## 4 Conclusions
Further research may explore additional enhancements to DNN models, such as incorporating attention mechanisms or hybrid approaches, to further boost their performance. While curriculum-based training has shown benefits in other contexts, its impact on solving IK problems within the scope of this project using DNNs appears to be minimal. Our experiments show that, in this case, training with evenly distributed curriculums, along with the callback method for curriculum adjustment, yields only slight improvements in performance. Specifically, the choice of curriculum boundaries and the threshold for transitioning between curriculums do not significantly affect the model's training time or accuracy. Thus, the suggested curriculum training strategies do not provide a substantial advantage in supervised learning for IK problems. Further investigation is needed into alternative curriculum designs, which could yield different outcomes. The practical value of the DNN approach to the IK problem has been assessed by comparing its performance to that of classic numeric solvers. The results indicate that it is both faster and more reliable, and can compete with classic solvers in terms of precision. Finally, the possible causes of error when transitioning from a simulated environment to a real-world scenario have been studied. The difference between the commanded joint positions and the ones achieved by the robot is minimal; however, even this small displacement causes orientation errors. The second source of errors, ascribed to mechanical aspects of the real robot that cannot be taken into account in a simulated model, adds an additional inaccuracy between the desired target and the reached pose. All of these factorshave to be taken into account when trying to deploy one of the methods presented in this study to real-world manipulation scenarios. Conceptualization, A.C.-G., J.G.V., F.J.N.-C. and C.B. ; methodology, A.C.-G. and J.G.V. ; software, A.C.-G.; validation, A.C.-G. and J.G.V. ; formal analysis, A.C.-G.; investigation, A.C.-G. and J.G.V. ; resources, A.C.-G. and J.G.V. ; data curation, A.C.-G. and J.G.V. ; writing--original draft preparation, A.C.-G.; writing--review and editing, J.G.V. ; visualization, A.C.-G.; supervision, J.G.V., F.J.N.-C. and C.B. ; project administration, J.G.V. and C.B. ; funding acquisition, J.G.V. and C.B. All authors have read and agreed to the published version of the manuscript. The research leading to these results received funding from \"iRoboCity2030-CM Cont\" (TEC 2024/TEC-62) of Comunidad de Madrid, \"iREHAB\" (DTS22/00105) of Instituto de Salud Carlos III, and EU structural funds. Not applicable. The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author(s). In the process of writing, the artificial intelligence tool ChatGPT was employed as a means of enhancing and verifying the accuracy of orthography and grammar of the introductory sections for each chapter and the conclusions. Its outputs were always reviewed and edited by the authors. The contributions and content of the paper are entirely by the authors. The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: \begin{tabular}{l l} DNN & Deep Neural Network \\ IK & Inverse Kinematics \\ FK & Forward Kinematics \\ MLP & Multilayer Perceptron \\ CNN & Convolutional Neural Network \\ RNN & Recurrent Neural Network \\ DOF & Degree of Freedom \\ LSTM & Long Short-Term Memory \\ BiLSTM & Bilateral Long Short-Term Memory \\ GRU & Gated Recurrent Unit \\ LR & Learning Rate \\ IQR & Interquartile Range \\ MSE & Mean Squared Error \\ \end{tabular}