral 3D ascending path in Experiment 3.  
Experiments have been coded in house in Scilab 5.4. No other public or private software solutions have been used. The code of the implementation has been published in an online repository ([[https://github.com/[PERSON]/Quadrotor-simulator/tree/master/catenary%20](https://github.com/[PERSON]/Quadrotor-simulator/tree/master/catenary%20) and%20 parabola%20 hybrid%20 modelling]([https://github.com/[PERSON]/Quadrotor-simulator/tree/master/catenary%20](https://github.com/[PERSON]/Quadrotor-simulator/tree/master/catenary%20) and%20 parabola%20 hybrid%20 modelling), accessed on 10 May 2022).