Research Article

Reaching The Pinnacle of the Digital WorldOpen Mathematical Problems in AI-Driven Robot Control

Authors

Ismail A Mageed * PhD, IEEE, IAENG & UK President of the ISFSEA Society, UK.
Hong Li IBM, Armonk, United States.

https://doi.org/10.22105/scfa.v2i2.54

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Abstract

The convergence of Artificial Intelligence (AI) and robotics has brought about a fresh period of autonomous systems able to execute sophisticated jobs in changing and unpredictable settings. Although significant advancements have been achieved, a multitude of unresolved mathematical issues limit the use of AI-driven robots in safety-critical and real-world uses. Focusing on robustness, safety, learning, Human-Robot Interaction (HRI), and complicated system management, this study investigates several significant unresolved concerns at the crossroads of AI, control theory, and mathematics. Creating intelligent, dependable, and trustworthy autonomous robots depends on addressing these obstacles. Several influential open problems are introduced within the folds of this paper, with final thoughts on mathematizing AI-driven robot control.

Keywords

Artificial intelligence Artificial intelligence-driven robots Machine learning Robotics Reinforcement learning Deep neural networks

References (66)

[1] Kim, S. W., Kong, J. H., Lee, S. W., & Lee, S. (2022). Recent advances of artificial intelligence in manufacturing industrial sectors: A review. International journal of precision engineering and manufacturing, 23(1), 111–129. https://doi.org/10.1007/s12541-021-00600-3

[2] Cantucci, F., Marini, M., & Falcone, R. (2025). Trustworthiness assessment of an adaptive and explainable robot in a real environment. International journal of social robotics, 1–12. https://doi.org/10.1007/s12369-025-01257-y

[3] Beck, J., Vuorio, R., Liu, E. Z., Xiong, Z., Zintgraf, L., Finn, C., & Whiteson, S. (2025). A tutorial on meta-reinforcement learning. Foundations and trends® in machine learning, 18(2–3), 224–384. http://dx.doi.org/10.1561/2200000080

[4] Jensen, K. T. (2023). An introduction to reinforcement learning for neuroscience. https://doi.org/10.48550/arXiv.2311.07315

[5] Aljamal, M., Patel, S., & Mahmood, A. (2025). Comprehensive review of robotics operating system-based reinforcement learning in robotics. Applied sciences, 15(4), 1–39. https://doi.org/10.3390/app15041840

[6] Manikandan, S., Kaviya, R. S., Shreeharan, D. H., Subbaiya, R., Vickram, S., Karmegam, N., … ., & Govarthanan, M. (2025). Artificial intelligence‐driven sustainability: Enhancing carbon capture for sustainable development goals–a review. Sustainable development, 33(2), 2004–2029. https://doi.org/10.1002/sd.3222

[7] Dhanwe, S. S., Abhangrao, C. M., & Liyakat, K. K. S. (2024). AI-driven IoT in robotics: A review. Journal of mechanical robotics, 9(1), 41–48. https://www.researchgate.net/publication/379654203

[8] Chan, K. Y., Abu-Salih, B., Qaddoura, R., Al-Zoubi, A. M., Palade, V., Pham, D. S., … ., & Muhammad, K. (2023). Deep neural networks in the cloud: Review, applications, challenges and research directions. Neurocomputing, 545, 126327. https://doi.org/10.1016/j.neucom.2023.126327

[9] Dai, H., Landry, B., Yang, L., Pavone, M., & Tedrake, R. (2021). Lyapunov-stable neural-network control. https://doi.org/10.48550/arXiv.2109.14152

[10] Mahmoud, A. T., Mohammed, A. A., Ayman, M., Medhat, W., Selim, S., Zayed, H., … ., & Elaraby, N. (2024). Formal verification of code conversion: A comprehensive survey. Technologies, 12(12), 1–28. https://doi.org/10.3390/technologies12120244

[11] Li, B., Wen, S., Yan, Z., Wen, G., & Huang, T. (2023). A survey on the control lyapunov function and control barrier function for nonlinear-affine control systems. IEEE/CAA journal of automatica sinica, 10(3), 584–602. https://doi.org/10.1109/JAS.2023.123075

[12] Wang, C., Qiang, X., Xu, M., & Wu, T. (2022). Recent advances in surrogate modeling methods for uncertainty quantification and propagation. Symmetry, 14(6), 1219. https://doi.org/10.3390/sym14061219

[13] Reiser, P., Aguilar, J. E., Guthke, A., & Bürkner, P. C. (2025). Uncertainty quantification and propagation in surrogate-based Bayesian inference. Statistics and computing, 35(3), 66. https://doi.org/10.1007/s11222-025-10597-8

[14] Schöning, J., & Pfisterer, H. J. (2023). Safe and trustful AI for closed-loop control systems. Electronics, 12(16), 1–15. https://doi.org/10.3390/electronics12163489

[15] Zakka, K., Wu, P., Smith, L., Gileadi, N., Howell, T., Peng, X. Bin, … ., & Zeng, A. (2023). Robopianist: Dexterous piano playing with deep reinforcement learning. https://doi.org/10.48550/arXiv.2304.04150

[16] Pfanschilling, V., Shindo, H., Dhami, D. S., & Kersting, K. (2025). NeST: The neuro-symbolic transpiler. International journal of approximate reasoning, 179, 109369. https://doi.org/10.1016/j.ijar.2025.109369

[17] Menghani, G. (2023). Efficient deep learning: A survey on making deep learning models smaller, faster, and better. Association for computing machinery computing surveys, 55(12), 1–37. https://doi.org/10.1145/3578938

[18] Barron, S. L., Oldroyd, S. V, Saez, J., Chernaik, A., Guo, W., McCaughan, F., … ., & Owens, R. M. (2024). A conformable organic electronic device for monitoring epithelial integrity at the air liquid interface. Advanced materials, 36(8), 2306679. https://doi.org/10.1002/adma.202306679

[19] Li, P., Rao, X., Blase, J., Zhang, Y., Chu, X., & Zhang, C. (2021). Cleanml: A study for evaluating the impact of data cleaning on ml classification tasks. 2021 IEEE 37th international conference on data engineering (ICDE) (pp. 13–24). IEEE. https://doi.org/10.1109/ICDE51399.2021.00009

[20] Geelen, R., Balzano, L., & Willcox, K. (2023). Learning latent representations in high-dimensional state spaces using polynomial manifold constructions. 2023 62nd IEEE conference on decision and control (CDC) (pp. 4960–4965). IEEE. https://doi.org/10.1109/CDC49753.2023.10384209

[21] Bin, M., & Parisini, T. (2023). A small-gain theory for abstract systems on topological spaces. IEEE transactions on automatic control, 68(8), 4494–4507. https://doi.org/10.1109/TAC.2023.3256760

[22] Luo, J., Xu, C., Wu, J., & Levine, S. (2024). Precise and dexterous robotic manipulation via human-in-the-loop reinforcement learning. https://doi.org/10.48550/arXiv.2410.21845

[23] Da, L., Turnau, J., Kutralingam, T. P., Velasquez, A., Shakarian, P., & Wei, H. (2025). A survey of sim-to-real methods in RL: Progress, prospects and challenges with foundation models. https://doi.org/10.48550/arXiv.2502.13187

[24] de Croon, G. C. H. E., Dupeyroux, J. J. G., Fuller, S. B., & Marshall, J. A. R. (2022). Insect-inspired AI for autonomous robots. Science robotics, 7(67), eabl6334. https://doi.org/10.1126/scirobotics.abl6334

[25] Aleixo, E. L., Colonna, J. G., Cristo, M., & Fernandes, E. (2023). Catastrophic forgetting in deep learning: A comprehensive taxonomy. https://doi.org/10.48550/arXiv.2312.10549

[26] Zhu, D., Bu, Q., Zhu, Z., Zhang, Y., & Wang, Z. (2024). Advancing autonomy through lifelong learning: A survey of autonomous intelligent systems. Frontiers in neurorobotics, 18, 1385778. https://doi.org/10.3389/fnbot.2024.1385778

[27] Song, Y. J. X., & Li, J. (2025). MDATA knowledge representation. In MDATA cognitive model: Theory and applications (pp. 24). Springer. https://us.amazon.com/MDATA-Cognitive-Model-Applications-Computer-ebook/dp/B0DN4VSWDL

[28] Xiang, Q., Zi, L., Cong, X., & Wang, Y. (2023). Concept drift adaptation methods under the deep learning framework: A literature review. Applied sciences, 13(11), 1–27. https://doi.org/10.3390/app13116515

[29] Mukherjee, A., Divya, A. B., Sivvani, M., & Pal, S. K. (2024). Cognitive intelligence in industrial robots and manufacturing. Computers & industrial engineering, 191, 110106. https://doi.org/10.1016/j.cie.2024.110106

[30] Malik, I. H. (2024). Can political ecology be decolonised? A dialogue with Paul Robbins. Geo: Geography and environment, 11(1), e00140. https://doi.org/10.1002/geo2.140

[31] Yan, S., Zhang, B., Zhang, Y., Boedecker, J., & Burgard, W. (2024). Learning continuous control with geometric regularity from robot intrinsic symmetry. 2024 IEEE international conference on robotics and automation (ICRA) (pp. 49–55). IEEE. https://doi.org/10.1109/ICRA57147.2024.10610949

[32] Wang, X., & Jia, W. (2025). Optimizing edge AI: A comprehensive survey on data, model, and system strategies. https://doi.org/10.48550/arXiv.2501.03265

[33] Winkle, K., McMillan, D., Arnelid, M., Harrison, K., Balaam, M., Johnson, E., & Leite, I. (2023). Feminist human-robot interaction: Disentangling power, principles and practice for better, more ethical HRI. Proceedings of the 2023 acm/IEEE international conference on human-robot interaction (pp. 72–82). Association for computing machinery. https://doi.org/10.1145/3568162.3576973

[34] Pilditch, T. D. (2024). The reasoning under uncertainty trap: A structural ai risk. https://doi.org/10.48550/arXiv.2402.01743

[35] Jonnavittula, A., Mehta, S. A., & Losey, D. P. (2024). SARI: Shared autonomy across repeated interaction. ACM transactions on human-robot interaction, 13(2), 1–36. https://doi.org/10.1145/3651994

[36] Proia, S. (2024). Control techniques for collaborative and cooperative robotic systems. Politecnico di Bari. https://tesidottorato.depositolegale.it/handle/20.500.14242/64911

[37] Robinson, N., Tidd, B., Campbell, D., Kulić, D., & Corke, P. (2023). Robotic vision for human-robot interaction and collaboration: A survey and systematic review. Association for computing machinery transactions on human-robot interaction, 12(1), 1–66. https://doi.org/10.1145/3570731

[38] Soori, M., Arezoo, B., & Dastres, R. (2023). Artificial intelligence, machine learning and deep learning in advanced robotics, a review. Cognitive robotics, 3, 54–70. https://doi.org/10.1016/j.cogr.2023.04.001

[39] Rahimi, I., Gandomi, A. H., Chen, F., & Mezura-Montes, E. (2023). A review on constraint handling techniques for population-based algorithms: From single-objective to multi-objective optimization. Archives of computational methods in engineering, 30(3), 2181–2209. https://doi.org/10.1007/s11831-022-09859-9

[40] Dawood, M., Pan, S., Dengler, N., Zhou, S., Schoellig, A. P., & Bennewitz, M. (2025). Safe multi-agent reinforcement learning for behavior-based cooperative navigation. IEEE robotics and automation letters, 10(6), 6256-6263. https://doi.org/10.1109/LRA.2025.3560830

[41] Cao, P., Lei, L., Cai, S., Shen, G., Liu, X., Wang, X., … ., & Guizani, M. (2024). Computational intelligence algorithms for UAV swarm networking and collaboration: A comprehensive survey and future directions. IEEE communications surveys & tutorials, 26(4), 2684–2728. https://doi.org/10.1109/COMST.2024.3395358

[42] Wan, K., Chen, Y., Zhao, J., & Yu, M. (2022). A decentralized fault-tolerant control for DC microgrids against disturbances and actuator faults. IEEE transactions on smart grid, 14(4), 2534–2544. https://doi.org/10.1109/TSG.2022.3229057

[43] Pal, S., Dorri, A., & Jurdak, R. (2022). Blockchain for IoT access control: Recent trends and future research directions. Journal of network and computer applications, 203, 103371. https://doi.org/10.1016/j.jnca.2022.103371

[44] Song, H., & Wang, Z. (2025). Dynamic event-triggered model predictive control for nonlinear discrete cyber-physical systems with hybrid attacks. IEEE transactions on automation science and engineering, 12, 15745–15756. http://dx.doi.org/10.1109/TASE.2025.3572469

[45] Jain, R., Parmar, K. J., Palaniappan, D., & Premavathi, T. (2025). Hybrid control systems: Integrating AI with traditional methods. In Harnessing AI for control engineering (pp. 37–62). IGI Global Scientific Publishing. http://dx.doi.org/10.4018/979-8-3693-7812-0.ch002

[46] Abbas, N., Abbas, Z., Zafar, S., Ahmad, N., Liu, X., Khan, S. S., … ., & Larkin, S. (2024). Survey of advanced nonlinear control strategies for UAVs: Integration of sensors and hybrid techniques. Sensors, 24(11), 1–51. https://doi.org/10.3390/s24113286

[47] Scheres, K. J. A., Postoyan, R., & Heemels, W. M. (2024). Robustifying event-triggered control to measurement noise. Automatica, 159, 111305. https://doi.org/10.1016/j.automatica.2023.111305

[48] Della Santina, C., Duriez, C., & Rus, D. (2023). Model-based control of soft robots: A survey of the state of the art and open challenges. IEEE control systems magazine, 43(3), 30–65. https://doi.org/10.1109/MCS.2023.3253419

[49] Nagami, K., & Schwager, M. (2024). State estimation and belief space planning under epistemic uncertainty for learning-based perception systems. IEEE robotics and automation letters, 9(6), 5118–5125. https://doi.org/10.1109/LRA.2024.3387139

[50] Tan, M., Zhuang, Z., Chen, S., Li, R., Jia, K., Wang, Q., & Li, Y. (2024). EPMF: Efficient perception-aware multi-sensor fusion for 3D semantic segmentation. IEEE transactions on pattern analysis and machine intelligence, 46(12), 8258–8273. https://doi.org/10.1109/TPAMI.2024.3402232

[51] Sun, R., & Ren, Y. (2024). A multi-source heterogeneous data fusion method for intelligent systems in the Internet of Things. Intelligent systems with applications, 23, 200424. https://doi.org/10.1016/j.iswa.2024.200424

[52] Shu, F., Wang, J., Pagani, A., & Stricker, D. (2022). Structure plp-slam: Efficient sparse mapping and localization using point, line and plane for monocular, rgb-d and stereo cameras. https://doi.org/10.48550/arXiv.2207.06058

[53] Wangwongchai, A., Waqas, M., Dechpichai, P., Hlaing, P. T., Ahmad, S., & Humphries, U. W. (2023). Imputation of missing daily rainfall data; A comparison between artificial intelligence and statistical techniques. MethodsX, 11, 102459. https://doi.org/10.1016/j.mex.2023.102459

[54] Kurniawati, H. (2022). Partially observable markov decision processes and robotics. Annual review of control, robotics, and autonomous systems, 5(1), 253–277. https://doi.org/10.1146/annurev-control-042920-092451

[55] Taniguchi, A., Tabuchi, Y., Ishikawa, T., El Hafi, L., Hagiwara, Y., & Taniguchi, T. (2023). Active exploration based on information gain by particle filter for efficient spatial concept formation. Advanced robotics, 37(13), 840–870. https://doi.org/10.1080/01691864.2023.2225175

[56] Bélisle-Pipon, J. C., Monteferrante, E., Roy, M. C., & Couture, V. (2023). Artificial intelligence ethics has a black box problem. AI & society, 38, 1507–1522. https://doi.org/10.1007/s00146-021-01380-0

[57] Zeraati, M., Sheibani, M. R., Jabari, F., & Heydarian-Forushani, E. (2024). A novel state estimation method for distribution networks with low observability based on linear AC optimal power flow model. Electric power systems research, 228, 110085. https://doi.org/10.1016/j.epsr.2023.110085

[58] Cifci, A. (2025). Interpretable prediction of a decentralized smart grid based on machine learning and explainable artificial intelligence. IEEE access, 13, 36285–36305. https://doi.org/10.1109/ACCESS.2025.3543759

[59] Dubey, S. R., Singh, S. K., & Chaudhuri, B. B. (2022). Activation functions in deep learning: a comprehensive survey and benchmark. Neurocomputing, 503, 92–108. https://doi.org/10.1016/j.neucom.2022.06.111

[60] Kuznetsov, S. D., Velikhov, P. E., & Fu, Q. (2023). Real-time analytics: Benefits, limitations, and tradeoffs. Programming and computer software, 49(1), 1–25. https://doi.org/10.1134/S036176882301005X

[61] Gupta, S. (2025). AI agents collaboration under resource constraints: Practical implementations. International journal of artificial intelligence research and development, 3(1), 51–63. http://dx.doi.org/10.34218/IJAIRD_03_01_004

[62] Alhussain, A. (2024). Efficient processing of convolutional neural networks on the edge: A hybrid approach using hardware acceleration and dual-teacher compression. https://stars.library.ucf.edu/etd2023/321/

[63] Flamm, B., Peter, C., Büchi, F. N., & Lygeros, J. (2021). Electrolyzer modeling and real-time control for optimized production of hydrogen gas. Applied energy, 281, 116031. https://doi.org/10.1016/j.apenergy.2020.116031

[64] Zhao, Z., Cheng, S., Ding, Y., Zhou, Z., Zhang, S., Xu, D., & Zhao, Y. (2024). A survey of optimization-based task and motion planning: From classical to learning approaches. IEEE/ASME Transactions On Mechatronics, 1-27. https://doi.org/10.1109/TMECH.2024.3452509

[65] Chacko, K., Augustine, M. T., Janardhanan, S., Patil, D. U., & Kar, I. N. (2023). Approximate dynamic programming based model predictive control of nonlinear systems. https://doi.org/10.48550/arXiv.2312.05952

[66] Sharony, E., Yang, H., Che, T., Pavone, M., Mannor, S., & Karkus, P. (2024). Learning multiple initial solutions to optimization problems. https://doi.org/10.48550/arXiv.2411.02158

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Published 2025-04-26
Issue Vol. 2 No. 2 (2025): Soft Computing Fusion with Applications
Section Articles
Document Type Research Article
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How to Cite

A Mageed, I. ., & Li, H. . (2025). Reaching The Pinnacle of the Digital WorldOpen Mathematical Problems in AI-Driven Robot Control. Soft Computing Fusion With Applications , 2(2), 74-84. https://doi.org/10.22105/scfa.v2i2.54

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