## 3 Methods
### Experimental Parameter Identification  
Comparing the actuator of investigation in Figure 3 to the partitioning scheme in Figure 2, we find that \(E^{II}=E^{III}=0\) since the actuator consists of individual chambers bonded by stiff components. In this case, Equations (23) and (29) simplify to  
\[E=3\cdot E^{I}, \tag{30}\] \[B=\frac{3}{2}\cdot E^{I}(r^{I})^{2}\cdot\frac{L_{c}}{L_{c,0}}. \tag{31}\]  
Consequently, the bending stiffness \(B\) of the actuator results from its extensional stiffness \(E\) and from the radius \(r^{I}\) of the circle on which the center points of the chambers are arranged. Independently from the actuator's design, the bending stiffness is always a function of the stretch ratio \(\frac{L_{c}}{L_{c,0}}\). The subscript \((. )_{c}\) refers to the length of the chambers, which needs to be distinguished from the length of the actuator \(L_{0}\), since the actuator also consists of stiff components which do not stretch. We use axial measurements in order to determine the extensional stiffness \(E\) of the actuator. However, the extensional stiffness of the individual chambers could also be determined by a model, as done in a preliminary study of the authors [18] and by many others [20; 21; 22]. If the actuator was more complex, as in Figure 2, the experimental parameter investigation would have to be extended. After axial measurements for the extensional stiffness \(E\), one (or several) bent positions would have to be analyzed in order to determine \(\left(E^{I}(r^{I})^{2}+E^{II}(r^{II})^{2}\right)\) from Equation (29) as a combined quantity and to determine the bending stiffness \(B\). In order to find the relationship between pressurization and axial force, we conducted axial force measurements according to Figure 5a, with the actuator fixed at its initial length (\(L=L_{0}\) and \(L_{c}=L_{c,0}\)). We used a _VTEM_ (_Festo GmbH & Co. KG, Germany_) pneumatic terminal to pressurize the chambers of the actuator (always equally) and an _S2M_ (_Hottinger Brul & Kjaer GmbH_, Germany_) 50 N sensor to measure axial forces. A measurement consists of ten cycles. As shown in Figure 5b, in each cycle the pressure is increased from 0 kPa to 96 kPa and decreased back to 0 kPa in steps of 24 kPa, resting 4 s at each pressure level. In order to suppress any transient effects, we defined the mean value of the last second of each step as the force measured, and calculated the mean value of all measurements for each pressure level. For both actuators tested, pressure and force are approximately proportional to each other. The maximum force is approximately 33 N.  
Additionally to the axial force measurements, we measured the length of the actuators (\(L\) and \(L_{c}\)) when purely pressurized (without external forces applied) with a sliding caliper  
Figure 5: Setup of axial force measurements (**a**) and an individual cycle of a corresponding measurement, with the raw force signal in blue and the mean value for each pressure level in red (**b**). for similar steps of pressure. This method was chosen in order to consider limited testing equipment. However, we verified the results by measurements with the same setup as presented in Section 3.2. The chambers of both actuators stretch approximately 20% at maximum pressure, undergoing a progressive curve. The extensional stiffness \(E\) of the actuator is the ratio of force to stretch. Due to the progressive curve of the stretch, the extensional stiffness \(E\) is not constant, where \(E\) is lower for higher forces. Since the model considers a constant extensional stiffness, we used the mean value of the curve, which is approximately \(E=200\) N for both actuators tested. While the identification method described is practical, it causes inaccuracies of the parameters in two ways. First, the extensional stiffness \(E\) is considered constant. Second, we determine it as the relationship of length to axial force, both with respect to pressure.