Celestial Mechanics and Dynamical Astronomy

, Volume 115, Issue 1, pp 1–19 | Cite as

Spacecraft intercept using minimum control energy and wait time

Original Article


A new approach to the minimum energy impulse intercept problem for spacecraft in orbit is explored. The types of orbits investigated in this paper are not restricted to a particular one. The constrained optimization technique is formulated with the universal variable, which is used to describe orbit information with sufficient accuracy for general types of orbits. Two optimization problems are posed. First, a problem for minimum velocity change and time of flight for intercept are investigated with the constraint on the final position of two satellites. Next, the so-called wait time is also added as an additional parameter to be determined. Although a closed-form solution is not obtained, the Newton iteration technique is successfully applicable. Finally, by numerically comparing the proposed solution to the Hohmann transfer, the suggested approach is demonstrated to be a feasible technique applicable to a broad class of orbit transfer problems.


Two-impulse rendezvous Minimum energy Lambert problem Non-coplanar elliptical orbits Orbit transfer 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bate R.R., Mueller D.D., White J.E.: Fundamentals of Astrodynamics, chap. 7. Dover Pub. Inc., New York (1971)Google Scholar
  2. Battin R.H.: An elegant lambert algorithm. J. Guid. Control Dyn. 7(6), 662–670 (1984)ADSMATHCrossRefGoogle Scholar
  3. Bryson A.E. Jr., Ho Y.-C.: Applied Optimal Control, chap. 1. Hemisphere, Washington, DC (1975)Google Scholar
  4. Carter T., Humi M.: A new approach to impulsive rendezvous near circular orbit. Celest. Mech. Dyn. Astron. 112(4), 385–426 (2012)MathSciNetADSCrossRefGoogle Scholar
  5. Chobotov V.A.: Orbital Mechanics, 3rd edn, chap. 4. AIAA Education Series, Reston, VA (2002)CrossRefGoogle Scholar
  6. Jezewski, D.J.: Optimal rendezvous trajectories subject to arbitrary perturbations and constraints. AIAA paper 92-4507-CP (1992)Google Scholar
  7. Kim Y.H., Spencer D.B.: Optimal spacecraft rendezvous using genetic algorithms. J. Spacecr. Rocket 39(6), 859–865 (2002)ADSCrossRefGoogle Scholar
  8. Leeghim H., Jaroux B.A.: Energy optimal solution to the Lambert problem. J. Guid. Control Dyn. 33(3), 1008–1010 (2009)CrossRefGoogle Scholar
  9. Luo Y.Z., Lei Y.J., Tang G.J.: Optimal multi-objective nonlinear impulsive rendezvous. J. Guid. Control Dyn. 30(4), 994–1002 (2007)CrossRefGoogle Scholar
  10. Prussing J.E.: Optimal four-impulse fixed-time rendezvous in the vicinity of a circular orbit. AIAA J. 7(5), 928–935 (1969)ADSMATHCrossRefGoogle Scholar
  11. Prussing, J.E.: A Class of Optimal Two-Impulse Rendezvous Using Multiple-Revolution Lambert Solutions. Advances in the Astronautical Sciences, vol. 106, Univelt, Inc., San Diego, CA, pp. 17–37 (2000)Google Scholar
  12. Prussing J.E., Chiu J.-H.: Optimal multiple-impulse time-fixed rendezvous between circular orbits. J. Guid. Control Dyn. 9(1), 17–22 (1986)ADSMATHCrossRefGoogle Scholar
  13. Shen H., Tsiotras P.: Optimal two-impulse rendezvous using multiple-revolution Lambert solutions. J. Guid. Control Dyn. 26(1), 50–61 (2003)CrossRefGoogle Scholar
  14. Vallado D.A.: Fundamentals of astrodynamics and applications, 2nd edn, chap. 7. Microcosm Press, El Segundo, CA (2001)Google Scholar
  15. Zhang G., Zhou D., Mortari D.: Optimal two-impulse rendezvous using constrained multiple-revolution Lambert solutions. Celest. Mech. Dyn. Astron. 110(4), 305–317 (2011)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Samsung ElectronicsSuwonSouth Korea

Personalised recommendations