## 4 Simulations  
The industrial scenarios considered in this work were simulated using CoppeliaSim (www.coppeliarobotics.com/coppeliaSim, accessed on 24 June 2021) and evaluated in terms of task execution time and motion feasibility. Simulations include a comparison between the dragging manipulation approach against a standard pick-and-place solution. One layer of 21 palletized boxes (of size 250 \(\times\) 150 \(\times\) 300 mm, arranged in a grid of 7 rows, 3 columns) must be transported from an initial pallet to a storage pallet, maintaining the initial grid arrangement of the boxes. It is assumed that during the manipulation phase of the items the total payload attached to the robot (i.e., the tool and the box) is always lower than the UR10e maximum payload. The first simulated scenario (Procedure 1) involves the usage of a shovel-shaped tool on the UR10e end-effector. The tool drags the item on the lifting device. In this case, it is assumed that the AMR can transport only two boxes per journey. Making such assumptions, the task can be accomplished in 11 journeys: for each of the seven rows of the box grid, the first two columns items are manipulated in the first seven journeys, then the items on the third column are handled in the remaining four journeys, with a quite different picking method. Indeed, a pair of items (in the same row) of the first two columns, once the AMR is positioned next to them, can be pulled by the manipulator without any additional motion of the AMR, whereas the AMR must be moved to manipulate a pair of items (in different rows) of the third column. Figure 4 shows the AMR/cobot system and the grid of 21 boxes highlighting the items involved in each of the 11 journeys. The shovel-shaped tool of the cobot allows to load a box on the lifting device by means of a linear dragging movement. Firstly, the manipulator executes a collision-free movement  
Figure 4: The grid of 21 boxes named according to the order of manipulation. from its current initial position towards the detected approaching frame between two consecutive boxes. As will be further described in Section 6, such a movement consists of different point-to-point motions, because of the need for taking a first 3D image of the pallet top layer and then a second image closer to the identified gap between two boxes to refine the detection accuracy. Afterwards, three linear motions are required to insert the tool into the detected gap, drag the box and finally bring the manipulator back to the next starting position. Procedure 1 lists the consecutive motions that are required to perform the loading (and similarly, the unloading) of a single box on the AMR. ```
1 Point-to-point motion to box target frame
2 Linear downward approaching movement (200 mm)
3 Linear dragging movement (600 mm)
4 Linear upward movement (300 mm)
```  
**Procedure 1**: one-box dragging motion sequence, shovel-shaped tool
1 Point-to-point motion to box target frame
2 Linear downward approaching movement (200 mm)
3 Linear dragging movement (600 mm)
4 Linear upward movement (300 mm) ```
**Procedure 2**: one-box dragging motion sequence, shovel-shaped tool  
The collision-free point-to-point motions are generated by means of the Open Motion Planning Library framework (OMPL) ([[https://ompl.kavrakilab.org/](https://ompl.kavrakilab.org/)]([https://ompl.kavrakilab.org/](https://ompl.kavrakilab.org/)), accessed on 24 June 2021), exploiting the OMPL wrapper included into CoppeliaSim. OMPL is also integrated into ROS/Movelt and employed in the real robot application. Table 1 shows the average simulated elapsed time for each manipulator motion performing the loading and the unloading of two boxes placed in the first two columns. The partial time taken to load and unload the first box are indicated as \({}^{s}T_{l1}\) and \({}^{s}T_{u1}\), respectively, while \({}^{s}T_{l}\) and \({}^{s}T_{u}\) represent the overall time needed for loading/unloading two boxes. The left superscript \(s\) indicates the shovel-shaped tool.