## 4 Simulations
The wrench signal is evaluated with respect to a predefined deadzone function \(\text{d}z(\cdot,\cdot)\) to prevent undesired oscillations of the control:

\[\text{d}z(F_{1},F_{2})= \begin{cases}F_{1}-F_{2},&F_{1}>F_{2}\\ 0,&-F_{2}<F_{1}<F_{2}\\ F_{1}+F_{2},&F_{1}<-F_{2}\end{cases}  \tag{7}\]

## 6 Experimental Results

Experiments were performed to show the capabilities of the robot platform and to evaluate its effectiveness in depalletizing tasks. We report unloading tasks in scenarios where the mobile platform is already in place to collect the cardboard boxes, as well as in more dynamic cases where the AMR first approaches the boxes. The experiments were performed with filter gains \(K_{F}=10e^{-3}\), \(K_{p}=0.1\) and force threshold \(F1=10N\). ### 2-Boxes Depalletizing and Transportation

A two-boxes depalletizing task is shown in Figure 7. First, the mobile base approaches a group of boxes by moving to a suitable configuration for the box unloading task, then the cobot rises the 3D camera to an elevated position to detect the boxes. The two-steps detection of the gap between adjacent boxes was then executed. Then, the tool is inserted into the gap between the first two boxes and the first box is pulled on the robot. Then, the procedure is repeated to manipulate the second box. Finally, the mobile base moves away with the two boxes onboard. In Figure 8, the Cartesian position and the measured wrench on the cobot end-effector are displayed along the task. The low values of the measured wrench confirm that the task was successfully completed without any collision of the tool. Figure 9 reports the success rate of the task for 50 box extractions. It can be noticed that in most cases, the system performed the extraction by the first attempt. Nonetheless, in a few cases, the first estimation of the gap between boxes was not correct, and a second

Figure 8: A depalletizing task where two boxes are successfully extracted. The mobile base is exploited to approach the boxes for the unloading task and to transport the boxes away once loaded on the robot. Figure 7: From top-left to bottom-right a sequence showing the execution of a 2-boxes depalletizing task by the mobile manipulator. attempt was required. This is probably due to unexpected changes in light conditions or slight motions of the mobile base. In all cases, the second estimation of the gap was successfully completed and the box was correctly loaded onto the robot. ### Single Box Extraction

The Cartesian position and the measured wrench on the cobot end-effector during the unloading of a single box are reported in Figure 10a. At first, the box position was estimated by the in-hand camera. Then, the estimated gap between two adjacent boxes was refined to obtain the target frame for tool insertion (\(t=4\,\mathrm{s}\)). Once the target frame was determined, the tool was aligned with the gap between the boxes (\(t=8\,\mathrm{s}\)), and an insertion attempt was performed (\(t=12.5\,\mathrm{s}\)). During the insertion phase, a collision was detected (\(t=15.5\,\mathrm{s}\)), possibly caused by an inaccurate evaluation of the gap position. Therefore, tool insertion was suspended and a new detection of the gap was performed (\(t=21\,\mathrm{s}\)). Since no further collisions were detected (\(t=32\,\mathrm{s}\)) the cobot completed the insertion and the box was successfully pulled onto the robot (\(t=36\,\mathrm{s}\)). It can be noticed that when a collision occurs, the admittance control allows for a smooth motion of the end-effector, thus reducing the risk of damaging the robot arm or the target box. ### Complete Layer Depalletizing

A successful example of unloading a pallet layer with four boxes, in a static scenario where the AMR was fixed, is shown in Figure 10a. In this test case, the target boxes were extracted one by one until the pallet layer was empty. The AMR was placed so that all four boxes were inside the robot arm workspace. The boxes were manually removed from the robot platform once unloaded since the robot platform can carry at most two boxes.