 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
|
| << Previous article | Volume 37, Issue 1 / 2002 | Next article >> |
| Yu. N. Chelnokov, "Construction of attitude control laws for a rigid body using quaternions and standard forms of equations governing transient processes. Part 1," Mech. Solids. 37 (1), 1-12 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
1 |
Pages |
1-12 |
| Title |
Construction of attitude control laws for a rigid body using quaternions and standard forms of equations governing transient processes. Part 1 |
| Author(s) |
Yu. N. Chelnokov (Moscow) |
| Abstract |
Theory and methods are developed for the analytical construction
of control laws for the attitude motion of a rigid body
that would provide the asymptotic stability in large or global
asymptotic stability for any chosen attitude motion and ensure
a desired behavior of the controlled motion of the body.
To construct such control laws, we use quaternion models
of rotation of a rigid body, the inverse dynamics concept,
the feedback control principle, and methods for reducing
the differential equations of the perturbed angular motion
of a rigid body to standard differential equations of a prescribed
structure.
In the first part of the paper, we consider quaternion models
of the rotational motion of a rigid body, formulate the problem
of attitude control of a rigid body, and present various forms
of differential equations of perturbed angular motion of the body
in quaternion and vector variables convenient for constructing
control laws.
In the second part of the paper, we will consider standard differential
equations governing the desired behavior of the controlled motion
of the body and synthesize three groups of control laws utilizing
quaternion and vector variables to describe the rotational motion.
We will discuss the construction of the desired (nominal) attitude motion
and the corresponding open-loop control, and the determination of scalar,
matrix or quaternion gains of nonlinear feedback laws providing the desired
qualitative and quantitative characteristics for transient processes.
Specific control algorithms will be proposed.
This work is a generalization and continuation of [1-5]. |
| References |
| 1. | Yu. N. Chelnokov, "Quaternion solution of kinematic problems
of attitude control of a rigid body: Equations of motion, problem formulation,
nominal motion and control,"
Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 7-14, 1993. |
| 2. | Yu. N. Chelnokov, "Quaternion solution of kinematic problems
of attitude control of a rigid body: Equations for errors;
correction (stabilization) laws and algorithms,"
Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 3-12, 1994. |
| 3. | Yu. N. Chelnokov, "Attitude control of a spacecraft
utilizing quaternions,"
Kosmicheskie Issledovaniya [Space Research], Vol. 32 No. 3, pp. 21-32, 1994. |
| 4. | Yu. N. Chelnokov, "Quaternion synthesis of a nonlinear
attitude control of a moving object,"
Izv. AN. Teoriya i Sistemy Upravleniya, No. 2, pp. 145-150, 1995. |
| 5. | Yu. N. Chelnokov, "Quaternions and dynamics of controlled
motion of a rigid body,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 13-23, 1996. |
| 6. | V. P. Solov'ev, "On the optimal rotation of a spacecraft
about an arbitrary fixed axis,"
Kosmicheskie Issledovaniya [Space Research], Vol. 7 No. 1, pp. 42-50, 1969. |
| 7. | V. I. Gurman, E. K. Lavrovskii, and S. I. Sergeev,
"Optimal attitude control of a rotating symmetric spacecraft,"
Kosmicheskie Issledovaniya [Space Research], Vol. 8 No. 3, pp. 341-349,
1970. |
| 8. | B. N. Petrov, V. A. Bodner, and K. B. Alekseev, "Analytical solution
of the control problem for a spatial rotation maneuver,"
Doklady AN SSSR, Vol. 192, No. 6, pp. 1235-1238, 1970. |
| 9. | V. N. Branets and I. P. Shmyglevskii, Application of Quaternions
to Problems of Orientation of a Rigid Body [in Russian], Nauka, Moscow, 1973. |
| 10. | V. N. Shklyar and A. M. Malyshenko, "To the problem of optimal
spatial rotation of a spacecraft about its center of mass,"
Kosmicheskie Issledovaniya [Space Research], Vol. 13, No. 4, pp. 473-480,
1975. |
| 11. | K. B. Alekseev, Extensive Attitude Control of Spacecraft [in
Russian], Mashinostroenie, Moscow, 1977. |
| 12. | S. R. Vadali and J. L. Junkins, "Spacecraft large angle
rotational maneuvers with optimal momentum transfer,"
J. Astronaut. Sci., Vol. 31, No. 2, pp. 217-235, 1983. |
| 13. | V. N. Branets, Yu. V. Kaznacheev, and M. B. Chertok,
"Optimal rotational maneuver of a rigid body with a single
axis of symmetry,"
Kosmicheskie Issledovaniya [Space Research], Vol. 22, No. 3, pp. 352-360,
1984. |
| 14. | T. A. W. Dwyer, "Exact nonlinear control of spacecraft slewing
maneuvers with inertial momentum transfer,"
J. Guidance, Control, and Dynamics, Vol. 9, No. 2, pp. 240-247, 1986. |
| 15. | V. I. Gulyaev, V. L. Koshkin, and I. V. Savilova,
"Time-optimal control of triaxial orientation of a rigid body
with constrained control parameters,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 11-15, 1986. |
| 16. | D. C. Redding and N. J. Adams, "Optimized rotation-axis
attitude maneuver controller for the space shuttle orbiter,"
J. Guidance, Control, and Dynamics, Vol. 10, No. 1, pp. 4-13, 1987. |
| 17. | D. V. Lebedev and A. I. Tkachenko, Inertial Control Systems:
Algorithmic Aspects [in Russian], Naukova Dumka, Kiev, 1991. |
| 18. | N. E. Zubov, "Optimal control of the spacecraft terminal
reorientation on the basis of an algorithm with a predicting model,"
Kosmicheskie Issledovaniya [Space Research], Vol. 29, No. 3, pp. 340-351,
1991. |
| 19. | R. E. Mortensen, "A globally stable linear attitude
regulator,"
Intern J. Control, Vol. 8, No. 3, pp. 297-302, 1968. |
| 20. | D. V. Lebedev, "Attitude control of a rigid body utilizing
Rodrigues-Hamilton parameters," Avtomatika, No. 4, pp. 29-32, 1974. |
| 21. | N. L. Gavrilova and A. I. Tkachenko, "On the attitude stabilization
of a rigid body,"
Avtomatika, No. 6, pp. 3-8, 1974. |
| 22. | D. V. Lebedev, "To the problem of attitude control of a rigid body,"
Prikladnaya Mekhanika, Vol. 12, No. 2, pp. 76-82, 1976. |
| 23. | D. V. Lebedev, "On the triaxial attitude control
of a rigid body," Avtomatika, No. 3, pp. 77-80, 1981. |
| 24. | B. Wie and P. M. Barba, "Quaternion feedback for spacecraft
large angle maneuvers,"
J. Guidance, Control, and Dynamics, Vol. 8, No. 3, pp. 360-365,
1985. |
| 25. | B. Wie, H. Wace, and E. Erepopstatis,
"Control of rotational maneuvers of a spacecraft about its axis
using feedback with respect to quaternion components,"
Aerokosmicheskaya Tekhnika. No. 3, pp. 3-11, 1990. |
| 26. | V. V. Martynenko and S. V. Pushkova, "Synthesis of
the optimal control of the spacecraft rotation,"
Kosmicheskie Issledovaniya [Space Research], Vol. 30 No. 1, pp. 52-59, 1992. |
| 27. | V. N. Branets and I. P. Shmyglevskii, "Application of quaternions
in problems of attitude control of a rigid body,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 24-31, 1972. |
| 28. | V. N. Branets and I. P. Shmyglevskii, "Kinematic problems
of orientation in the rotating reference frame,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 3, pp. 36-43, 1972. |
| 29. | P. K. Plotnikov, A. N. Sergeev, and Yu. N. Chelnokov,
"Kinematic problem of attitude control for a rigid body,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 9-18, 1991. |
| 30. | V. N. Branets and I. P. Shmyglevskii,
Introduction to the Theory of Strapdown Inertial Navigation Systems
[in Russian], Nauka, Moscow, 1992. |
| 31. | A. A. Pankov and Yu. N. Chelnokov,
"Analysis of quaternion laws of attitude control of a rigid
body with respect to the angular velocity,"
Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 3-13, 1995. |
| 32. | J. S-C. Yuan, "Closed-loop manipulator control
using quaternion feedback," IEEE J. Rob. and Autom.,
No. 4, pp. 434-440, 1988. |
| 33. | G. I. Zubenko, G. A. Peisakhovich, Yu. B. Vlasov,
Yu. N. Chelnokov, and A. A. Pankov, "Principles and problems
stabilized platform using the information about the motion
of control of motion of the complex manipulator-triaxial
of the manipulator end-effector," in
Abstracts of the Third Scientific Conference
"Automation in Creation of Software and Architecture of Real-time
Systems," pp. 84-85, GosNIIAS, Moscow, 1992. |
| 34. | A. A. Pankov, G. A. Peisakhovich, R. N. Rudakov,
G. V. Utkin, S. V. Fedoseev, Yu. N. Chelnokov, and V. S. Yaroshevskii,
"Models and algorithms of orientations and control of motion
of the platform complex TSP-ARGUS of the project MARS,"
in Materials of the 7th Science and Technology Conference
"Extremal Robotics," pp. 186-196, Izd-vo SPbGTU, St. Petersburg, 1996. |
| 35. | Yu. N. Chelnokov, V. V. Baturin, Yu. V. Sadomtsev,
A. A. Pankov, G. A. Peisakhovich, R. N. Rudakov, S. V. Fedoseev,
G. V. Utkin, and V. S. Yaroshevskii, "Models and algorithms
of orientation and control of motion of the platform complex TSP-ARGUS
of the project MARS,"
in Materials of the Intern. Conf. "Problems and Prospects of
High-precision Mechanics and Control in Machine Industry," pp. 68-79,
Izd-vo Saratov. Un-ta, Saratov, 1997. |
| 36. | K. S. Fu, R. C. Gonzalez, and C. S. G. Lee,
Robotics: Control, Sensing, Vision, and Intelligence,
McGraw-Hill, N.J., 1987. |
| 37. | G. M. Nilson and R. B. Heiland,
"Multiplicative rotations on a 4-dimensional sphere
by means of quaternions and splines,"
Programmirovanie, No. 4, pp. 17-27, 1992. |
|
| Received |
08 December 1999 |
| << Previous article | Volume 37, Issue 1 / 2002 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English