International Journal of Aeronautical and Space Sciences

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Collision Avoidance Using Linear Quadratic Control in Satellite Formation Flying

  • Mok, Sung-Hoon (Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology) ;
  • Choi, Yoon-Hyuk (Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology) ;
  • Bang, Hyo-Choong (Department of Aerospace Engineering, Korea Advanced Institute of Science and Technology)
  • Published : 2010.12.15
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Abstract

This paper proposes a linear system control algorithm with collision avoidance in multiple satellites. Consideration of collision avoidance is augmented by adding a weighting term in the cost function of the original tracking problem in linear quadratic control (LQC). Because the proposed algorithm relies on a similar solution procedure to the original LQC, its inherent advantages, including gain-robustness and optimality, are preserved. To confirm and visualize the derived algorithm, a simple example of two-vehicle motion in the two-dimensional plane is illustrated. In addition, the proposed collision avoidance control is applied to satellite formation flying, and verified by numerical simulations.

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References

  1. Anderson, B. D. O. and Moore, J. B. (1990). Optimal Control: Linear Quadratic Methods. Englewood Cliffs: Prentice Hall.
  2. Bellman, R. E. (1952). On the theory of dynamics programming. Proceeding of the National Academy of Sciences, California, pp. 716-719.
  3. Clohessy, W. H. and Wiltshire, R. S. (1960). Terminal guidance system for satellite rendezvous. Journal of the Aerospace Science, 27, 653-658. https://doi.org/10.2514/8.8704
  4. Dorato, P., Abdallah, C. T., and Cerone, V. (1995). Linear-Quadratic Control: an Introduction. Englewood Cliffs: Prentice Hall.
  5. Fravolini, M. L., Ficola, A., Napolitano, M. R., Campa, G., and Perhinschi, M. G. (2003). Development of modeling and control tools for aerial refueling for UAVs. AIAA Guidance, Navigation, and Control Conference and Exhibit, Austin, TX, pp. AIAA 2003-5798.
  6. Gribble, J. J. (1993). Linear quadratic Gaussian/loop transfer recovery design for a helicopter in low-speed flight. Journal of Guidance, Control, and Dynamics, 16, 754-761. https://doi.org/10.2514/3.21077
  7. Hadaegh, F. Y., Ghavimi, A. R., Singh, G., and Quadrelli, M. (2000). A centralized optimal controller for formation flying spacecraft. International Conference of Intelligence and Technology.
  8. Lim, H., Bang, H., and Kim, H. (2005). Sliding mode control for the configuration of satellite formation flying using potential functions. International Journal of Aeronautical and Space Sciences, 6, 56-63. https://doi.org/10.5139/IJASS.2005.6.2.056
  9. Lovren N. and Tomic, M. (1994). Analytic solution of the Riccati equation for the homing missile linear-quadratic control problem. Journal of Guidance, Control, and Dynamics, 17, 619-621. https://doi.org/10.2514/3.21242
  10. McCambish, S. B. Romano M., Nolet, S., Edwards C. M., and Miller, D. W. (2009). Flight testing of multiple-spacecraft control on SPHERES during close-proximity operations. Journal of Guidance, Control, and Dynamics, 46, 1202-1213.
  11. Plumlee, J. H. and Bevly, D. M. (2004). Control of a ground vehicle using quadratic programming based control allocation techniques. Proceeding of the American Control Conference, Boston, MA, 4704-4709
  12. Psiaki, M. L. (2001). Magnetic torquer attitude control via asymptotic periodic linear quadratic regulation. Journal of Guidance, Control, and Dynamics, 24, 386-394. https://doi.org/10.2514/2.4723
  13. Ridgely, D. B., Banda, S. S., McQuade, T. E., and Lynch, P. J. (1987). Linear-quadratic-Gaussian with loop-transfer recovery methodology for an unmanned aircraft. Journal of Guidance, Control, and Dynamics, 10, 82-89. https://doi.org/10.2514/3.20184
  14. Slater, G. L., Byram, S. M., and Williams, T. W. (2006). Collision avoidance for satellites in formation flight. Journal of Guidance, Control, and Dynamics, 29, 1140-1146. https://doi.org/10.2514/1.16812
  15. Speyer, J. L. (1979). Computation and transmission requirements for a decentralized linear-quadratic-Gaussian control problem. IEEE Transactions and Automatic Control, 24, 262-269. https://doi.org/10.1109/TAC.1979.1101973
  16. Xing, G. Q., Parvez, S. A., and Folta, D. (2000). Design and implementation of synchronized autonomous orbit and attitude control for multiple spacecraft formation using GPS measurement feedback. Advances in the Astronautical Sciences, 105I, 115-134.
  17. Wang, S. and Schaub, H. (2008). Spacecraft collision avoidance using coulomb forces with separation distance and rate feedback. Journal of Guidance, Control, and Dynamics, 31, 740-750. https://doi.org/10.2514/1.29634
  18. Wiener, N. (1948). Cybernetics. New York: John Wiley.

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