phone +7 (3412) 91 60 92

Archive of Issues


Russia Yekaterinburg
Year
2018
Volume
28
Issue
2
Pages
252-259
<<
>>
Section Mechanics
Title Optimal stabilization of spacecraft in an inertial coordinate system based on a strapdown inertial navigation system
Author(-s) Mityushov E.A.a, Misyura N.E.a, Berestova S.A.a
Affiliations Ural Federal Universitya
Abstract We consider the optimal control problem for spacecraft motion during correction of its position in an inertial coordinate system by means of control torques. Control torques arise from the acceleration of inertial flywheels of a strapdown inertial navigation system. We investigate optimal control, which ensures a smooth change in the spacecraft orientation. This smooth corrective motion is described as the motion along the shortest path in the configuration space of a special orthogonal group $SO(3)$. The shortest path coincides with the large circle arc of the unit hypersphere $S^3$. We also consider a control algorithm using the original procedure of nonlinear spherical interpolation of quaternions. Four inertial flywheels are used as the main executive bodies for orientation of the dynamic control loop of the strapdown inertial navigation system when solving the optimal control problem. Three flywheels are oriented along the axes of the spacecraft. The fourth flywheel is oriented along the bisector. The simulation results are presented. We consider examples for corrective motion in which the spacecraft has zero velocity and acceleration at the beginning and end of the maneuver. We give an animation of the corrective movement of the spacecraft. The proposed formalism can be extended to control the spacecraft motion at an initial angular velocity different from zero, as well as in the orbital coordinate system.
Keywords spacecraft, strapdown inertial navigation systems, control moments, smooth motion
UDC 514.85, 531.383
MSC 70Q05, 70M20
DOI 10.20537/vm180211
Received 15 May 2018
Language Russian
Citation Mityushov E.A., Misyura N.E., Berestova S.A. Optimal stabilization of spacecraft in an inertial coordinate system based on a strapdown inertial navigation system, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 2, pp. 252-259.
References
  1. Sevast'yanov N.N. The concept of building the system of orientation and motion control of the Yamal communication satellite. The nominal operation scheme, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2013, no. 2 (22), pp. 85-96 (in Russian). http://mi.mathnet.ru/eng/vtgu/y2013/i2/p85
  2. Branets V., Sevast'yanov N. Control system of Yamal-100 communication satellite, Integrirovannye navigatsionnye sistemy: sbornik statei VII Sankt-Peterburg. mezhdunar. konf. (Integrated navigation system: proceedings of VII int. conf.), Saint Petersburg, 2000, pp. 7-11 (in Russian).
  3. Semenov Yu.P., Sevast'yanov N.N., Branets V.N. New generation of the Russian Yamal communication satellite, Raketno-kosmicheskaya tekhnika. Raschet, proektirovanie, konstruirovanie i ispytaniya kosmicheskikh sistem: sbornik statei raketno-kosmicheskoi korporatsii «Energiya» im. S.P. Koroleva (Rocket and space technology. Calculation, design, construction and testing of space systems: proceedings of S.P. Korolev rocket and space corporation «Energia»), Korolev, 2002, vol. XII, issue 1-2, pp. 5-6 (in Russian).
  4. Sevast'yanov N.N., Branets V.N., Kotov O.S., Orlovskii I.V.,Platonov V.N., Chertok M.B. The onboard control complex of Yamal communication satellite, Raketno-kosmicheskaya tekhnika. Raschet, proektirovanie, konstruirovanie i ispytaniya kosmicheskikh sistem: sbornik statei raketno-kosmicheskoi korporatsii «Energiya» im. S.P. Koroleva (Rocket and space technology. Calculation, design, construction and testing of space systems: proceedings of S.P. Korolev rocket and space corporation «Energia»), Korolev, 2002, vol. XII, issue 1-2, pp. 7-15 (in Russian).
  5. Kulik A.S., Firsov S.N., Taran A.N. Usage of minimally redundant reaction wheel block for spacecraft angular orientation, Aviatsionno-kosmicheskaya tekhnika i tekhnologiya, 2009, no. 6 (63), pp. 42-47 (in Russian). https://www.khai.edu/csp/nauchportal/Arhiv/AKTT/2009/AKTT609/Kulik.pdf
  6. Davydov A.A., Ignatov A.I., Sazonov V.V. The analysis of dynamic capabilities of the control systems by the spacecraft built on the basis of the reaction wheels, Keldysh Institute preprints, 2005, 047. http://mi.mathnet.ru/eng/ipmp/y2005/p47
  7. Kilin A.A., Vetchanin E.V. The contol of the motion through an ideal fluid of a rigid body by means of two moving masses, Rus. J. Nonlin. Dyn., 2015, vol. 11, no. 4, pp. 633-645 (in Russian). DOI: 10.20537/nd1504001
  8. Borisov A.V., Mamaev I.S., Kilin A.A., Kalinkin A.A., Karavaev Yu.L., Klekovkin A.V., Vetchanin E.V. Screwless underwater robot. The application for a utility model 2016144812, 15.11.2016.
  9. Vetchanin E.V., Tenenev V.A., Kilin A.A. Optimal control of the motion in an ideal fluid of a screw-shaped body with internal rotors, Computer Research and Modeling, 2017, vol. 9, no. 5, pp. 741-759. DOI: 10.20537/2076-7633-2017-9-5-741-759
  10. Borisov A.V., Vetchanin E.V., Kilin A.A. Control of the motion of a triaxial ellipsoid in a fluid using rotors, Mathematical Notes, 2017, vol. 102, issue 3-4, pp. 455-464. DOI: 10.1134/S0001434617090176
  11. Borisov A.V., Mamaev I.S., Kilin A.A., Karavaev Yu.L. Spherical robots: mechanics and control, Nonlinear Dynamics of Machines: Proc. of the 4-th Intern. School-Conf. for Young Scientists, Moscow, 2017, pp. 477-482 (in Russian). http://school.dyvis.ru/download/Proceedings_SchoolNDM2017.pdf
  12. Shoemake K. Animating rotation with quaternion curves, Proceedings of the 12th annual conference on Computer graphics and interactive techniques – SIGGRAPH’ 85, New York, USA, 1985, pp. 245-254. DOI: 10.1145/325334.325242
  13. Borisov A.V., Mamaev I.S. Dinamika tverdogo tela (Rigid body dynamics), Izhevsk: Regular and Chaotic Dynamics, 2001, 384 p.
  14. Golubev Yu.F. Quaternion algebra in rigid body kinematics, Keldysh Institute preprints, 2013, 039. http://mi.mathnet.ru/eng/ipmp/y2013/p39
  15. Mathematical modeling at Ural Federal University. Control of the spacecraft orientation by three main engines-flywheels. https://www.youtube.com/watch?v=uCgJuyOO5Lo
  16. Mathematical modeling at Ural Federal University. Control of the spacecraft orientation with the use of a backup flywheel engine. https://www.youtube.com/watch?v=ugNsZfojclI
Full text
<< Previous article
Next article >>