## 5 Discussion  
The novelty of the modeling approach presented in this study is the practicability of finding the beam parameters of a multi-chamber bending actuatorand that the bending stiffness depends on the axial stretch of the actuator. If the actuator to be modeled has an elementary design, axial measurements are enough to obtain sufficient model parameters for accurate three-dimensional simulations, which is demonstrated by the results in Section 4. The model approach is of advantage for adopters with limited testing equipment and provides the possibility of estimating the influence of design changes on the deformation characteristics of the actuator. However, from the authors' perspective, the results imply another two important aspects. First, experimental investigation of soft robots suffers from manufacturing errors. Hence, transferring parameters determined from one robot to another, as is done in this study, is always limited. For example, the deviation between the extreme positions of the two actuators tested is 2.1% relative to the actuator length, which means that simulations can never be reliably below this limit. This problem is well-known, and typically addressed in the literature by using the same robot for determination of parameters and validation of the model [3; 8; 10; 12]. Figure 9: Actuator 2 (without markers) with an individual chamber at maximum pressurization in vertical position (**A**) and horizontal position (**B**), both with and without load applied. The simulated results are presented in two ways: the centerline of the actuator (solid) and, for better comparison of the results, an offset curve [26] of the centerline between the two chambers visible (dashed). Second, the interrelation of pressurization, forces induced by pressure and material stiffness is complex. For example, while the simulations without external load predict the shape of the actuator well, the predicted shape deviates from the experimental results with a load applied to the tip of the actuator. Besides possible inaccuracies in the model itself, this is caused by errors in the experimentally identified relationship between pressurization and force, since the relationship is determined at the initial length but is also applied to the stretched actuator. This error also has an influence on the extensional stiffness and the bending stiffness. As long as the forces induced by pressure dominate external loads, the error is eliminated in the simulation, because the stiffness and the dominating forces both include the same error. For higher external loads, the error is not eliminated because it is included in the stiffness but only partially in the loads. Our future work is motivated by these aspects. [PERSON] et al. [12] show that hybrid modeling (combination of classical modeling and data based approaches) is a promising approach to take the complex interrelation of pressurization, forces and material stiffness into account. Vice versa, the results of the experimental investigation in this study suggest that underlaying the presented modeling approach with hybrid modeling would reduce the experimental data required, while keeping accuracy and increasing generality, since evaluation of the parameters determined becomes possible. Likewise, additional parameters such as the shear stiffness, which is neglected in this study and which is shown to be important in some scenarios, can be included with little effort. Conceptualization, F.L. ; methodology, F.L. ; validation, F.L. ; investigation, F.L. ; data curation, F.L. ; writing--original draft preparation, F.L. ; writing--review and editing, K.M.d.P. ; visualization, F.L. ; supervision, K.M.d.P. ; project administration, K.M.d.P. ; funding acquisition, K.M.d.P. All authors have read and agreed to the published version of the manuscript. Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)-404986830-SPP2100. Not applicable. The data presented in this study are available on request from the corresponding author.