## 6 Conclusions  
DNNs hold considerable promise for improving the computational cost and precision of long-standing solutions to the inverse kinematics (IK) and obstacle avoidance problems. Theoretically, deep learning provides an ideal framework to tackle these complex problems, given its ability to model high-dimensional, non-linear relationships, and the significant progress made in this field in the latest years. DNNs, similar to traditional numeric methods, can be implemented in a much more generic and robot-agnostic manner than analytical methods. However, they can potentially achieve faster and more accurate solutions than traditional numeric methods, which often rely on iterative processes and approximations.  
Our findings prove that these expectations are well-founded, as interesting results are being achieved even with relatively simple DNN architectures. However, there is still a gap between the expectation and the practical outcomes. This is evidenced by the lack of experimental testing in real robots, with most advances being made in simulated environments. While simulation provides valuable insights, it cannot fully account for the complexities and unpredictability of real-world scenarios, such as sensor noise, environmental variations, and hardware limitations.  
Further investigation is required to refine the methodologies and enhance their robustness, ensuring that DNNs can be effectively deployed in real-world robotic systems. This will involve not only optimizing network architectures and training techniques but also developing hybrid approaches that combine deep learning with traditional control theory. Additionally, testing on actual robots under a range of dynamic and challenging conditions is essential to fully understand the practical limitations and potential of deep learning for these applications. By addressing these challenges, we can unlock the full capabilities of deep learning in solving robot IK, motion control, and motion planning, paving the way for more efficient and autonomous robotic systems.  
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.  
**Funding:** This research was funded by \"iREHAB: AI-powered Robotic Personalized Rehabilitation\", ISCIII-AES-2022/003041 funded by ISCIII and UE; \"COMPANION-CM: Inteligencia artificial y modelos cognitivos para la interaccion simetrica humano-robot en el ambito de la robotica asistencial\", Y2020/NMT-666, funded by \"Proyectos Sinergicos de I+D la Comunidad de Madrid\"; and EU structural funds; \"IROPER: Robotica inteligente para necesidades personales\", PLEC2021-007819, funded by MCIN/AEI/10.13039/501100011033 and by \"NextGenerationEU/PRTR\" of European Union.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
**Acknowledgments:** 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 final paragraph of the Section 6. Its outputs were always reviewed and edited by the authors. The contributions and content of the paper are entirely from the authors.  
**Conflicts of Interest:** The authors declare no conflicts of interest.