## 5 Conclusions  
In accordance with the prevailing trend towards mass customization [29], product life cycles are becoming increasingly shorter and batch sizes are decreasing. Therefore, as illustrated by [30], forming processes and production processes in general need to be flexibilized, which is accompanied by the requirement for process control. RL algorithms are a promising approach for this purpose. In this paper, a novel concept for flexible V-die bending is presented which allows the bending angle to be adjusted and hence allows springback compensation. As springback is mutually dependent on numerous parameters, this results in a complex control task. At first, a parameterized FEM model is developed to accommodate variable angles, sheet thicknesses, and material properties. The general effectiveness of RL as a product property controller could be proven, as the mean bending angle deviation is reduced to 0.16\({}^{\circ}\) across all data sets. Additionally, the maximum occurring deviations could be reduced significantly as well. However, when applied to the real-world process, a noticeable sim-to-real gap was observed due to dissimilarities in springback behavior. To address this gap, retraining of the agent on the experimental data set was conducted. This improves the accuracy noticeably, but the process is subject to uncertainty  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Set** & \(|\overline{\Delta\alpha}_{\text{ctrl}}|\) & \(\text{max}\ |\overline{\Delta\alpha}_{\text{ctrl}}|\) & \(\text{R}^{2}\) \\ \hline Sim-to-Real & 1.28 & 4.5 & \(-\)0.03 \\ Training & 0.48 & 3.13 & 0.88 \\ Validation & 0.57 & 1.86 & 0.86 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Error metrics for bending angle deviations.  
Figure 16: Comparison of the experimental springback of the _validation dataset_ and the predicted springback of the SAC algorithm retrained on experimental data (dashed line).  
Figure 17: PDF of bending angle deviations.  
that the agent cannot detect in the real environment. In the simulative environment, it was shown that the prediction quality of the agent could be improved when the agent possesses knowledge of the actual material properties. Earlier studies by [20; 31] show that force contains valuable information about the material properties and therefore springback behavior. Deriving from this, the integration of force sensors as additional input for the agent seems to be a promising approach to take process fluctuations into account and further reduce the deviation. The use of RL as a product property controller improves the dimensional accuracy of the bending workpieces in the shown process, which is why its application to other forming processes should be further investigated. It is of particular interest to consider more complex forming processes with multiple DOF, which allows for advanced manipulation.  
Conceptualization, C.-V.V., D.A.M. and V.A.; methodology, D.A.M. and V.A.; investigation, C.-V.V.; writing--original draft preparation, C.-V.V.; writing--review and editing, D.A.M., V.A. and P.G.; visualization, C.-V.V. and D.A.M.; supervision, P.G.; project administration, P.G.; funding acquisition, P.G. All authors have read and agreed to the published version of the manuscript.  
The results of this paper are achieved within the project \"ProKI--Demonstrations und Transfernetzwerk KI fur die Umformtechnik ProKI-Darmstadt\" funded by the German Federal Ministry of Education and Research (BMBF). The authors wish to thank for funding and supporting this project.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflicts of interest.