## 5 Case Study
### Collaborative Workplace for Inspection of Welded Parts
It does not involve physical contact between the resources, but it is carried on in the same workspace, on the same workpiece and at the same time. However, the minimum separation distance is guaranteed. Finally, tasks 3, 4, and 5 are \"control\" tasks. They do not contribute to the actual process but concern the cobot control. The related task center is different from those previously identified. It affects the position of the HMI within the available space. Task 8, i.e., \"loading workpiece in the storage station\", is treated as task 1 since it involves the transport of the workpiece from _Human Task Center 2_ to _Human Task Center 3_. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ID** & **Task** & **Task Type** & **Active Resource** & **Level of Interaction** & **Task Center** \\ \hline
1 & Positioning the workpiece on the & Transport & Human Operator & Sequential & HTC 1-HTC 2 \\  & inspection stand & & & & \\
2 & Checking the correct positioning & Process & Human Operator & Sequential & HTC 2 \\
3 & Selecting the inspection plans & Control & Human Operator & Sequential & HTC C \\
4 & Entering workpiece ID number & Control & Human Operator & Sequential & HTC C \\
5 & Starting the control cycle & Control & Human Operator & Sequential & HTC C \\
6 & Achieving all inspection positions & Process & Cobot UR10 & Collaborative & RTC 1 = HTC2 \\
7 & Monitoring the operation & Process & Human Operator & Collaborative & HTC 2 \\  & Loading the workpiece on the & & & & \\  & outfeed stand & Transport & Human Operator & Sequential & HTC 2-HTC 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The information emerging from the task analysis. Figure 8: Task assignment related to the quality check of welding points performed in a collaborative manner. Task center allocationThen, the passive resource, which is needed to carry out a specific task, is associated with the task center related to that task by setting the matrix \(L_{cp}\) of task center-passive resource assignments (see Section 4.2). In particular, the infeed and outfeed stands are associated, respectively, to the _Human Task Center 1_ and 3, whereas the inspection stand is associated with _Human Task Center 2_ (that coincides with _Robot Task Center 1_). Finally, the Human-Machine Interface is associated with _Human Task Center C_. The robot pedestal supports the cobot. Constrained optimization problem solvingThis phase consists of defining the task centers position. As a result, the related passive resources are also placed. The available space is a rectangular area of 49 square meters. There are no pre-existing obstacles. The position of the logistic spaces (i.e., the set of basic locations within the workplace where the workpiece enters/exits as defined in Section 4.2) is defined considering the possible scenarios presented in Section 4.1.1. The solution of the constrained optimization (see Equations (1) and (2)), which minimizes the occupied floor space (see Equation (3)), is found by means of a Matlab solver. Rough layout definitionThe elementary workspaces are identified by defining the matrix \(F_{ap}\) of active resource-passive resource assignments (see Section 4.2). The envelope of the four _Unitary Human Spaces_ (UHSs), which are needed to carry out all the tasks assigned to a human, identifies the Human Space. The Robot Space is software-defined. The intersection between the elementary spaces identifies the Collaborative Space, while their union identifies the Operational Space. The logistic spaces intersect the Human Space. Infeed space and outfeed space are placed on the same side according to the presented possible scenarios (see Section 4.1.1). Figure 9 shows the layout obtained by applying the proposed approach. At the end of the design process, the workplace can be completed with additional fixtures and safety devices if these are really needed.