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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 43

Optimal Control of Manipulator

Author(s)
Yurii F. Dolgii1,2, Ilya A. Chupin1

1Ural Federal University, Yekaterinburg, Russian Federation

2Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, Russian Federation

Abstract
When solving the problem of optimal performance for manipulative robots, the scientific team headed by F. L. Chernousko actively uses the Pontryagin maximum principle. The application of the maximum principle is complicated by the nonlinearities of controlled systems of manipulation robots. Therefore, when using it, the original mathematical model is replaced with a simpler one. These substitutions made it possible to analytically solve the problems of finding the switching points of relay controls for individual models of manipulation robots. In this paper, when finding the switching moments of relay controls for a manipulating robot, the original nonlinear controlled system is used. The problem is reduced to the problem of the existence of a solution to the boundary value problem for a controlled nonlinear system in the selected class of permissible controls that guarantee the arrival of the manipulator in the final position with zero speeds.
About the Authors

Yurii F. Dolgii, Dr. Sci. (Phys.–Math.), Prof., Ural Federal University, Yekaterinburg, 620002, Russian Federation; Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the RAS, Yekaterinburg, 620137, Russian Federation, jury.dolgy@urfu.ru

Ilya A. Chupin, Postgraduate, Ural Federal University, Yekaterinburg, 620002, Russian Federation, mr.tchupin@yandex.ru

For citation
Dolgii Yu. F., Chupin I. A. Optimal Control of Manipulator. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 43, pp. 3–18. https://doi.org/10.26516/1997-7670.2023.43.3
Keywords
optimal control, Pontryagin’s maximum principle, manipulator
UDC
517.977
MSC
93C10, 49J10
DOI
https://doi.org/10.26516/1997-7670.2023.43.3
References
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