## 5 Detailed System Design
### Speed and Torque Features Setting  
According to the technical specification ISO TS 15066 [16], collaborative robots are designed to adequately reduce risks to an operator depending on the type of collaborative operations in which both are involved. In the current paper, the Power and Force Limiting (PFL) is stated as the collaborative operation type for autonomous mobile robots. This means that physical contact between the cobot and an operator can occur either intentionally or unintentionally. Technical specification annexes establish thresholds for the cobot joints speed to ensure that contact with the human body cannot be harmful. The same references are adopted in the current paper to assign a safety speed value to the interface. Speed thresholds laid down by ISO TS 15066 are based on a simple two-body model. In the model, the effective mass of the robot is moving to come in fully inelastic contact with the effective mass of the human body region at a relative velocity, \(v_{rel}\). The effective mass of the robot, \(m_{r}\), can be estimated as a function of the total mass of the moving parts of the robot, \(M\), and the effective payload, \(m_{I}\), calculated as in (1). The effective mass of twenty-nine body regions, \(m_{h}\), is set out in Table 10 of the ISO TS 15066 [16]. \[m_{r}=\frac{M}{2}+m_{I}. \tag{1}\]  
The maximum speed of the interface is assumed as the maximum admissible value of relative speed, \(v_{rel,max}\), between human and robot; it is computed as follow:  
\[v_{rel,max}=\frac{F_{max}}{\sqrt{m_{rel}k}}. \tag{2}\]It depends on the maximum contact force, \(F_{max}\), and the stiffness, \(k\), for specific body region, both provided in [16], and on the reduced mass of the human body and the robot, \(m_{red}\), calculated as in (3):  
\[m_{red}=\bigg{(}\frac{1}{m_{h}}+\frac{1}{m_{r}}\bigg{)}^{-1}. \tag{3}\]  
To reduce the possibility of contact during the mobile manipulator operation, it is recommended to set at the stowed position of the cobot the configuration with minimum bounding-box, i.e., the configuration characterized by the minimum height and the minimum outreach (Figure 12). Due to this stowed configuration, the system is more stable during motion and the most hazardous contact, which involves skull or face, is avoided in case of human standing upright. In fact, considering the highest mobile robot of the representative group and assuming a first approximate height of 100 mm for the interface, the total height of the system is lower than the level of human head whatever the selected cobots [37]. The possible regions of contact between the system and the human body have been found by considering the human average height (\(h=1712\) mm) and the typical ratios of human body [37]. The maximum allowed speed for the interface has been calculated for each of the possible human body's regions of contact (Table 3). \begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{2}{*}{**Body Region**} & **Maximum** & \multirow{2}{*}{**Stiffness**} & **Effective** & **Reduced** & **Maximum** \\  & **Force** & & **Mass** & **Mass** & **Speed** \\  & **\(F_{max}\), [N]** & \(k\), [N/mm] & \(m_{br}\), [kg] & \(m_{red}\), [kg] & \(v_{max}\), [m/s] \\ \hline Skull and forehead & 130 & 150 & 4.4 & 3.91 & 0.17 \\ Face & 65 & 75 & 4.4 & 3.91 & 0.12 \\ Lower legs & 260 & 60 & 75 & 24.10 & 0.216 \\ Thighs and knees & 440 & 50 & 75 & 24.10 & 0.401 \\ Chest & 280 & 25 & 40 & 18.81 & 0.408 \\ Abdomen & 220 & 10 & 40 & 18.81 & 0.408 \\ Pelvis & 360 & 25 & 40 & 18.81 & 0.507 \\ Upper arms & 300 & 30 & 3 & 2.77 & 1.041 \\ Lower arms & 320 & 40 & 2 & 1.89 & 1.163 \\ Hands & 280 & 75 & 0.6 & 0.59 & 1.331 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Maximum admissible velocities according to the ISO/TS 15066:2016. Figure 12: Stowed position for the collaborative robot UR10.