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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». 2025. Vol 54

Decomposition Method for Finding Suboptimal Impulse Controls of Electric Drives of Manipulation Robots

Author(s)

Yurii F. Dolgii1,2, Alexander N. Sesekin1,2

1 Ural Federal University, Yekaterinburg, Russian Federation 

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

Abstract
Modeling the motion of a manipulation robot with a large number of degrees of freedom leads to complex nonlinear control systems of high-dimensional differential equations. Decomposition methods allow us to separate the motions and move on to low-dimensional control systems. In this paper, a constraint freezing procedure is used to separate generalized coordinates for a manipulation robot with electromechanical drives. This procedure allows us to replace the original problem of controlling the movements of a manipulation robot with a sequence of simple control problems for systems with a single degree of freedom. Solutions to these problems are sought in the class of impulse controls. Their determination involves searching for trajectories of straight paths according to Hamilton’s principle of least action for an uncontrolled system. At the initial instant, impulse control transfers motion to a straight path trajectory and dampens its velocity at the final instant. A specified constraint on the energy of impulse control allows us to find a suboptimal control with respect to motion time.
About the Authors

Yurii F. Dolgii, Dr. Sci. (Phys.-Math.), Prof., Ural Federal University, Yekaterinburg, 620002, Russian Federation; Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, 620108, Russian Federation, yurii.dolgii47@mail.ru 

Alexander N. Sesekin, Dr. Sci. (Phys.–Math.), Prof., Ural Federal University, Yekaterinburg, 620002, Russian Federation; Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, 620108, Russian Federation

For citation
Dolgii Yu. F., Sesekin A. N. Decomposition Method for Finding Suboptimal Impulse Controls of Electric Drives of Manipulation Robots. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 54, pp. 3–17. (in Russian) https://doi.org/10.26516/1997-7670.2025.54.3
Keywords
decomposition, impulse control, manipulator, electromechanical drive
UDC
517.97
MSC
34K20
DOI
https://doi.org/10.26516/1997-7670.2025.54.3
References
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