Mathematical model development for a six-link industrial robotic arm with mechanical gripper

Z.L. Khakimov, V.V. Shukhin, M.A. Labazanov

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Abstract: The need to develop an accurate mathematical model for this type of manipulator is driven by increasing demands on the precision, speed, and autonomy of robotic systems.
Aim. This study is to develop a comprehensive mathematical model of a six-link robotic manipulator, including a kinematic and dynamic description, as well as a model of its mechanical gripper.
Research methods. This study utilizes an integrated approach combining classical robotics methods with consideration of the specific features of a force gripper to solve contact interaction problems. The Denavit-Hartenberg methods, the Lagrange-Euler equations, and a polygonal representation are also used.
Results. This article presents an approach to developing a comprehensive mathematical model of a six-link robotic manipulator equipped with a mechanical gripper. A unified formalism for modeling, control, and analysis of the manipulator is proposed. The model includes a kinematic, dynamic, and geometric description necessary for solving problems of precise positioning and force interaction with manipulated objects. Numerical simulations conducted in MATLAB/Simulink confirm the model’s validity and demonstrate its applicability for trajectory and control system synthesis.
Conclusion. The developed model is a universal tool and can be adapted to specific industrial manipulators by adjusting the D-H parameters and inertial characteristics, opening up broad possibilities for its practical application in robotics.

Keywords: robot manipulator, six-link kinematic chain, direct and inverse kinematic problems, manipulator dynamics, mathematical modeling, control system

For citation. Khakimov Z.L., Shukhin V.V., Labazanov M.A. Mathematical model development for a six-link industrial robotic arm with mechanical gripper. News of the Kabardino-Balkarian Scientific Center of RAS. 2026. Vol. 28. No. 1. Pp. 75–89. DOI: 10.35330/1991-6639-2026-28-1-75-89

©   Khakimov Z.L., Shukhin V.V., Labazanov M.A., 2026

References

1. Kutafin A.A., Zakharkina S.V. Control of motors in a mobile robot using a PID controller. In: Innovative Development of Engineering and Technology in Industry (INTEX-2021): Proceedings of the All-Russian Scientific Conference of Young Researchers with International Participation, Moscow, April 12–15, 2021. Vol. Part 4. Moscow: Rossiyskiy gosudarstvennyy universitet imeni A. N. Kosygina (Tekhnologii. Dizayn. Iskusstvo.). 2021. Pp. 208–212. EDN: XKLAGG. (In Russian)
2. Berkaev A.R., Nenashev A.A., Klyuchikov A.V. Development of a localization and positioning system for a mobile device. In: Mathematical Methods in Engineering and Technology (MMTT). 2020. Vol. 12–3. Pp. 152–157. EDN: QDGESL. (In Russian)
3. Guo P., Shi H., Wang Sh., Tang L., Wang Z. An ROS architecture for autonomous mobile robots with UCAR platforms in smart restaurants. Machines. MDPI AG – 2022. Vol. 10. No. 10. P. 844. DOI: 10.3390/machines10100844. EDN: ADSREE
4. Alkhalili A.S., Lukyanov E.A. Motion control of a wheeled mobile robot based on simulation modeling. Bulletin of the BSTU named after V.G. Shukhov. 2022. No. 8. Pp. 112–121. EDN: XJSZPY. (In Russian)
5. Lapshinov S.A., Shakhnov V.A., Yudin A.V. Directions for intelligent mobile robot motion control. Neurocomputers: Development, Application. 2021. Vol. 23. No. 1. Pp. 50–62. EDN: FKKKGV. (In Russian)
6. Deshmukh A., Gupta M. PID Controller: A review of literature. International Journal of Scientific Research in Computer Science, Engineering and Information Technology (IJSRCSEIT). Vol. 6. No. 3. Pp. 48–53. DOI: 10.32628/IJSRCSEIT.0639
7. Shahbazi M. Machine learning-based approaches for obstacle detection and avoidance in autonomous vehicles: A review. Expert Systems with Applications. 2021. 172:114535. DOI: 10.1016/j.eswa.2021.114535
8. Rubio JdJ, Garcia E., Aquino G. et al. Learning of operator hand movements via least angle regression to be taught in a manipulator. Evol Syst. 2018. Pp. 1–16.
9. Rubio JdJ. Robust feedback linearization for nonlinear processes control. ISA Trans. 2018. No. 74. Pp. 155–164.
10. Alvardat M.Ya., Mbolo O.E.L., Kochneva O.V. et al. Study of the singularity of robotic manipulators. Automation. Modern Technologies. 2024. Vol. 78. No. 4. Pp. 173–179. DOI: 10.36652/0869-4931-2024-78-4-173-179. EDN: PIXMWL. (In Russian)
11. Boshlyakov A.A., Novak A.V. Genetic algorithm for solving the problem of planning the trajectory of a manipulator with redundant degrees of freedom taking into account obstacles. Naukosphere. 2024. No. 4-1. Pp. 129–135. DOI: 10.5281/zenodo.10992535. EDN: LWSMST. (In Russian)
12. Kalyashina A.V., Smirnov Yu.N. Programming a robot controller for the implementation of the laser cutting process. Engineering Bulletin of the Don. 2024. No. 4(112). Pp. 90–98. EDN: JFUPHM. (In Russian)
13. Afonin D.V., Pechurin A.S., Yatsun S.F. Dynamic analysis of a two-link coupled system. International Journal of Open Information Technologies. 2024. Vol. 12. No. 5. Pp. 49–56. EDN: NOHWHH
14. Arkhipov M.V., Vartanov M.V., Mishchenko R.S. Promyshlennyye roboty: upravleniye manipulyatsionnymi robotami: uchebnik dlya srednego professional’nogo obrazovaniya [Industrial Robots: Control of Manipulation Robots: Textbook for Secondary Vocational Education]. 2nd ed., corrected. and add. Moscow: Izdatelstvo Yurait, 2025. 170 p. ISBN: 978-5-534-13082-9. (In Russian)
15. Moskvichev A.A., Kvartalov A.R., Ustinov B.V. Zakhvatnyye ustroystva promyshlennykh robotov i manipulyatorov [Gripping Devices of Industrial Robots and Manipulators]: textbook. Moscow: FORUM; INFRA-M, 2020. 176 p. (In Russian)

Information about the authors

Zaur L. Khakimov, Candidate of Technical Sciences, Associate Professor, Department of Automation of Technological Processes and Production, Grozny State Oil Technical University named after academician M.D. Millionshchikov;
100, Isaev avenue, Grozny, 364051, Russia;
deffender_95@mail.ru, ORCID: https://orcid.org/0009-0007-1665-8631, SPIN-code: 3540-6580
Vladimir V. Shukhin, Candidate of Technical Sciences, Associate Professor, Department of Automation of Technological Processes and Production, Grozny State Oil Technical University named after academician M.D. Millionshchikov;
100, Isaev avenue, Grozny, 364051, Russia;
shukhin86@bk.ru, ORCID: https://orcid.org/0009-0003-0273-0058, SPIN-code: 2895-3434
Magomed A. Labazanov, Senior Lecturer, Department of Automation of Technological Processes and Production, Grozny State Oil Technical University named after academician M.D. Millionshchikov;
100, Isaev avenue, Grozny, 364051, Russia;
labazanov.90@inbox.ru, ORCID: https://orcid.org/0009-0005-9714-5146, SPIN-code: 5981-5217

Funding

The study was performed without external funding.