Stochastic Optimal Maneuver Strategies for Transfer Trajectories
Publication: Journal of Aerospace Engineering
Volume 27, Issue 2
Abstract
After being initially launched into the parking orbit, a spacecraft usually implements several maneuvers to insert its nominal orbit as the geostationary orbit for global communication, a Halo orbit to survey the solar wind, and an adjacent orbit to rendezvous with other spacecraft. The transfer problem between two different trajectories is very important in academic research and practical engineering. Trajectory correction maneuvers are necessary to keep actual flight trajectories near the nominal ones because of the errors produced by control maneuvers, measurements, launching, and modeling. However, an inappropriate strategy costs more time and fuel and may even result in mission failure. This study investigates optimal maneuver strategies from the stochastic control viewpoint to track interesting and typical trajectories, including the Halo-transfer and Lambert rendezvous orbits. This study proposes an improved correction algorithm to eliminate modeling errors for reference transfer trajectories. Moreover, this study develops an innovative approach to obtain the optimal correction maneuver strategy that uses the stochastic control theory in determining corrections and adopts the genetic-algorithm and Monte Carlo joint simulation to yield the schedules of maneuvers. Finally, numerical simulations indicate that the proposed approach has potential applications in the tracking of reference trajectories in closed-loop correction maneuvers.
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Acknowledgments
The research is supported by the National Natural Science Foundation of China (11172020), Talent Foundation supported by the Fundamental Research Funds for the Central Universities, Aerospace Science and Technology Innovation Foundation of China Aerospace Science Corporation, and the National High Technology Research and Development Program of China (863 Program: 2012AA120601).
References
Avanzini, G. (2008). “A simple Lambert algorithm.” J. Guid. Control Dyn., 31(6), 1587–1594.
Battin, R. (1964). Astronautical guidance, McGraw Hill, New York.
Battin, R. (1999). An introduction to the mathematics and methods of astrodynamics, American Institute of Aeronautics and Astronautics (AIAA), Reston, VA.
Blanchard, R., Devaney, R., and Lancaster, E. (1966). “A note on Lambert’s theorem.” J. Spacecr. Rockets, 3(9), 1436–1438.
Breakwell, J. (1960). “Fuel requirements for crude interplanetary guidance.” Proc., 2nd Western National Meeting of the American Astronautical Society, American Astronautical Society, Springfield, VA, 5, 53–65.
Cherry, G. (1964). “A general explicit optimizing guidance law for rocket-propelled spaceflight.” Proc., Astrodynamics Guidance and Control Conf., MIT Press, Cambridge, MA, 64–638.
Cho, D., Chung, Y., and Bang, H. (2012). “Trajectory correction maneuver design using an improved B-plane targeting method.” Acta Astronaut., 72(2), 47–61.
Fraser-Andrews, G. (1999). “A multiple-shooting technique for optimal control.” J. Optim. Theory Appl., 102(2), 299–313.
Goldstein, H. (1980). Classical mechanics, Addison Wesley, New York.
Gómez, G., Marcote, M., and Masdemont, J. (2005). “Trajectory correction manoeuvres in the transfer to libration point orbits.” Acta Astronaut., 56(7), 652–669.
Howell, K., Barden, B., and Lo, M. (1997). “Application of dynamical systems theory to trajectory design for a libration point mission.” J. Astronaut. Sci., 54(2), 161–178.
Jenkin, A., and Campbell, E. (2002). “Generic Halo orbit insertion and dispersion error analysis.” Proc., Astrodynamics Specialist Conf. and Exhibit, American Institute of Aeronautics and Astronautics (AIAA)/ American Astronomical Society (AAS), Reston, VA, 2002–4527.
Kasdin, N. J., and Stankievech, L. J. (2009). “On simulating randomly driven dynamic systems.” J. Astronaut. Sci., 57(1), 135–153.
Keller, H., Ritter, M. A., and Mackie, T. R. (2003). “Optimal stochastic correction strategies for rigid-body target motion.” Int. J. Radiat. Oncol. Biol. Phys., 55(1), 261–270.
Kizner, W. (1969). A method of describing miss distances for lunar and interplanetary trajectories, Jet Propulsion Laboratory, Pasadena, CA.
Koon, W., Lo, M., Marsden, J., and Ross, S. (2007). Dynamical systems, the three-body problem and space mission design, Springer, New York.
Nelson, S., and Zarchan, P. (1992). “Alternative approach to the solution of Lambert’s problem.” J. Guid. Control Dyn., 15(4), 1003–1009.
Noton, M. (1998). Space navigation and guidance, Springer, London.
Pfeiffer, C. G. (1965). “A dynamic programing analysis of multiple guidance corrections of a trajectory.” AIAA J., 3(9), 1674–1681.
Prado, A. F. B. A., and Rios-Neto, A. (1994). “A stochastic approach to the problem of spacecraft optimal maneuvers.” Braz. J. Mech. Sci., 16(3), 268–278.
Richardson, D. (1980). “Analytical construction of periodic orbits about the collinear points.” Celestial Mech., 22(3), 241–253.
Rios-Neto, A., and Pinto, R. L. U. (1986). A stochastic approach to generate a projection of the gradient type method, National Institute for Space Research, Sao Jose dos Campos, Brazil.
Rosengren, M. (1992). “Fuel optimal two-impulse orbit correction strategies for the ESA/NASA Ulysses mission.” Proc., 2nd AIAA/AAS Meeting, American Institute of Aeronautics and Astronautics (AIAA)/American Astronomical Society (AAS), Reston, VA, 92–161.
Serban, R., Koon, W. S., Lo, M. W., Marsden, J. E., Petzold, L. R., Ross, S. D., and Wilson, R. S. (2002). “Halo orbit mission correction maneuvers using optimal control.” Automatica, 38(4), 571–683.
Song, Y. (2005). “Optimal trajectory correction maneuver design using the B-plane targeting method for future Korean Mars missions.” J. Astronaut. Space Sci., 22(4), 451–462.
Stengel, R. (1993). Optimal control and estimation, Dover Publications, New York.
Vallado, D. (1997). Fundamentals of astrodynamics and applications, McGraw Hill, New York.
White, K., and Tunnell, P. (1965). A guidance scheme for lunar descent based on linear perturbation theory, National Aeronautics and Space Administration (NASA), Moffett Field, CA.
Xu, M., Tan, T., and Xu, S. (2012a). “Research on the transfers to Halo orbits from the view of invariant manifolds.” Sci. Chin. Phys. Mech. Astron., 55(4), 671–683.
Xu, M., Wang, Y., and Xu, S. (2012b). “On the existence of invariant relative orbit from the dynamical system point of view.” Celestial Mech. Dyn. Astron., 112(4), 427–444.
Xu, M., and Xu, S. (2007). “ invariant relative orbits via differential correction algorithm.” Acta Mech. Sin., 23(5), 585–595.
Yong, J., and Zhou, X. Y. (1999). Stochastic controls: Hamiltonian systems and HJB equations, Springer, London.
Zhou, W., and Yang, W. (2004). “Mid-correction of trans-lunar trajectory of lunar explorer.” Chin. J. Aeronaut., 25(1), 89–96.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 27 • Issue 2 • March 2014
Pages: 225 - 237
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Apr 30, 2012
Accepted: Sep 5, 2012
Published online: Sep 6, 2012
Published in print: Mar 1, 2014
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