Synthesis of spacecraft attitude control algorithms using quaternions

1Volosov, VV, 2Tyutyunnik, LI
1Space Research Institute of the National Academy of Science of Ukraine and the National Space Agency of Ukraine, Kyiv, Ukraine
2Space Research Institute of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine, Kyiv, Ukraine
Kosm. nauka tehnol. 1999, 5 ;(4):61–69
Publication Language: Russian
The problem are solved in the synthesis of algorithms for spacecraft attitude control relative to orbital and inertial bases. The known generalizations of the direct Lyapunov method to the investigation of the stability of invariant sets of dynamic systems are used to solve the above problems. The efficiency of the algorithms obtained is il­lustrated by computer modelling of attitude system dynamics in whose loops these algorithms are used.
Keywords: algorithms for spacecraft attitude control, Lyapunov method, orbital and inertial bases
1. Branets V. N., Shmyglevskii I. P. Use of Quaternions in the Problems of Orientation of Solid Bodies, 320 p. (Nauka, Moscow, 1973) [in Russian].
2. Wie B., Wace H., and Erepopstatis E. Control of rotational maneuvers of a spacecraft about its axis using feedback with respect to quaternion components. Aerokosmicheskaya Tekhnika, No. 3, 3—11 (1990) [in Russian].
3. Volosov V. V. Control of the orientation of the spacecraft in orbital coordinate system using ellipsoidal estimates its state vector. Probl. Upravl. Inform., No. 5, 31—41 (1998) [in Russian].
4. Gantmacher F. R. Theory of Matrices, 575 p. (Nauka, Moscow, 1967) [in Russian].
5. Demidovich B. P. Lectures on the Mathematical Theory of Stability, 472 p. (Nauka, Moscow, 1967) [in Russian].
6. Efimov N. V., Rozendorn E. R. Linear Algebra and Multidimensional Geometry, 528 p. (Nauka, Moscow, 1970) [in Russian].
7. Zubov V. I. Stability of Motion. Methods of Lyapunov and their Application, 271 p. (Vysshaya Shkola, Moscow, 1973) [in Russian].
8. Koshlyakov V. N. Problems in Dynamics of Rigid Bodies and in Applied Theory of Gyroscopes, 288 p. (Nauka, Moscow, 1985) [in Russian].
9. Krasovsky N. N. Some of Problems of Theories of Stability of Motion, 211 p. (Fizmatgiz, Moscow, 1959) [in Russian].
10. Krasovsky N. N. Obobshhenie teorem vtorogo metoda Ljapunova. (Dopolnenie III). In: Malkin I. G. Theory of Motion Stability, P. 463—467 (Nauka, Moscow, 1966) [in Russian].
11. LaSalle J. P., Lefschetz S. Stability by Lyapunov's Direct Method, 168 p. (Mir, Moscow, 1964) [in Russian].
12. Lebedev D. V. Attitude control of a rigid body utilizing Rodrigues-Hamilton parameters. Avtomatika, No. 4, 29—32 (1974) [in Russian].
13. Lebedev D. V., Tkachenko A. I., Shtepa Yu. N. Magnetic system for controlling the angular motion of a micro-satellite. Kosm. nauka tehnol., 2 (5-6), 17— 25 (1996) [in Russian].
14. Raushenbakh B. V., Tokar E. N. Orientation control of spacecraft, 600 p. (Nauka, Moscow, 1974) [in Russian].
15. Rosenfeld B. A. Multidimensional Spaces, 647 p. (Nauka, Moscow, 1966) [in Russian].
16. Filimonov A. B., Filimonov N. B. Negladkij analiz i sintez sistem regulirovanija na osnove prjamogo metoda Ljapunova. Priborostroenie, 37 (7-8), 5—15 (1994) [in Russian].
17. Filippov A. F. Differential Equations with Discontinuous Righthand Sides, 224 p. (Nauka, Moscow, 1985) [in Russian].

18. Mortensen R. E. A globaly stable linear atlitude regulator. Internal. J. Control., 8 (3), 297—302 (1968).