Algorithmic and software tools for parametric optimization of gantry robot motion
DOI:
https://doi.org/10.15407/fmmit2026.42.085Keywords:
портальний робот, дволанковий маніпулятор, оптимальне керування, параметризація законів руху, нелінійне програмування, програмний застосунокAbstract
An algorithm and a software application for the parametric optimization of motion laws for a gantry robot with a two-link manipulator are described. Under the control stimuli (active forces and torques in the joints), the robot performs plane-parallel motion in a vertical plane, executing a transport operation to move a load from a specified initial state to a given final state. The problem of finding optimal controls that ensure the execution of the transport operation while minimizing a given functional is formulated. An algorithm for the approximate solution of the problem is constructed, based on the parameterization of each generalized coordinate of the mechanical system by the sum of a cubic polynomial and a finite trigonometric series with unknown coefficients. The polynomial coefficients are determined from the boundary conditions of the transport operation, while the trigonometric series coefficients are found as a solution to the corresponding nonlinear programming problem. The algorithm is implemented as a software application, through which a series of calculations was conducted. The results of numerical simulation confirmed the effectiveness of the parametric optimization method in problems of optimal motion control for the investigated gantry robot
References
Shynkarenko H., Malashniak P. Analysis of an h-adaptive finite element method in the statics problem of cylindrical shells: I. Correctness of the axisymmetric variational formulation. Physical and Mathematical Modeling and Information Technologies, 2025, No. 40, pp. 27-36.
https://doi.org/10.15407/10.15407/fmmit2025.40.027
Bernakevych I.E., Vahin P.P., Shynkarenko H.A. Mathematical model of acoustic interaction of shells with fluid. II. Projection-grid approximations and their convergence. Mathematical Methods and Physico-Mechanical Fields, 2004, 47(3), pp. 37-44.
Vahin P.P., Ivanova N.V., Shynkarenko H.A. Formulation, solvability and approximation of variational problems of statics of shear shells. Mathematical Methods and Physico-Mechanical Fields, 1999, 42(2), pp. 53-61.
Hryhorenko Ya.M., Savula Ya.H., Mukha I.S. Linear and nonlinear problems of elastic deformation of shells of complex shape and methods of their numerical solution. Applied Mechanics, 2000, 36(8), pp. 3-27.
https://doi.org/10.1023/A:1026645731095
Savula Ya.H., Shynkarenko H.A., Vovk V.N. Some applications of the finite element method. Lviv: Lviv University Press, 1981.
Savula Ya.H., Fleishman N.P. Calculation and optimization of shells with curved midsurfaces. Lviv: Vyshcha Shkola, 1989.
Trushevskyi V.M., Shynkarenko H.A., Shcherbyna N.M. Finite element method and artificial neural networks. Theoretical aspects and applications. Lviv: Ivan Franko National University of Lviv Publishing Center, 2014.
Radwańska M., Stankiewicz A., Wosatko A., Pamin J. Plate and Shell Structures: Selected Analytical and Finite Element Solutions. Wiley, 2017.
https://doi.org/10.1002/9781118934531
Babuška I., Rheinboldt W. Error estimates for adaptive finite element computations. SIAM Journal on Numerical Analysis, 1978, 15, pp. 736-754.
https://doi.org/10.1137/0715049
Shynkarenko H., Malashniak P. Analysis of h-adaptive FEM approximations in cylindrical shell statics problems. Proceedings of the 11th International Conference "Mathematical Problems of Mechanics of Heterogeneous Structures", Lviv, 2024, pp. 41-42.
Ainsworth M., Oden J.T. A Posteriori Error Estimation in Finite Element Analysis. Wiley, 2000.
https://doi.org/10.1002/9781118032824
Babuška I., Strouboulis T. The Finite Element Method and Its Reliability. Oxford University Press, 2001.
https://doi.org/10.1093/oso/9780198502760.001.0001
Babuška I., Whiteman J.R., Strouboulis T. Finite Elements: An Introduction to the Method and Error Estimation. Oxford University Press, 2011.
Verfürth R. A Review of A Posteriori Error Estimates and Adaptive Mesh-Refinement Techniques. Wiley-Teubner, 1996.
Zienkiewicz O.C., Taylor R.L., Zhu J. The Finite Element Method: Its Basis and Fundamentals (7th ed.). Elsevier, 2015.
Downloads
Published
Versions
- 2026-06-25 (2)
- 2026-06-23 (1)
How to Cite
Issue
Section
License
Copyright (c) 2026 Мирослав Демидюк, Богдан Проць (Автор)
This work is licensed under a Creative Commons Attribution 4.0 International License.
