# Aerial Tele-Manipulation with Passive Tool via Parallel Position/Force Control +
## 5 Experimental Results
### Results
#### 5.2.2 Movable Object Experiment  
In the second experiment, the robot was initially located at the global frame origin. The movable object, which was a cart with plate of 0.15 m \(\times\) 0.15 m attached to it, was located at [0.5 m, 0.0 m and \(-\)0.90 m], with downward pointing \(\mathbf{z}_{w}\). The human operator was driving the quadrotor towards the cart, and once the robot reached the cart, the driver pushed it until it passed 1.0 m, and eventually the driver commanded the robot to leave the object, and brought the robot back to free flight. Figure 7-bottom shows the snapshots of this experiment, while Figures 8-right, 9-right, and 10-right depict the results of the experiment. Figure 8a' shows the position tracking during the experiment. The difference between the new situation (a movable object) compared to the previous experiment (a stationary object) can be seen through this plot, where after establishing the contact, while the quadrotor is applying the force to the object (cart), its position is not changing until the moment (in this experiment at 14.5 s) the applied force overcomes the static friction of the cart wheels with the ground. Then, the cart (and the aerial manipulator too) experiences an accelerated motion. The position error is explicitly reported in Figure 9-right), for the reader's convenience. As in the previous scenario, before the interaction the error is relatively close to zero,  
Figure 10: Stationary (**left**) and movable (**right**) object experiments: (**a**,**a**) spring–damper force brings back the master device’s handle to the center of its workspace, (**b**,**b**) the haptic feedback \(f_{pf}\) that renders the applied force to the object in contact and position error in free flight. Figure 9: Position error in the stationary object experiment (**left**) and movable object experiment (**right**): as can be seen, the error is bigger during the interaction phase, in both cases, as a consequence of the force tracking. Furthermore, the error is higher in the movable object experiment, in particular during the undocking phase. that is, bounded below 7 cm, while during the contact there is significant position error, that is, \(\approx\)50 cm, specifically in \(x\)-direction which corresponds to the normal component of force. As already mentioned, this is in accordance with the fact that, in this phase, the robot is tracking the desired force provided by the user, and not the desired position. During the undocking phase, namely when the human operator sees the accelerating cart passing the goal line and pushes back the handle of the haptic device in order to bring the robot back, a peak of \(\approx\)75 cm is reached due to a small false contact detection, after which the position error converges back to its typical free-flight values. The large error value in the detachment phase can be improved by limiting the integral term of the PI-force controller, and increasing the proportional gain of PI-controller, or also using a more agile controller in the inner position loop. It is worth noting that, in this experiment, the goal was to evaluate the efficiency of the proposed controller in applying force to objects in order to move them in a way the human operator wants, rather than performing precise force tracking. In relation to this last point, another meaningful note is that the two experiments here discussed were explicitly designed and performed with the main goal of validating the presented aerial robotic solution in indoor laboratory conditions, which imply the use of a motion capture system for state estimation, a cabled connection between the robot and the ground workstation, and the absence of non-negligible external disturbances. Under these conditions, we basically experienced a rate of success of 100%.