Skip to main content
Log in

Nonlinear programming control using differential aerodynamic drag for CubeSat formation flying

  • Published:
Frontiers of Information Technology & Electronic Engineering Aims and scope Submit manuscript

Abstract

Because of their volume and power limitation, it is difficult for CubeSats to configure a traditional propulsion system. Atmospheric drag is one of the space environmental forces that low-orbit satellites can use to realize orbit adjustment. This paper presents an integrated control strategy to achieve the desired in-track formation through the atmospheric drag difference, which will be used on ZJUCubeSat, the next pico-satellite of Zhejiang University and one of the participants of the international QB50 project. The primary mission of the QB50 project is to explore the near-Earth thermosphere and ionosphere at the orbital height of 90–300 km. Atmospheric drag cannot be ignored and has a major impact on both attitude and orbit of the satellite at this low orbital height. We conduct aerodynamics analysis and design a multidimensional nonlinear constraint programming (MNLP) strategy to calculate different desired area–mass ratios and corresponding hold times for orbit adjustment, taking both the semimajor axis and eccentricity into account. In addition, area–mass ratio adjustment is achieved by pitch attitude maneuver without any deployable mechanism or corresponding control. Numerical simulation based on ZJUCubeSat verifies the feasibility and advantage of this design.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bazaraa, M.S., Sherali, H.D., Shetty, C.M., 2013. Nonlinear Programming: Theory and Algorithms. John Wiley & Sons, New Jersey.

    MATH  Google Scholar 

  • Byrd, R.H., Hribar, M.E., Nocedal, J., 1999. An interior point algorithm for large-scale nonlinear programming. SIAM J. Optim., 9(4): 877–900. https://doi.org/10.1137/S1052623497325107

    Article  MathSciNet  MATH  Google Scholar 

  • Cai, B., Wang, H., Zhu, X., et al., 2011. Design of the Earth magnetic field measurement system for pico-satellites. Chin. J. Sens. Actuat., 27(8): 1–5 (in Chinese). https://doi.org/10.3969/j.issn.1004-1699.2011.08.026

    Google Scholar 

  • Campbell, M., Fullmer, R.R., Hall, C.D., 2000. The ION-F formation flying experiments. AAS/AIAA Space Flight Mechanics Meeting, p.135–149. https://doi.org/10.13140/2.1.3903.3603

    Google Scholar 

  • Drob, D., Emmert, J., Crowley, G., et al., 2008. An empirical model of the Earth’s horizontal wind fields: HWM07. J. Geophys. Res. Space Phys., 113:A12304. https://doi.org/10.1029/2008JA013668

    Article  Google Scholar 

  • Eyer, J.K., Damaren, C.J., Zee, R.E., et al., 2007. A formation flying control algorithm for the CanX-4&5 low Earth orbit nanosatellite mission. Space Technol., 27(4): 147–158.

    Google Scholar 

  • Gaposchkin, E.M., 1994. Calculation of Satellite Drag Coef-ficients. Technical Report, DTIC Document.

    Google Scholar 

  • Horsley, M., Nikolaev, S., Pertica, A., 2013. Small satellite rendezvous using differential lift and drag. J. Guid. Contr. Dynam., 36(2): 445–453. https://doi.org/10.2514/1.57327

    Article  Google Scholar 

  • Lambert, C., Kumar, B.S., Hamel, J.F., et al., 2012. Imple-mentation and performance of formation flying using differential drag. Acta Astronaut., 71: 68–82. https://doi.org/10.1016/j.actaastro.2011.08.013

    Article  Google Scholar 

  • Leonard, C.L., Hollister, W.M., Bergmann, E.V., 1989. Orbital formationkeeping with differential drag. J. Guid. Contr. Dynam., 12(1): 108–113. https://doi.org/10.2514/3.20374

    Article  Google Scholar 

  • Liu, L., 2000. Orbit Theory of Spacecraft. National Defense Industry Press, Beijing, p.86–90 (in Chinese).

    Google Scholar 

  • Lohn, J.D., Hornby, G.S., Linden, D.S., 2005. An evolved antenna for deployment on NASA’s Space Technology 5 Mission. In: O’Reilly, U.M., Yu, T., Riolo, R., et al. (Eds.), Genetic Programming Theory and Practice II. Springer, New York, p.301–315. https://doi.org/10.1007/0-387-23254-0_18

    Chapter  Google Scholar 

  • Marcos, F.A., 2006. New satellite drag modeling capabilities. 44th AIAA Aerospace Sciences Meeting and Exhibit, p.1–13. https://doi.org/10.2514/6.2006-470

    Google Scholar 

  • Meng, T., Wang, H., Jin, Z.H., et al., 2009. Attitude stabiliza-tion of a pico-satellite by momentum wheel and magnetic coils. J. Zhejiang Univ.-Sci. A, 10(11): 1617–1623. https://doi.org/10.1631/jzus.A0820425

    Article  MATH  Google Scholar 

  • Moe, K., Moe, M.M., 2005. Gas–surface interactions and satellite drag coefficients. Planet. Space Sci., 53(8): 793–801. https://doi.org/10.1016/j.pss.2005.03.005

    Article  Google Scholar 

  • Montenbruck, O., Gill, E., 2012. Satellite Orbits: Models, Methods and Applications. Springer Science & Business Media.

    MATH  Google Scholar 

  • Pérez, D., Bevilacqua, R., 2013. Differential drag spacecraft rendezvous using an adaptive Lyapunov control strategy. Acta Astronaut., 83: 196–207. https://doi.org/10.1016/j.actaastro.2012.09.005

    Article  Google Scholar 

  • Picone, J.M., Hedin, A.E., Drob, D.P., et al., 2002. NRLMSISE-00 empirical model of the atmosphere: sta-tistical comparisons and scientific issues. J. Geophys. Res. Space Phys., 107(A12): SIA15-1-SIA15-16. https://doi.org/10.1029/2002JA009430

    Article  Google Scholar 

  • Reid, T., Misra, A.K., 2011. Formation flight of satellites in the presence of atmospheric drag. J. Aerosp. Eng. Sci. Appl., 3(1): 64–91.

    Google Scholar 

  • Reinhard, R., Asma, C., Muylaert, J., 2012. The QB50 project: a Network of 50 Cubesats. Von Karman Institute for Fluid Dynamics, Rhode Saint Genese, Belgium.

    Google Scholar 

  • Schamberg, R., 1959. A New Analytic Representation of Sur-face Interaction for Hyperthermal Free Molecule Flow with Application to Neutral-Particle Drag Estimates of Satellites. Rand Corporation.

    Google Scholar 

  • Schaub, H., Alfriend, K.T., 2002. Hybrid Cartesian and orbit element feedback law for formation flying spacecraft. J. Guid. Contr. Dynam., 25(2): 387–393. https://doi.org/10.2514/2.4893

    Article  Google Scholar 

  • Vallado, D.A., 2001. Fundamentals of Astrodynamics and Applications. Springer Science & Business Media, Berlin.

    MATH  Google Scholar 

  • Vallado, D.A., Finkleman, D., 2014. A critical assessment of satellite drag and atmospheric density modeling. Acta Astronaut., 95: 141–165. https://doi.org/10.1016/j.actaastro.2013.10.005

    Article  Google Scholar 

  • Varma, S., Kumar, K.D., 2012. Multiple satellite formation flying using differential aerodynamic drag. J. Spacecr. Rock., 49(2): 325–336. https://doi.org/10.2514/1.52395

    Article  Google Scholar 

  • Wang, J., Wang, H., Ying, P., et al., 2012. Design of four-quadrant analog Sun sensor. Chin. J. Sens. Actuat., 25(12): 1659–1663 (in Chinese). https://doi.org/10.3969/j.issn.1004-1699.2012.12.007

    Google Scholar 

  • Yang, M., Wang, H., Wu, C.J., et al., 2012. Space flight vali-dation of design and engineering of the ZDPS-1A pico-satellite. Chin. J. Aeronaut., 25(5): 725–738. https://doi.org/10.1016/S1000-9361(11)60439-1

    Article  Google Scholar 

  • Yao, H., Zeng, G.Q., Hu, M., 2010. Time-optimal aerodynamic control for along-track separation of spacecraft formation flying. J. Acad. Equip. Comm. Technol., 21(1): 70–73 (in Chinese). https://doi.org/10.3783/j.issn.1673-0127.2010.01.017

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tao Meng.

Additional information

Project supported by the National Science Fund for Distinguished Young Scholars of China (No. 61525403) and the National Natural Science Foundation of China (No. 61503334)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, Sc., Meng, T. & Jin, Zh. Nonlinear programming control using differential aerodynamic drag for CubeSat formation flying. Frontiers Inf Technol Electronic Eng 18, 867–881 (2017). https://doi.org/10.1631/FITEE.1500493

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1631/FITEE.1500493

Key words

CLC number

Navigation