Skip to main content
SpringerLink
Log in

An active time-optimal control for space debris deorbiting via geomagnetic field

  • Original Article
  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

This paper is concerned with an approach for active removing of space debris by electrodynamic tether (EDT) systems in a time-optimal maneuver. In this regard, a collector–emitter system is comprised of the insulated EDT in order to generate the required electric current over a virtual circuit once the induced electric current is adopted as control force producer. To this end, a simulation program is initially developed, during which dynamic and mathematical models of the EDT as well as the geomagnetic field are encompassed, respectively. This toolset is first utilized for prediction of orbital characteristics during the deorbit process; and subsequently, using the direct transcription method, the time-optimal problem is well solved. The efficacy of the suggested technique is verified through extensive simulations once all hard constraints of the underlying problem are well satisfied. In short, while the altitude varies from 1413 to 200 km, the optimized deorbit time would reduce about 17 days.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  • Argatov, I., Rautakorpi, P., Silvennoinen, R.: Apparent wind load effects on the tether of a kite power generator. J. Wind Eng. Ind. Aerodyn. 99(10), 1079–1088 (2011)

    Article  Google Scholar 

  • Betts, J.T.: Survey of numerical methods for trajectory optimization. J. Wind Eng. Ind. Aerodyn. 21(2), 193–207 (1998)

    MathSciNet  MATH  Google Scholar 

  • Bitzer, M.S.: Optimal electrodynamic tether phasing and orbit-raising maneuvers. Doctoral Dissertation, Virginia Polytechnic Institute and State University (2009)

  • Blumer, J.H., Donahue, B.B., Bangham, M.E., Roth, A.: Practicality of using a tether for electrodynamic reboost of the International Space Station (2001)

  • Bombardelli, C., Pelaez, J.: Ion beam shepherd for contactless space debris removal. J. Wind Eng. Ind. Aerodyn. 34(3), 916–920 (2011)

    Google Scholar 

  • Buck, A.J.: An approach to optimal control of electrodynamic tethers in a stochastically varying drag environment (No. USNA-TSPR-396). Naval Academy, Annapolis, MD (2011)

    Google Scholar 

  • Carlson, A.F.: Optimal orbit maneuvers with electrodynamic tethers. Naval Postgraduate School, Monterey, CA (2006)

    Google Scholar 

  • Covello, F.: Application of electrical propulsion for an active debris removal system: a system engineering approach. J. Wind Eng. Ind. Aerodyn. 50(7), 918–931 (2012)

    Google Scholar 

  • Deluca, L.T., Bernelli, F., Maggi, F., Tadini, P., Pardini, C., Anselmo, L., et al.: Active space debris removal by a hybrid propulsion module. Acta Astronaut. 91, 20–33 (2013)

    Article  ADS  Google Scholar 

  • Falugi, P., Kerrigan, E., Wyk E.: ICLOCS—Imperial College London Optimal Control Software, http://www.ee.ic.ac.uk/ICLOCS/user_guide.pdf (2015)

  • Forward, R.L., Hoyt, R.P., Uphoff, C.: Application of the terminator tether electrodynamic drag technology to the deorbit of constellation spacecraft. Acta Astronaut. 98, 3491 (1998)

    Google Scholar 

  • Garg, D.: Advances in global pseudospectral methods for optimal control. Doctoral Dissertation, University of Florida (2011)

  • Gittins, G.L., Swinerd, G.G., Lewis, H.G., Williams, D.N.: A study of debris impact collision probabilities to space tethers. Acta Astronaut. 34(5), 1080–1084 (2004)

    Google Scholar 

  • Gläßel, H., Zimmermann, F., Brückner, S., Schöttle, U.M., Rudolph, S.: Adaptive neural control of the deployment procedure for tether-assisted re-entry. Acta Astronaut. 8(1), 73–81 (2004)

    MATH  Google Scholar 

  • Hoyt, R.P.: Design of a tether boost facility for the human Mars mission. Tethers Unlimited Inc, Seattle, WA (1999)

    Google Scholar 

  • Iki, K., Kawamoto, S., Morino, Y.: Experiments and numerical simulations of an electrodynamic tether deployment from a spool-type reel using thrusters. Acta Astronaut. 94(1), 318–327 (2014)

    Article  ADS  Google Scholar 

  • Ishige, Y., Kawamoto, S., Kibe, S.: Study on electrodynamic tether system for space debris removal. Acta Astronaut. 55(11), 917–929 (2004)

    Article  ADS  Google Scholar 

  • Kojima, H., Sugimoto, T.: Nonlinear control of electro-dynamic tether system. In: AIAA/AAS Astrodynamics Specialist Conference and Exhibit (2006)

  • Kojima, H., Sugimoto, T.: Switching delayed feedback control for an electrodynamic tether system in an inclined elliptic orbit. Acta Astronaut. 66(7), 1072–1080 (2010)

    Article  ADS  Google Scholar 

  • Kumar, K.D., Tan, B.: Nonlinear optimal control of tethered satellite systems using tether offset in the presence of tether failure. Acta Astronaut. 66(9), 1434–1448 (2010)

    ADS  Google Scholar 

  • Lanoix, E.L., Misra, A.K., Modi, V.J., Tyc, G.: Effect of electromagnetic forces on the orbital dynamics of tethered satellites. Acta Astronaut. 28(6), 1309–1315 (2005)

    Google Scholar 

  • Misra, A.K.: Dynamics and control of tethered satellite systems. Acta Astronaut. 63(11), 1169–1177 (2008)

    Article  ADS  Google Scholar 

  • Nylin, R.: Evaluation of optimization solvers in mathematica with focus on optimal control problems. Master’s Diss., Chalmers University of Technology (2013)

  • Pardini, C., Hanada, T., Krisko, P.H.: Benefits and risks of using electrodynamic tethers to de-orbit spacecraft. Acta Astronaut. 64(5), 571–588 (2009)

    Article  ADS  Google Scholar 

  • Phipps, C.R., Baker, K.L., Libby, S.B., Liedahl, D.A., Olivier, S.S., Pleasance, L.D., et al.: Removing orbital debris with pulsed lasers. Acta Astronaut. 1464(1), 468 (2012)

    Google Scholar 

  • Sánchez-Arriaga, G., Bombardelli, C., Chen, X.: Impact of nonideal effects on bare electrodynamic tether performance. Acta Astronaut. 31(3), 951–955 (2015)

    Google Scholar 

  • Tintori, C., Emanuelli, M.: An active space debris removal mission: orbit, engine and gasification of residue, Doctoral Dissertation, Polytechnic of Milano, Italy (2011)

  • Ueno, H., Dubowsky, S., Lee, C., Zhu, C., Ohkami, Y., Matsumoto, S., et al.: Space robotic mission concepts for capturing stray objects. J. Space Technol. Sci. 18(2), 2_1–2_8 (2002)

    Google Scholar 

  • Vannaroni, G., Dobrowolny, M., De Venuto, F.: Deorbiting with electrodynamic tethers: comparison between different tether configurations. Acta Astronaut. 1(3), 159–172 (1999)

    Google Scholar 

  • Wen, H., Jin, D.P., Hu, H.Y.: Advances in dynamics and control of tethered satellite systems. Acta. Mech. Sin. 24(3), 229–241 (2008)

    Article  ADS  MATH  Google Scholar 

  • Yamaigiwa, Y., Hiragi, E., Kishimoto, T.: Dynamic behavior of electrodynamic tether deorbit system on elliptical orbit and its control by Lorentz force. Acta. Mech. Sin. 9(4), 366–373 (2005)

    MATH  Google Scholar 

  • Zhong, R., Zhu, Z.H.: Libration dynamics and stability of electrodynamic tethers in satellite deorbit. Acta. Mech. Sin. 116(3), 279–298 (2013)

    MathSciNet  Google Scholar 

  • Zimmermann, F., Schöttle, U.M., Messerschmid, E.: Optimization of the tether-assisted return mission of a guided re-entry capsule. Acta. Mech. Sin. 9(8), 713–721 (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of New Sciences and Technologies, Flight Dynamics and Control, University of Tehran, Tehran, Iran

    M. A. Amiri Atashgah & Abolfazl Lavaei

  2. Faculty of New Sciences and Technologies, Space Engineering, University of Tehran, Tehran, Iran

    Hamid Gazerpour & Yaser Zarei

Authors
  1. M. A. Amiri Atashgah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamid Gazerpour
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abolfazl Lavaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yaser Zarei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Amiri Atashgah.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Amiri Atashgah, M.A., Gazerpour, H., Lavaei, A. et al. An active time-optimal control for space debris deorbiting via geomagnetic field. Celest Mech Dyn Astr 128, 343–360 (2017). https://doi.org/10.1007/s10569-017-9755-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10569-017-9755-y

Keywords

Search

Navigation