Nonholonomic mechanical systems and stabilization of motion

Kalenova, V. I.; Karapetjan, A. V.; Mоrоzоv, V. М.; Salmina, Maria

doi:10.1007/s10958-007-0403-z

Cited by 11 publications

(3 citation statements)

References 24 publications

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“…The results of these studies are based on the systematic application of nonlinear vector-matrix equations of perturbed motion. The vector-matrix equations of disturbed motion used widely [14][15][16][17][18][19][20][21][22] in the stability and stabilization problems of motions of complex Holonomic and nonholonomic mechanical systems. It should be noted, that the systematic application of such a form of equations to study the dynamics of nonholonomic systems has already begun [15][16][17][18] (compare [14,[19][20][21] with a far incomplete list of bibliographic references).…”

Section: Overview Of Previous Resultsmentioning

confidence: 99%

“…In the method developed by the authors of this work, in contrast to [14,[19][20][21], the equations have a form that allows one to analyze in detail the structure of the linear and nonlinear terms of the perturbed equations of motion after replacing the theory of critical cases. The use of vector-matrix equations obtained by the authors in the Shulgin form gave an essential development of the method [22] with respect to systems with geometric constraints.…”

Section: Overview Of Previous Resultsmentioning

confidence: 99%

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Modeling of Dynamics of Manipulators with Geometrical Constraints as a Systems with Redundant Coordinates

Aleks

Krasinkiy

Krasinkaya

2017

IRATJ

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Earlier, a method was developed for modeling the dynamics of systems with geometric constraints using the analytical mechanics of systems with redundant coordinates and the theory of nonlinear stability. In the present paper, the previously obtained results are applied to the construction of a mathematical model and to the solution of the stabilization problem of steady motion for the simplest manipulator with one positional, one cyclic and one dependent coordinate. The analysis is carried out taking into account the dynamics of the drives. For steady motion, the solvability of the problem of determining the stabilizing control (additional voltage on the executive motors) by solving the linearly quadratic problem by the method of NN Krasovskii is proved. Asymptotic stability in a complete nonlinear closed system follows from the previously proved theorem on asymptotic stability in the presence of zero roots of the characteristic equation corresponding to redundant coordinates. However, for the manipulator design under consideration, stable operation modes can be distinguished even with constant voltage on the drive motors. These voltages play the role of program controls, ensuring the implementation of this mode of operation. The results of numerical simulation are presented.

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Section: Overview Of Previous Resultsmentioning

confidence: 99%

Section: Overview Of Previous Resultsmentioning

confidence: 99%

Modeling of Dynamics of Manipulators with Geometrical Constraints as a Systems with Redundant Coordinates

Aleks

Krasinkiy

Krasinkaya

2017

IRATJ

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“…A significant number of publications are devoted to modeling the dynamics of systems for various purposes and the construction of control algorithms, of which we mention, for example, the works [42][43][44][45][46][47][48][49][50][51][52][53][54][55]. In [56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72], various algorithms are proposed for compiling differential equations of motion for exoskeletons, anthropomorphic mechanisms, and rod systems, including systems with variable link lengths.…”

Section: Main Directions Of the Use Of Exoskeletons In Medicinementioning

confidence: 99%

On Mathematical Modeling of the Dynamics of Multilink Systems and Exoskeletons

Borisov

Kaspirovich

Mukharlyamov

2021

J. Comput. Syst. Sci. Int.

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A review of well-known publications is given and some results of the authors' research on modeling the dynamics of systems of rigid bodies and exoskeletons are presented. Various approaches to the problem of modeling the dynamics of multilink systems are described, including the problems of constructing equations of motion and solving control problems. Matrix and recurrent methods of composing equations for the dynamics of anthropomorphic mechanisms and exoskeletons, as well as problems of modeling flat and spatial systems containing links of variable length, are considered. The results of the research on the analytical design of exoskeletons, anthropomorphic mechanisms, and their analogs seem to be relevant for the design of systems designed to enhance human motor functions and the development of robotic systems for various purposes.

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Schemes of momentum/reaction wheels unloading by mechanical restructuring and gearbox for spacecraft

Doroshin

2022

Communications in Nonlinear Science and Numerical Simulation

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Nonholonomic mechanical systems and stabilization of motion

Abstract: Theoretical results on the stability and stabilization of the steady-state motion of nonholonomic systems are systematized. A set of theorems on stability and controllability is formulated. Numerous applications of these theoretical results are pointed out.

Cited by 11 publications

References 24 publications

Modeling of Dynamics of Manipulators with Geometrical Constraints as a Systems with Redundant Coordinates

Modeling of Dynamics of Manipulators with Geometrical Constraints as a Systems with Redundant Coordinates

On Mathematical Modeling of the Dynamics of Multilink Systems and Exoskeletons

Schemes of momentum/reaction wheels unloading by mechanical restructuring and gearbox for spacecraft

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