The algorithm to control the in-plane relative motion of a spacecraft for contactless space debris removal

1Khoroshylov, SV
1Institute of Technical Mechanics of the National Academy of Science of Ukraine and the State Space Agency of Ukraine, Dnipropetrovsk, Ukraine
Space Sci. & Technol. 2019, 25 ;(1):14-26
https://doi.org/10.15407/knit2019.01.014
Publication Language: Russian
Abstract: 
The article is devoted to the improvement of the technology for contactless space debris removal called "Ion Beam Shepherd". The control law has been synthesized to maintain the required position of the shepherd spacecraft relative to the space debris object in the orbital plane by changing the thrust of only one compensating ion thruster in a certain small range compared to its nominal value. The synthesis is carried out using the method of mixed sensitivity. The method provides the necessary trade-off between robust stability, performance, and control costs.  This takes into account the impact of the ion beam, external disturbances, inaccurate determination of the relative position, as well as non-ideal reactive actuator. The requirements for the synthesized controller are set in the frequency domain using the selected weight functions.
         The results of the synthesis are verified using a formal criterion based on the concept of structured singular values and by computer simulation using a non-linear mathematical model.  The latter takes into account a wide range of orbital perturbations acting on the system. The control law ensures that the shepherd spacecraft moves at a certain small distance in front of a debris object while the ion beam effectively transfers the de-orbiting impulse to it. A significant advantage of the proposed control from the point of view of the propellant consumption is shown in comparison with the traditional approach based on the use of hydrazine thrusters. This advantage is one of the key factors for the choice of control due to the significant duration of the phase of space debris removal.
Keywords: compensating thruster, control law, ion beam shepherd, propellant consumption, robustness, space debris
References: 
1. Alpatov A. P., Maslova A. I., Khoroshylov S. V. Contactless de-orbiting of space debris by the ion beam. Dynamics and control. — Beau Bassin: LAP Lambert Academic Publishing. 330 р. (2018) [In Russian].
2. Alpatov A. P., Khoroshylov S. V. Analysis of ways of the attitude control of the space solar station. Tekhnicheskaya mekhanika. vol 4, 3—12 (2005) [In Russian].
3. Fokov A. A., Khoroshylov S. V. Validation of simplified method for calculation of impact of electric thruster plume to orbital object. Aviatsionno-kosmicheskaya tekhnika i tekhnologiya. N 2/129, 55—66 (2016) [In Russian].
4. Khoroshylov S. V. Attitude control of space-based solar power station using extended state observer. Tehnicheskaja mehanika. N 3, 117—125 (2011) [In Russian].
5. Khoroshylov S. V. Synthesis of suboptimal compensators in form of extended state observer. Tehnicheskaja mehanika. N 2, 79—92 (2014) [In Russian].
6. Khoroshylov S. V. Relative Motion Control System of Spacecraft for Contactless Space Debris Removal. Sci. innov. Vol 14(4), 5—16 (2018). 
7. Alpatov A., Cichocki F., Fokov A., Khoroshylov S., Merino M., Zakrzhevskii A. Algorithm for Determination of Force Transmitted by Plume of Ion Thruster to Orbital Object Using Photo Camera. 66th International Astronautical Congress (12—16 October 1015, Jerusalem) (2015).
8. Alpatov A., Cichocki F., Fokov A., Khoroshylov S., Merino M., Zakrzhevskii A. Determination of the force transmitted by an ion thruster plasma plume to an orbital object. Acta Astronautica. Vol. 119, 241—251 (2016).
https://doi.org/10.1016/j.actaastro.2015.11.020
9. Alpatov A. P., Fokov A. A., Khoroshylov S. V., Savchuk A. P. Error Analysis of Method for Calculation of Non-Contact Impact on Space Debris from Ion Thruster. Mechanics, Materials Science & Engineering Journal. July, 13 pages (2016).
10. Bombardelli C., Peláez J. Ion Beam Shepherd for Contactless Space Debris Removal. Journal of Guidance, Control, and Dynamics. Vol. 34, N 3, 916—920 (2011).
https://doi.org/10.2514/1.51832
11. Bombardelli C., Urrutxua H., Merino M., Ahedo E., Peláez J. Relative Dynamics and Control of an Ion Beam Shepherd Satellite. Advances in the Astronautical Sci. Vol. 143 (2012).
12. Clark F., Spehar P., Brazzel J., Hinkel H. Laser based relative navigation and guidance for space shuttle proximity operations. Advances in the Astronautical Sciences. Vol. 113, 171—186 (2003).
13. Clohessy W., Wiltshire R. Terminal guidance system for satellite rendezvous . Journal of the Aerospace Sciences. Vol. 27, N 9, 653—658 (1960).
https://doi.org/10.2514/8.8704
14. Corbett M. H., Edwards C. H. Thrust Control Algorithms for the GOCE Ion Propulsion Assembly. The 30th International Electric Propulsion Conference (17—20 September 2007. Italy, Florence) (2007).
15. Doyle J., Packard A., Zhou K. Review of LFTs, LMIs and μ. IEEE Conference on Decision and Control (December 1991, Brignton, England), (1991).
16. Doyle J. C., Stein G. Multivariable Feedback Design: Concepts for a Classical. Modern Synthesis. IEEE Transactions on Automatic Control. N 26(1), 4—16 (1981).
17. Kumara K. D., Bang H. C., Tahk M. J. Satellite formation flying using along-track thrust. Acta Astronautica. Vol. 61, N 7—8, 553—564 (2007).
https://doi.org/10.1016/j.actaastro.2007.01.069
18. Lawden D. F. Optimal Trajectories for Space Navigation, London: Butterworths, 1963. 126 p.
19. Leonard C. L., Hollister W. M., Bergmann E. V. Orbital formation keeping with differential drag. Journal of Guidance, Control, and Dynamics. Vol. 12 (1), 108—113 (1989). 
https://doi.org/10.2514/3.20374
20. Nesterov Y. The Projective Method for Solving Linear Matrix Inequalities. Math. Programming Ser. B. Vol. 77, 163—190 (1997). 
https://doi.org/10.1007/BF02614434
21. Redding D. C., Adams N. J., Kubiak, E. T. Linear quadratic stationkeeping for the STS orbiter // Charles Stark Draper Laboratory, Cambridge, MA, Kept. CSDL-R-1879. (1986).
https://doi.org/10.2514/6.1986-2222
22. Rems F., Risse E. A., Benninghoff H. Rendezvous GNCsystem for autonomous orbital servicing of uncooperative targets. 10th International ESA Conference on Guidance, Navigation & Control Systems (29 May — 2 June 2017, Salzburg, Austria) (2017).
23. Starin R. S., Yedavalli R. K., Sparks A. G. Spacecraft formation flying maneuvers using linear-quadratic regulation with no radial axis inputs. AIAA Paper. August, 2001—4029 (2001).
https://doi.org/10.2514/6.2001-4029
24. Vassar R. H., Sherwood R. B. Formationkeeping for a pair of satellites in a circular orbit. Journal of Guidance, Control, and Dynamics. Vol. 8, 235—242 (1985).
https://doi.org/10.2514/3.19965
25. Zhao K., Stoustrup J. Computation of the maximal robust H2 performance radius for uncertain discrete time systems with nonlinear parametric uncertainties. Inter. J. Control. N 67(1), 33—43 (1997). 
https://doi.org/10.1080/002071797224342
26. Zhou K., Doyle J. C., Glover K. Robust and Optimal Control, N. J., USA: Prentice-Hall, 1996. — 596 p.
27. Zhou K., Khargonekar P., Stoustrup J., Niemann H. Robust Performance of Systems with Structured Uncertainties in State Space. Automatica. N 31(2), 249— 255 (1995).