Establishment of Satellite Formation with Initial Uncertainty by Control Lyapunov Function Approach

Navabi, M.; Barati, M.; Khamseh, Hossein Bonyan

doi:10.5028/jatm.2012.04014511

Abstract

In recent years, dynamics and control of satellite formation flying have been active areas of research. From the mission planning perspective, three main areas namely formation establishment, maintenance and reconfiguration have been discussed. In this paper, a study of formation establishment under initial uncertainty is presented. In this regard, dynamics of low Earth orbit satellite formation is discussed. Control Lyapunov function approach is adopted to bring a deputy satellite, with perturbed initial conditions into formation with a chief satellite. In order to take account of the initial orbit insertion error, uncertainty in initial conditions of the deputy satellite is considered. For a case study, a relatively small formation is adopted, with air-launched Pegasus as the launch vehicle. For several initial conditions, control function and required time to achieve a given mission accuracy are determined, and results are provided as illustration.

Keywords:
Satellite Formation; Lyapunov Function; Dynamics; Control

Full text available only in PDF format.

REFERENCES

Alfriend, K. T. et al., 2009, "Spacecraft formation flying, dynamics, control and navigation", Published by Butterworth-Heinemann.
Baoyin, H. et al., 2002, "Dynamical behaviors and relative trajectories ofthe spacecraft formation flying," Journal of Aerospace Science and Technology, Vol. 6, Issue 4, pp. 295-301.
Carpenter, J. R. et al., 2003, "Benchmark problems for spacecraft formation flying missions," in Proceedings of the AIAA Guidance Navigation and Control Conference.
Hang, Y et al., 2008, "Comparison study of relative dynamic models for satellite formation flying," Proceedings of 2^nd IEEE ISSCAA.
Kapila, V. et al., 1499, "Spacecraft formation flying: dynamics and control," Proceedings of the American Control Conference, San Diego, CA, pp. 4137-4141.
Mukherjee, R., and Chen, D., 1993, "Asymptotic Stability Theorem for autonomous Systems," Journal of Guidance, Control, and Dynamics, Vol. 16, No. 5, p. 961-963.
Navabi, M. et al., 2011, "A comparative study of dynamics models for satellite formation flying - Ordinary Differential Equations approach," IEEE RAST Conference, Istanbul, Turkey, pp. 829-832.
No, T. S. et al., 2009, "Spacecraft formation-keeping using a closed-form orbit propagator and optimization technique," Acta Astronautica, Vol. 65, Issue 4, pp. 537-548.
Orr, N. G. et al., 2007, "Precision formation flight: the CanX-4 and Can-X 5 dual nanosatellite mission," 21st AIAA/USU Conference on Small Satellites, Salt Lake City, UT.
"Pegasus User's Guide", 2000, Orbital Science Inc, Verison 5.0.
Peterson, E., and Zee, R. E., 2008, "Possible Orbit Scenarios for an InSAR Formation Flying Microsatellite Mission, 2" 2nd AIAA/USU Conference on Small Satellites Logan, Utah.
Sabol, C. et al., 2001,"Satellite formation flying design and evolution," Journal of Spacecraft and Rockets, Vol. 38, No. 2, pp. 270-278.
Schaub, H., 2004, "Relative orbit geometry through classical orbit element differences," Journal of Guidance, Control, and Dynamic, Vol. 27, No. 5, pp. 839-848.
Schaub, H., and Junkins, J. L., 2002, "Analytical Mechanics of Space Systems", AIAA education series, p. 539-40.

Publication Dates

Publication in this collection
Jan-Mar 2012

History

Received
05 Oct 2011
Accepted
29 Jan 2012

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[1] Alfriend, K. T. et al., 2009, "Spacecraft formation flying, dynamics, control and navigation", Published by Butterworth-Heinemann.

[2] Baoyin, H. et al., 2002, "Dynamical behaviors and relative trajectories ofthe spacecraft formation flying," Journal of Aerospace Science and Technology, Vol. 6, Issue 4, pp. 295-301.

[3] Carpenter, J. R. et al., 2003, "Benchmark problems for spacecraft formation flying missions," in Proceedings of the AIAA Guidance Navigation and Control Conference.

[4] Hang, Y et al., 2008, "Comparison study of relative dynamic models for satellite formation flying," Proceedings of 2^nd IEEE ISSCAA.

[5] Kapila, V. et al., 1499, "Spacecraft formation flying: dynamics and control," Proceedings of the American Control Conference, San Diego, CA, pp. 4137-4141.

[6] Mukherjee, R., and Chen, D., 1993, "Asymptotic Stability Theorem for autonomous Systems," Journal of Guidance, Control, and Dynamics, Vol. 16, No. 5, p. 961-963.

[7] Navabi, M. et al., 2011, "A comparative study of dynamics models for satellite formation flying - Ordinary Differential Equations approach," IEEE RAST Conference, Istanbul, Turkey, pp. 829-832.

[8] No, T. S. et al., 2009, "Spacecraft formation-keeping using a closed-form orbit propagator and optimization technique," Acta Astronautica, Vol. 65, Issue 4, pp. 537-548.

[9] Orr, N. G. et al., 2007, "Precision formation flight: the CanX-4 and Can-X 5 dual nanosatellite mission," 21st AIAA/USU Conference on Small Satellites, Salt Lake City, UT.

[10] "Pegasus User's Guide", 2000, Orbital Science Inc, Verison 5.0.

[11] Peterson, E., and Zee, R. E., 2008, "Possible Orbit Scenarios for an InSAR Formation Flying Microsatellite Mission, 2" 2nd AIAA/USU Conference on Small Satellites Logan, Utah.

[12] Sabol, C. et al., 2001,"Satellite formation flying design and evolution," Journal of Spacecraft and Rockets, Vol. 38, No. 2, pp. 270-278.

[13] Schaub, H., 2004, "Relative orbit geometry through classical orbit element differences," Journal of Guidance, Control, and Dynamic, Vol. 27, No. 5, pp. 839-848.

[14] Schaub, H., and Junkins, J. L., 2002, "Analytical Mechanics of Space Systems", AIAA education series, p. 539-40.

Brasil