Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
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Low Thrust, Fuel Optimal Earth Escape Trajectories Design

저추력기를 이용한 연료 최적의 지구탈출 궤적 설계 연구

  • 이동헌 (한국과학기술원 항공우주공학과 대학원) ;
  • 방효충 (한국과학기술원 항공우주공학과)
  • Published : 2007.07.31
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Abstract

A Discrete continuation Method/homotopy approaches are studied for energy/fuel optimal low thrust Earth escape trajectory by solving a two point boundary value problem(TPBVP). Recently, maneuvers using low thrust propulsion system have been identified as emerging technologies. The low thruster is considered as the main actuator for orbit maneuvers. The cost function consists of a energy/fuel consumption function, and constraints are position and velocity vectors at the terminal escape point. Solving the minimum energy/fuel problem directly is not an easy task, so we adopt the homotopy analysis. Using a solution of the minimum energy, which is solved by discrete continuation method, we obtain the solution of the minimum fuel problem.

본 논문에서는 일정한 추력을 이용한 지구-달의 연료 최적 궤적해를 이용하여, 가변 추력기를 이용한 지구 탈출 궤적에서의 에너지 및 연료 최적 궤적을 설계하였다. 에너지 최적의 지구 탈출 궤적은 여러 차례 지구를 공전하게 되고, 궤도 천이 시간이 일반적인 궤도 천이 시간 보다 상대적으로 오래 소요되므로 최적화 문제를 해를 구하기가 쉽지 않다. 따라서 에너지 최적 해를 구하기 위하여, 초기 상태변수를 조정하면서 Discrete continuation의 기법을 적용하였다. 최적화 문제의 종말 조건은 일정한 추력기를 이용한 지구 탈출 궤적의 종말 조건을 이용하였고, 구속 시간은 일정한 추력기를 이용한 궤도 천이의 경우보다 큰 값으로 설정하였다. 한편, 연료 최적 궤적은 제어 입력의 형태가 불연속적이기 때문에 해를 구하기가 쉽지 않다. 따라서 연료 최적 궤적은 에너지 최적의 해와 호모토피(Homotopy) 기법을 적용시켜 그 해를 구하였다.

Keywords

References

  1. Guelman, M., 'Earth-to-Moon Transfer with a Limited Power Engine', Journal of Guidance, Control, and Dynamics, Vol. 18, No.5, 1995, 1133-1138 https://doi.org/10.2514/3.21515
  2. Pierson, B. L., and Kluever, C. A, 'Three-Stage Approach to Optimal Low-Thrust Earth-Moon Trajectories', Journal of Guidance, Control, and Dynamics, Vol. 17, No.6, 1994, 1275-1282 https://doi.org/10.2514/3.21344
  3. Pierson, B. L., and Kluever, C. A, 'Optimal Low-Thrust Three-Dimensional Earth-Moon Trajectories', Journal of Guidance, Control, and Dynamics, Vol. 18, No.4, 1995, 830-837 https://doi.org/10.2514/3.21466
  4. Herman, A.L., and Conway, B. A, 'Optimal, Low-Thrust, Earth-Mon Orbit Transfer', Journal of Guidance, Control, and Dynamics, Vol. 21, No.1, January-February 1998, 141-147 https://doi.org/10.2514/2.4210
  5. Betts, J. T., 'Survey of Numerical Methods for trajectory Optimization', Journal of Guidance, Control, and Dynamics, Vol. 21, No.2, March-Apr il 1998, 193-207 https://doi.org/10.2514/2.4231
  6. Haberkorn, T., Martinon, P., and Gergaud, J., 'Low-Thrust Minimum-Fuel Orbital Transfer: A Homotopic Approach', Journal of Guidance, Control, and Dynamics, Vol. 27, No.6, November-December 2004, 1046-1060 https://doi.org/10.2514/1.4022
  7. Kirk, D.E., Optimal Control Theory: An Introduction, Prentice-Hall, Englewood Cliffs, NJ, 1970
  8. Milam, M., 'A Homotopy Technique for constrained Trajectory Generation', Research report, Division of Engineering and Applied Science California Institute of Technology, 1998
  9. Garcia, C. S., and Zangwill, W. I., 'An approach to Homotopy and Degree Theory', Mathematics of Operations Research, Vol. 4. No. 4, 1979, p. 390-405 https://doi.org/10.1287/moor.4.4.390
  10. C. Lawrence, L.L. Zhou, and A.L. Tits, User's Guide for CFSQP Version 2.5: AC Code for Solving(Large Scale) Constrained Nonlinear (Minmax) Optimization Problems, Generating Iterates Satisfying All Inequality Constraints, Institute for System Reasearch, University of Maryland, 1997

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