# Aerial Physical Interaction in Grabbing Conditions with Lightweight and Compliant Dual Arms
## 5 Experimental Results
### Grabbing Interaction on Flight with Impedance Control  
The goal of this experiment was to analyze the behavior of the aerial manipulation robot on flight when the grabbing arm was actively controlling the impedance in the \(x\)- and \(z\)-axes, considering a desired Cartesian stiffness \(K_{d,X}=K_{d,Z}=50\)\([N/m]\). The performance of the controller was evaluated by injecting a disturbance on the multirotor position that emulates the effect of an external force, such as a wind gust. The zero-torque controller of the first joint (shoulder yaw) was disabled, relying only on the passive compliance to support the lateral displacements (\(y\)-axis) and heading variations (yaw angle) of the multirotor. The flight test consists of eight phases:  
1. The aerial manipulator takes off with the arms resting in landing configuration.
2. The grabbing arm adopts the nominal pose (L-shaped) while the operation arm is retracted.
3. The impedance controller is enabled, imposing a zero reference for the first joint (\(\theta_{1}^{2}=0\)).
4. The aerial manipulator approaches to the linear structure until the magnetic gripper grabs it.
5. The aerial manipulator hovers while the impedance controller of the grabbing arm is active.
6. A position disturbance is injected through the radio controller to observe the response of the aerial manipulator and the reaction of the grabbing arm.
7. The torque control of the servos is disabled to release the grabbing arm.
8. The arms adopt the landing pose, and the platform goes back and lands.  
Figures 13 and 14 show the evolution of the system in the time intervals corresponding to phase 5 and phase 6, respectively. On the one hand, Figure 13 covers the time interval from t = 25 to t = 35 s, in which the multirotor was hovering at fixed position while the grabbing arm exerted a small force in the \(x\)-axis, around 0.5 N, due to the slight displacement of the platform with respect to the nominal pose. On the other hand, Figure 14 covers the interval from t = 48 to t = 70 s. At t = 49.6 [s], we intentionally applied a 10 cm displacement in the \(x\)-axis position of the multirotor, emulating a wind gust. The grabbing arm reacted, exerting a pushing force with a peak of 2.2 [N] that counteracted the disturbance, recovering the nominal operation pose in 2 s. The instantaneous stiffness varied w.r.t. the desired value (50 N/m) due to the singularity in the displacement (\(K_{d,x}=F_{x}/\varepsilon_{x}\)). Note also that, since the grabbing arm was not aligned with the \(\mathbf{X_{B}Z_{B}}\) plane of the base but it was displaced a distance \(D/2\) (see Section 3.1), then the force exerted during the interaction would cause a reaction torque in the yaw angle of the multirotor, and with it, a position deviation in the \(y\)-axis, as can be seen in Figure 14. The effect was accentuated as the pilot disturbed the multirotor controller between t = 52 and t = 60 s. Although the passive deflection of the shoulder yaw joint provided a certain level of accommodation, the motion constraint associated with the grabbing condition had a more significant effect on the \(y\)-axis and yaw angle, in accordance with the results shown in Figure 9.  
Figure 14: Evolution of the grabbing arm and the multirotor, disturbed at t = 49.6 seconds, during the grabbing maneuver (phase 6) with impedance control in the \(x\)- and \(z\)-axes (\(K_{x}=K_{z}=50\,N/m\)).  
Figure 13: Evolution of the grabbing arm while the multirotor hovers with no disturbance during the grabbing maneuver (phase 5) with impedance control in the \(x\)- and \(z\)-axes (\(K_{x}=K_{z}=50\,N/m\)).