Email this article On the motion stabilization of a three-link robotic manipulator with incomplete measurement
- Authors: Kolegova L.V.1
-
Affiliations:
- Ulyanovsk State University
- Issue: Vol 26, No 1 (2024)
- Pages: 60-73
- Section: Mathematical modeling and computer science
- Published: 07.01.2026
- URL: https://journals.rcsi.science/2079-6900/article/view/364129
- DOI: https://doi.org/10.15507/2079-6900.26.202401.60-73
- ID: 364129
Cite item
Full Text
Abstract
This paper considers a mathematical model of a manipulator which consists of a vertical column, two links, connected to it in series, and a gripper with a load. The column resting on a fixed base can rotate around its vertical axis. The links are connected by cylindrical hinges allowing them to rotate in the same vertical plane. The column and the links are modeled as rigid bodies with the links having unequal principal moments of inertia. The position of the manipulator in space is determined by three rotation angles of the column and the links. The manipulator can have several types of steady-state program movements. When gravitational torques are compensated by control torques applied in the cylindrical hinges, the manipulator has a program equilibrium position. The manipulator can also have a program motion when the column rotates at a given constant angular velocity, and the links have given relative equilibrium positions in their plane. The stabilization problem of manipulator motion is investigated by means of control torques with feedback when only the rotation angles of the column and links are measured. The problem posed is solved in the form of a nonlinear proportional-integral controller taking into account the cylindrical phase space of the manipulator's mathematical model. The solution includes construction of a Lyapunov functional with a semi-definite derivative and application of the corresponding theorems on the asymptotic stability of non-autonomous functional differential retarded-type equations. The obtained conditions for the program motion stabilization are robust with respect to the mass-inertial parameters of the manipulator. The numerical simulation results demonstrate global attraction to its given position in cylindrical phase space.
About the authors
Lubov V. Kolegova
Ulyanovsk State University
Author for correspondence.
Email: flv_603@mail.ru
ORCID iD: 0009-0008-7734-983X
Assistant, Department of Information Security and Control Theory
Russian Federation, 42, Leo Tolstoy st., Ulyanovsk 432017, RussiaReferences
- M. K. Jangid, S. Kumar, J. Singh, "Trajectory tracking optimization and control of a three link robotic manipulator for application in casting", International Journal of Advanced Technology and Engineering Exploration, 8:83 (2021), 1255. DOI: https://doi.org/10.19101/IJATEE.2021.874468
- S. E. Ivanov, T. Zudilova, T. Voitiuk, L. N. Ivanova, "Mathematical modeling of the dynamics of 3-DOF robot-manipulator with software control", Procedia Computer Science, 178 (2020), 311—319. DOI: https://doi.org/10.1016/j.procs.2020.11.033
- J. Wu, R.-J. Yan, K.-S. Shin, C.-S. Han, I-M. Chen, "A 3-DOF quickaction parallel manipulator based on four linkage mechanisms with high-speed cam", Mechanism and Machine Theory, 115 (2017), 168—196. DOI:
- https://doi.org/10.1016/j.mechmachtheory.2017.04.012
- A. Arian, B. Danaei, H. Abdi, S. Nahavandi, "Kinematic and dynamic analysis of the Gantry-Tau, a 3-DoF translational parallel manipulator", Applied Mathematical Modelling, 51 (2017), 217—231. DOI: https://doi.org/10.1016/j.apm.2017.06.012
- L. Zhang, X. Yan, Q. Zhang, "Design and analysis of 3-DOF cylindrical-coordinate-based manipulator", Robotics and Computer-Integrated Manufacturing, 52 (2018), 35—45. DOI: https://doi.org/10.1016/j.rcim.2018.02.006
- S. G. Ahmad, A. S. Elbanna, M. S. Elksas, F. G. Areed, "Dynamic modelling with a modified PID controller of a three link rigid manipulator", Int. J. Comput. Appl., 179 (2018), 1–6.
- L. Sciavicco and B. Siciliano, Modelling and Control of Robot Manipulators. – 2nd ed., Springer, 2000 DOI: https://doi.org/10.1088/0957-0233/11/12/709.
- A. O’Dwyer, Handbook of PI and PID Controller Tuning Rules, 3rd ed., Imperial College Press, London, 2009, 623 p.
- A. Zhang, X. Lai, M. Wu, J. She, "Global stabilization of underactuated spring-coupled three-link horizontal manipulator using position measurements only", Applied Mathematical Modelling, 39:7 (2015), 1917—1928. DOI:
- http://dx.doi.org/10.1016/j.apm.2014.10.010
- V. T. Yen, W. Y. Nan, P. Van Cuong, "Robust adaptive sliding mode neural networks control for industrial robot manipulators", International Journal of Control, Automation and Systems, 17 (2019), 783—792. DOI: https://doi.org/10.1007/s12555-018-0210-y
- X. Yang, X. Zhang, Z. Chen, Sh. Xu, P. X. Liu, "Udwadia-Kalaba approach for three link manipulator dynamics with motion constraints", IEEE Access, 7 (2019), 49240—49250. DOI: https://doi.org/10.1109/ACCESS.2019.2909934
- A. S. Andreev, O. A. Peregudova, "Stabilization of the preset motions of a holonomic mechanical system without velocity measurement", Journal of Applied Mathematics and Mechanics, 81:2 (2017), 95–105.
- A. S. Andreev, O. A. Peregudova, "Nonlinear regulators in the position stabilization problem of the holonomic mechanical system", Mechanics of Solids, 53 (2018), 22–38.
- F. L. Chernous’ko, I. M. Ananievski, S. A. Reshmin, Control of nonlinear dynamical systems: methods and applications, Springer Science & Business Media, 2008.
- V. A. Chertopolokhov, "On the problem of synchronization of virtual and real movements for virtual reality systems", Journal of Physics: Conference Series, 2056:1 (2021), 012052. DOI: https://doi.org/10.1088/1742-6596/2056/1/012052
- I. Z. Nikolic, I. Milivojevic, "Application of pseudo-derivative feedback in industrial robots controllers", Facta Univ. (Nis), Mech. Autom. Contr. Robot, 2:8 (1998), 741–756.
Supplementary files
