 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11262 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3251 |
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| Chelnokov Yu.N., "Synthesis of Control of Spatial Motion of a Rigid Body Using Dual Quaternions," Mech. Solids. 55 (7), 977-998 (2020) |
| Year |
2020 |
Volume |
55 |
Number |
7 |
Pages |
977-998 |
| DOI |
10.3103/S0025654420070080 |
| Title |
Synthesis of Control of Spatial Motion of a Rigid Body Using Dual Quaternions |
| Author(s) |
Chelnokov Yu.N. (Institute of Precision Mechanics and Control, Russian Academy of Sciences, Saratov, 410028 Russia, ChelnokovYuN@gmail.com) |
| Abstract |
In this paper, we develop a new method of analytical design and control of the spatial
motion of a rigid body (in particular, a spacecraft considered as a rigid body) in a nonlinear dynamic
formulation using dual quaternions (Clifford biquaternions). The control provides the asymptotic stability in general of any selected programmed motion in the inertial coordinate system and the desired
dynamics of the controlled motion of the body. To build control laws, new biquaternion differential
equations of perturbed spatial motion of a rigid body are proposed, in which unnormalized biquaternions of finite displacements, biquaternions of angular and linear velocities of the body and accelerations with nonzero dual scalar parts are used. The concept of solving the inverse problems of dynamics,
the feedback control principle, and the approach based on the reduction of the equations of perturbed
body motion to linear stationary differential forms of the selected structure invariant with respect to
any selected programmed motion due to the corresponding choice of dual nonlinear feedbacks in the
proposed biquaternion control laws is presented. Analytical solutions of biquaternion differential
equations are designed to describe the dynamics of controlling the spatial body motion using the proposed biquaternion control laws. The properties and patterns of such control are analyzed. |
| Keywords |
rigid body, spatial motion, perturbed motion equations, program and stabilizing controls, control laws, biquaternion, dual quaternion |
| Received |
11 April 2019 | Revised |
11 June 2019 | Accepted |
03 October 2019 |
| Link to Fulltext |
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