## 4 Simulations
Once the estimation is obtained, the robot tool is aligned with the gap center and a tool insertion operation is attempted. During the insertion, the tool wrench is continuously evaluated to identify any unexpected collision, possibly due to wrong detection. An admittance control scheme allows to prevent any damages to the robot and the boxes during the insertion as reported in Section 5.3. As soon as a collision occurs, the insertion operation is interrupted, and the estimation of the gap is tried again. If no collision is detected, the insertion is considered successful and the box, dragged by the robot tool, is loaded on the robot support surface, which will be replaced by the lifting device in our future work. \begin{table}
\begin{tabular}{c c c c} \hline  & & **Loading** & **Unloading** \\ \hline  & Motion & Time (s) & Time (s) \\ \hline  & 1 & 4.25 & 5.90 \\  & 2 & 1.05 & 1.05 \\ Box & 4 & 1.05 & 1.05 \\
1 & 5 & 3.09 & 3.10 \\  & 7 & 1.05 & 1.05 \\  & 8 & 1.55 & 1.54 \\ \hline  & Partial & \({}^{v}T_{l1}=12.04\,\mathrm{s}\) & \({}^{v}T_{u1}=13.69\,\mathrm{s}\) \\ \hline  & 1 & 3.65 & 3.35 \\  & 2 & 1.05 & 1.05 \\ Box & 4 & 1.05 & 1.00 \\
2 & 5 & 3.10 & 3.10 \\  & 7 & 1.05 & 1.10 \\  & 8 & 1.54 & 1.54 \\ \hline  & Total & \({}^{v}T_{l}=23.48\,\mathrm{s}\) & \({}^{v}T_{u}=24.88\,\mathrm{s}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Simulated elapsed time for loading/unloading two boxes with the vacuum gripper. Figure 5: The experimental setup: the mobile manipulator (**a**), the paddle tool and the in-hand 3D camera (**b**). ```
Data: 3D camera image, robot tool wrench Result: depalletizing of a box layer move camera in the detection pose; perform detection of parcel boxes; define box picking sequence in box depalletizing plan; while box picking sequence is not empty do extraction start: consider the first box in the sequence; evaluate the box edge position; move the 3D camera to the evaluated position; perform refined estimation of the gap between boxes using the 3D camera image; move the robot tool above the refined gap; whileinsert the robot tool in the gap do if vertical tool wrench \(>\) wrench threshold then extract robot tool; go to beginning of current section: extraction start;  end if  end for drag the box toward the robot; remove current box from the sequence;  end
```

**Algorithm 1**Robotized Depalletizing Algorithm

### Detection of parcel Boxes

In the _detection of parcel boxes_ phase, the robot arm first moves to an observation configuration, where the upper layer of the pallet can be fully observed by the eye-in-hand infra-red 3D camera (IFM Electronics O3D303). Furthermore, the camera exposure time \(t_{\text{exp}}\) is set to a constant value \(t_{\text{exp,far}}\), suitable to observe objects from the current distance of the sensor to the pallet, as shown in Figure 5(a). Then, the camera acquires a depth image with a of resolution 352 \(\times\) 264 pixels, which is converted into an organized point cloud containing 3D points \(p_{ij}\). The camera also produces an intensity value \(r_{ij}\) for each pixel that contains the amount of light returned to the sensor. As light intensity \(r_{ij}\) decreases with distance according to the inverse square law, and since the amount of light received by the sensor is proportional to the current exposure time \(t_{\text{exp}}\), a corrected intensity image \(R^{\prime}=\left\{r_{ij}^{\prime}\right\}\) is computed as \(r_{ij}^{\prime}=r_{ij}\ \|p_{ij}\|^{2}\ /\ t_{\text{exp}}\). As the camera provides its own infra-red lighting, both depth and intensity measurements proved robust to changes to environmental light conditions compatible with indoor industrial environments. In order to ensure stability, pallets are generally arranged as a stack of layers. Each layer above the first one lies on the top planar faces of the parcel boxes of the layer below. In industrial environments, the content and the configuration of a pallet is known in advance. Pallets stored in a warehouse usually contain parcel boxes of the same type.