“Spacecraft Magnetic Control Using Dichotomous Coordinate Descent Algorithm with Box Constraints”

Authors: Rune Schlanbusch, Raymond Kristiansen and Per J. Nicklasson,
Affiliation: Narvik University College
Reference: 2010, Vol 31, No 4, pp. 123-131.

Keywords: Magnetic attitude control, numerical algorithm, sliding surface control, space vehicle control

Abstract: In this paper we present magnetic control of a spacecraft using the Dichotomous Coordinate Descent (DCD) algorithm with box constraints. What is common for most work on magnetic spacecraft control is the technique for solving for the control variables of the magnetic torquers where a cross product is included which is well known to be singular. The DCD algorithm provides a new scheme which makes it possible to use a general control law and then adapt it to work for magnetic torquers including restrictions in available magnetic moment, instead of designing a specialized controller for the magnetic control problem. A non-linear passivity-based sliding surface controller is derived for a fully actuated spacecraft and is then implemented for magnetic control by utilizing the previous mentioned algorithm. Results from two simulations are provided, the first comparing the results from the DCD algorithm with older results, and the second showing how easily the derived sliding surface controller may be implemented, improving our results.

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[1] Vitor H. Nascimento and Yuriy V. Zakharov (2016), doi:10.1109/LSP.2016.2551468
[2] Zhou Kaixing, Huang Hai, Wang Xinsheng and Sun Liang (2016), doi:10.1016/j.ast.2016.11.003
[3] Ahmet Sofyal , Elbrous M. Jafarov and Rafael Wisniewski (2018), doi:10.1016/j.ast.2018.01.022
[4] Ahmet Sofyal and Elbrous M. Jafarov (2019), doi:10.1002/rnc.4586
[5] M. Yu. Ovchinnikov and D.S. Roldugin (2019), doi:10.1016/j.paerosci.2019.05.006
[6] M. Yu. Ovchinnikov and D. S. Roldugin (2019), doi:10.26732/2618-7957-2019-2-73-86
[1] Berghuis, H. Nijmeijer, H. (1993). A passivity approach to controller-observer design for robots, IEEE Transactions on Robotics and Automation, .6:740--754 doi:10.1109/70.265918
[2] Egeland, O. Gravdahl, J.T. (2002). Modeling and Simulation for Automatic Control, Marine Cybernetics, Trondheim, Norway, ISBN 82-92356-01-0.
[3] Fjellstad, O.-E. (1994). Control of Unmanned Underwater Vehicles in Six Degrees of Freedom, Ph.D. thesis, Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway.
[4] Fossen, T.I. (2002). Marine Control Systems: Guidance, Navigation, and Control of Ships, Rigs and Underwater Vehicles, Marine Cybernetics, Trondheim, Norway, sISBN 82-92356-00-2.
[5] Golub, G.H. VanLoan, C.F. (1996). Matrix Computations, Third Edition, The John Hopkins University Press, ISBN 0-8018-5414-8.
[6] Gravdahl, J., Eide, E., Skavhaug, A., Fauske, K.M., Svartveit, K., Indergaard, F.M. (2003). Three axis attitude determination and control system for a picosatellite: Design and implementation, In Proceedings of the 54th International Astronautical Congress. Bremen, Germany.
[7] Hahn, W. (1967). Stability of Motion, Springer-Verlag, Berlin, Germany.
[8] Horn, R.A. Johnson, C.R. (1985). Matrix Analysis, Cambridge University Press, ISBN 0-521-38632-2.
[9] Kelly, R., Santibanez, V., Loria, A. (2005). Control of robot manipulators in joint space, Series Advanced textbooks in control engineering. Springer Verlag, ISBN: 1-85233-994-2.
[10] Khalil, H.K. (2002). Nonlinear Systems, third edition, Pearson Education International Inc., Upper Saddle River, New Jersey, USA, ISBN 0-13-067389-7.
[11] Kristiansen, R. (2008). Dynamic Synchronization of Spacecraft - Modeling and Coordinated Control of Leader-Follower Spacecraft Formations, Ph.D. thesis, Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway.
[12] Lovera, M. Astolfi, A. (2001). Global attitude regulation using magnetic control, In Proceedings of the 40th IEEE Conference on Descision and Control. Orlando, Florida USA, pages 4604--4609.
[13] Lovera, M. Astolfi, A. (2004). Spacecraft attitude control using magnetic actuators, Automatica, 4.8:1405--1414 doi:10.1016/j.automatica.2004.02.022
[14] Paden, B. Panja, R. (1988). Globally asymptotically stable ´PD+´ controller for robot manipulators, International Journal of Control, 4.6:1697--1712 doi:10.1080/00207178808906130
[15] Psiaki, M.L. (2001). Magnetic torquer attitude control via asymptotic periodic linear quadratic regulation, Journal of Guidance, Control and Dynamics, 2.2:386--394 doi:10.2514/2.4723
[16] Reyhanoglu, M. Drakunov, S. (2008). Attitude stabilization of small satellite using only magnetic actuation, In IECON 2008, 34th Annual Conference of IEEE Industrial Electronics.
[17] Schaub, H. Junkins, J.L. (2003). Analytical Mechanics of Space Systems, AIAA Education Series. American Institute of Aeronautics and Astronautics, Reston, VA, ISBN 1-56347-563-4.
[18] Sidi, M.J. (1997). Spacecraft Dynamics and Control, Cambridge University Press, New York, ISBN 0-521-78780-7.
[19] Sira-Ramirez, H. Siguerdidjane, H.B. (1996). A redundant dynamical sliding mode control scheme for an asymptotic space vehicle stabilization, International Journal of Control, 6.6:901--912 doi:10.1080/00207179608921729
[20] Slotine, J. J.-E. Li, W. (1987). On the adaptive control of robot manipulators, International Journal of Robotics Research, 6:49--59 doi:10.1177/027836498700600303
[21] Wang, P., Shtessel, Y.B., Wang, Y.-Q. (1998). Satellite attitude control using only magnetorquers, In Proceedings of the Thirtieth Southeastern Symposium on System Theory. IEEE, Morgantown USA, pages 500--504.
[22] Wertz, J.R., editor. (1978). Spacecraft Attitude Determination and Control, Kluwer Academic Publishers, London, ISBN 90-277-0959-9.
[23] Wisniewski, R. (1996). Satellite Attitude Control Using Only Electromagnetic Actuation, Ph.D. thesis, Department of Control Engineering, Aalborg University, Aalborg, Denmark.
[24] Wisniewski, R. Blanke, M. (1999). Fully magnetic attitude control for spacecraft subject to gravity gradient, Automatica, 35:1201--1214 doi:10.1016/S0005-1098(99)00021-7
[25] Zakharov, Y. Tozer, T.C. (2004). Multiplication-free iterative algorithm for ls problem, IEE Electronics Letters, 4.9.
[26] Zakharov, Y., White, G.P., Liu, J. (2008). Low-complexity RLS algorithms using dichotomous coordinate descent iterations, IEEE Transactions on Signal Processing, 5.7:3150--3161 doi:10.1109/TSP.2008.917874

  title={{Spacecraft Magnetic Control Using Dichotomous Coordinate Descent Algorithm with Box Constraints}},
  author={Schlanbusch, Rune and Kristiansen, Raymond and Nicklasson, Per J.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}