Mathematical model of adaptive hierarchical high-level control of a three-link collaborative robot-manipulator
DOI:
https://doi.org/10.30837/2522-9818.2025.2.058Keywords:
Industry 5.0; collaborative robot; mathematical model; hierarchical control; fuzzy logic; adaptive control; manipulator; PyCharm; Python;, Fuzzy Logic.Abstract
In the context of the development of the Industry 5.0 concept, which envisages close interaction between humans and intelligent automated systems, research into mechanisms for flexible and safe control of collaborative robot manipulators is becoming particularly important. The objective of this study is to construct a mathematical model of hierarchical high-level control for a three-link collaborative robot that allows the manipulator's behavior to be adapted to dynamic changes in the production environment and the presence of humans in the work area. The purpose of this article is to develop a mathematical model that combines the classical approach to modeling dynamics with the following methods: using Euler-Lagrange equations and modern adaptive control algorithms implemented through fuzzy logic, which allows optimizing the speed and trajectory of the executive bodies under variable load and partial uncertainty of the environment. The proposed model implements a multi-level control architecture that takes into account not only the physical parameters of the manipulator, but also the cognitive aspects of interaction with the operator and the environment by constructing a Fuzzy-Rule-based controller. The article presents the formalization of mathematical expressions, describes all levels of the control system, their purpose and interconnection, and performs numerical modeling using Python and PyCharm. The results of the modeling confirmed the effectiveness of the proposed system in the presence of humans, ensuring a safe distance, adaptation to the load, and compliance with the specified production parameters. Conclusions indicate that the proposed model can significantly improve the quality of manipulator control in Industry 5.0 conditions, especially when working in hybrid environments. The developed model can be adapted to different types of collaborative robots, which opens up prospects for its further improvement, in particular through integration with neural network approaches, deep learning, and multi-agent systems within the framework of distributed intelligent manufacturing.
References
Список літератури
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References
Rijwani, T., Kumari, S., Srinivas, R., Abhishek, K., Iyer, G., Vara, H., Gupta ,M. (2025), "Industry 5.0: A review of emerging trends and transformative technologies in the next industrial revolution". International Journal on Interactive Design and Manufacturing (IJIDeM), 19(2), Р. 667–679. DOI: https://doi.org/10.1007/s12008-024-01943-7
Sun, X., Song, Y. (2025), "Unlocking the Synergy: Increasing productivity through Human-AI collaboration in the industry 5.0 Era". Computers & Industrial Engineering, 200, 110657 р. DOI: https://doi.org/10.1016/j.cie.2024.110657
Gonçalves, A., Pereira, T., Lopes, D., Cunha, F., Lopes, F., Coutinho, F., Ferreira, N. M. F. (2025), "Enhancing Nut-Tightening Processes in the Automotive Industry: Integration of 3D Vision Systems with Collaborative Robots". Automation, 6(1), 8. DOI: https://doi.org/10.3390/automation6010008
Nevliudov, I., Yevsieiev ,V., Baker, J. H., Ahmad, M. A., Lyashenko, V. (2020), "Development of a cyber design modeling declarative Language for cyber physical production systems". Journal of Mathematical and Computational Science, 11(1), Р. 520–542. DOI: https://doi.org/10.28919/jmcs/5152
Yuan, F., Ren, G., Deng, Q., Wang, X. (2025), "Steam Generator Maintenance Robot Design and Obstacle Avoidance Path Planning". Sensors, 25(2), 514 р. DOI: https://doi.org/10.3390/s25020514
Recker, T., Raatz, A. (2025), "Design and control of flexible handling systems based on mobile cooperative multi-robot-systems". CIRP Annals. DOI: https://doi.org/10.1016/j.cirp.2025.04.059
Pan, Y. J., Buchanan, S., Chen, Q., Wan, L., Chen, N., Forbrigger, S., Smith, S. (2025), "Survey on recent advances in planning and control for collaborative robotics". IEEJ Journal of Industry Applications, 14(2), Р. 139–151. DOI: https://doi.org/10.1541/ieejjia.24005652
Nevlyudov, I., Yevsieiev, V., Gurin, D. (2025), "Model development of dynamic representation a model description parameters for the environment of a collaborative robot manipulator within the industry 5.0 framework". Control, Navigation and Communication System. 1(79), Р. 42–48. DOI: https://doi.org/10.26906/SUNZ.2025.1.42-48
Hu, S., Wan, Y., Liang, X. (2025), "Adaptive nonsingular fast terminal sliding mode trajectory tracking control for robotic manipulators with model feedforward compensation". Nonlinear Dynamics, Р. 1–19. DOI: https://doi.org/10.3390/electronics11223672
Ben, Hazem Z., Guler, N., Altaif, A. H. (2025), "A study of advanced mathematical modeling and adaptive control strategies for trajectory tracking in the Mitsubishi RV-2AJ 5-DOF Robotic Arm". Discover Robotics, 1(1), 2. DOI: https://doi.org/10.1007/s44430-025-00001-5
Zhou, H., Lin, X. (2025), "Intelligent redundant manipulation for long-horizon operations with multiple goal-conditioned hierarchical learning". Advanced Robotics, 39(6), Р. 291–304. DOI: https://doi.org/10.1080/01691864.2025.2475295
Sun, Z., Pang, B., Yuan, X., Xu, X., Song, Y., Song, R., Li, Y. (2025), "Hierarchical reinforcement learning with curriculum demonstrations and goal-guided policies for sequential robotic manipulation". Engineering Applications of Artificial Intelligence, №153, 110866 р. DOI: https://doi.org/10.1016/j.engappai.2025.110866
Wei, Z., Luo, X., Liu, C. (2025), "Hierarchical Temporal Logic Task and Motion Planning for Multi-Robot Systems". Accepted by Robotics: Science and Systems. 2025. DOI: https://doi.org/10.48550/arXiv.2504.18899
Fan, S., Meng, M., Fu, Y., Deng, C. (2025), "Distributed adaptive tracking control for fuzzy nonlinear MASs under round-robin protocol". IEEE Transactions on Fuzzy Systems. 2025. DOI: https://doi.org/10.1109/TFUZZ.2025.3525989
Liu, H., Xu, S., Song, J., Ma, B. (2025), "Fuzzy control of uncertain dual-arm cooperative robots with quantitative performance and input deadzone". Journal of the Brazilian Society of Mechanical Sciences and Engineering, № 47(3), 126 р. DOI: https://doi.org/10.1007/s40430-024-05377-w
Urrea, C. (2025), "Hybrid Fault-Tolerant Control in Cooperative Robotics: Advances in Resilience and Scalability". In Actuators. Vol. 14, No. 4, 177 р. DOI: https://doi.org/10.3390/act14040177
Babiyola, A. (2025), "Recurrent Neural Networks for Real-Time Position Estimation of Robotic Arm End-Effector Coordinates". In 2025 International Conference on Artificial Intelligence and Data Engineering (AIDE). Р. 34–40. DOI: https://doi.org/10.1109/AIDE64228.2025.10986815
Alwardat, M. Y., Alwan, H. (2025), "Geometric jacobians derivation and kinematic singularity analysis for 6-dof robotic manipulator". International Journal of Advanced Research in Computer Science, №16(1). DOI: https://doi.org/10.26483/ijarcs.v16i1.7178
Wang, Z., Xu, L., Zhu, X., Quan, L., Chen, W. H., Xu, L., Ding, S. (2025), "Euler-Lagrange-Model-Based Torque Assignment Control for Dual In-Wheel PM Motors With Voltage Vectors Integrated Modulation". IEEE Transactions on Industrial Electronics. Р. 1–14. DOI: https://doi.org/10.1109/TIE.2025.3555041
Lavaill, M., Chen, X., Heinrich, S., Pivonka, P., Leyendecker, S. (2025), "Muscle path predictions using a discrete geodesic Euler-Lagrange model in constrained optimisation: comparison with OpenSim and experimental data". Multibody System Dynamics, Р. 1–23. DOI: https://doi.org/10.1007/s11044-025-10055-3
Tran, H. C., Tran, A. D., Le, K. H. (2025), "DetectVul: A statement-level code vulnerability detection for Python". Future Generation Computer Systems, № 163, 107504 р. DOI: https://doi.org/10.1016/j.future.2024.107504
Mechri, A., Ferrag, M. A., Debbah, M. (2025), "Secureqwen: Leveraging llms for vulnerability detection in python codebases". Computers & Security, № 148, 104151 р. 2025. DOI: https://doi.org/10.1016/j.cose.2024.104151
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