 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| Chelnokov Yu.N., "Controlling the Spatial Motion of a Rigid Body Using Biquaternions and Dual Matrices," Mech. Solids. 56 (1), 13-33 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
1 |
Pages |
13-33 |
| DOI |
10.3103/S0025654421010064 |
| Title |
Controlling the Spatial Motion of a Rigid Body Using Biquaternions and Dual Matrices |
| Author(s) |
Chelnokov Yu.N. (Institute of Precision Mechanics and Control Problems of the Russian Academy of Sciences, Saratov, 410028 Russia, ChelnokovYuN@gmail.com) |
| Abstract |
The method of analytical construction of the control of the spatial motion of a rigid body (control of screw motion, equivalent to the composition of angular (rotational) and translational movements) is being developed in a nonlinear dynamic setting using Clifford biquaternions and dual matrices. The controls provide asymptotic stability in large for any selected programmed spatial motion in the inertial coordinate system and the desired dynamics of the controlled spatial motion of a rigid body. To construct control laws, biquaternionic and dual matrix models of the spatial motion of a rigid body, the concept of solving inverse problems of dynamics, the principle of feedback control and reduction of the constructed nonlinear differential equations of the perturbed spatial motion of a rigid body to the reference linear stationary differential forms of the selected structure by using the proposed nonlinear feedbacks in control laws.
Biquaternion models of the spatial motion of a rigid body are considered, a statement of the problem of control of the motion of a rigid body is given, various forms of nonlinear differential equations of the perturbed spatial motion of a rigid body in biquaternion and screw variables are presented, which are convenient for constructing control laws. Various dual matrix (screw) laws of control of the spatial motion of a rigid body are proposed, for which the nonlinear nonstationary differential equations of the perturbed spatial motion of a rigid body take the form of linear stationary dual matrix differential equations of the second order (with respect to the screw part of the biquaternion of the rigid body position error), invariant with respect to any chosen programmed spatial motion of a rigid body. Constant coefficients (scalar duals or matrix duals) of these equations are the amplification coefficients of nonlinear feedbacks in the proposed dual control laws that ensure the required quality of transient control processes. The determination of the amplification factors of nonlinear feedbacks and the properties of the controlled motion of a rigid body are discussed. |
| Keywords |
rigid body, spatial motion, programmed and stabilizing controls, screw control laws, biquaternion |
| Received |
20 January 2019 | Revised |
17 February 2019 | Accepted |
28 February 2019 |
| Link to Fulltext |
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