## 5 Application of STPA with POMDP in Collaborative Tasks  
We apply the SPTA analysis in a human-robot collaborative manufacturing task in order to identify the safe and unsafe states along with the respective control actions. Then, we deploy the proposed POMDP interpretation methodology to extract a policy graph to be utilized as a supervision tool during the operational phase.  
As shown in Figure 3, a human worker and a collaborative arm manipulator in a fenceless manufacturing cell is considered for our application scenario. To this end, we apply the STPA hazard analysis technique to a Safe Robot Manipulator (SRM) in an unconstrained cell with a human operator. To keep our analysis as straightforward as possible, yet with realistic parameters, the SRM has specific inherent safety features such as force/torque control, proximity sensing, adaptive operation speed and vision-based monitoring. The human operator employs specific tools for the collaboration with the robot such as gestures, AR-wearable interfaces and hand-held devices. These safety tools are considered as standard technologies in the contemporary collaborative robots, where the means to established the safe collaboration with human are also well studied [3]. We identified two aspects in collaboration for our application:  
* **Sequential tasks**, in which the robot performs one task and after its completion the human performs the next task (e.g., the robot places the components on the workstation and, later, the human handles these components).  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Description** \\ \hline \(S\) & The set of different states of the environment \\ s & A specific system state \\ \(A\) & The set of different actions that can take place \\ \(a\) & A specific action \\ \(\Omega\) & The set of all observations appear upon the action space \\ \(\omega\) & A unique observation based on an action \(a\) \\ \(b_{0}\) & The probability distribution of the initial state \(s\) \\ \(T\) & The probability distribution of the transition among states \\ \(O\) & The probability distribution of the observations \\ \(\pi\) & Optimal policy \\ \(\overline{S}\) & The safety related partitioned state space \\ \(S_{U}\) & A specific unsafe state \\ \(S_{R}\) & A specific recovery state \\ \(S_{S}\) & A specific safe state \\ \(\overline{A}\) & The safety related action space \\ \(A_{UCA}\) & A specific unsafe control action \\ \(A_{RCA}\) & A specific recovery control action \\ \(A_{SCA}\) & A specific safe control action \\ \hline \hline \end{tabular}
\end{table}
Table 1: Table with mathematical notations.  
* **Simultaneous collaboration tasks**, in which the robot and the operator work together on the same component in order to complete a task (e.g., the robot holds a heavy component tight while the human processes its subordinate parts).  
We follow the standard formalization of STPA steps to perform our analysis, which are summarized below for the sake of completeness of the present study:  
1. Investigate the system structure, goals, components, requirements, functions and components interaction.
2. Elicit the system requirements and safety constraints.
3. Identify the potential accidents and unacceptable losses and the hazards at system level.
4. Draw the functional control diagram of the system.
5. Apply step 2 and step 3 of STPA to the control structure.
6. Refine the safety requirements and constraints.