Optimal interior Earth-Moon Lagrange point transfer trajectories using mixed impulsive and continuous thrust

Daero Lee, Eric A. Butcher, Amit Sanyal

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Optimal interior Earth-Moon Lagrange point transfer trajectories results with fixed flight time using mixed impulsive and continuous thrust propulsion in the framework of the planar Circular Restricted Three-BodyProblem are presented. A virtual spacecraft departs geosynchronous or low-Earth orbit and enters a specified Lyapunov orbit around the interior Earth-Moon Lagrange point. For these transfer trajectory designs, a direct transcription and collocation method is employed to reformulate the continuous dynamic optimization problem into a discrete optimization problem, which then is solved using nonlinear programming software. As the design parameters, flight time and relative weighting factor between impulsive and continuous thrust are adjusted in the transfer trajectory design procedure. For practically implementable transfer trajectory designs, the constraints for coast arc and bounded control thrust are applied in the problem formulation as equality and inequality constraints, respectively. In addition, both quadratic performance index and minimum fuel performance index are used to show the relative comparison and analysis in the transfer trajectory design results. According to the relative weighting factor, the transfer trajectories are classified into direct and spiral departure trajectories whose virtual spacecraft directly departs the Earth parking orbit and departs after generating spirals around the Earth, respectively. The convergence of these transfer trajectory design methods are numerically verified by generating varying numbers of nodes and comparing their design results. Especially, the primer vector theory is utilized to analyze the transfer trajectory design results using minimum fuel performance index. Finally, the progressive homotopy continuation method is applied to design low-Earth departure transfer trajectories. These transfer trajectories show that they are numerically and theoretically valid results with the benefit of mixed impulsive and continuous thrust.

Original languageEnglish (US)
Pages (from-to)281-292
Number of pages12
JournalAerospace Science and Technology
Volume39
DOIs
StatePublished - Jan 1 2014
Externally publishedYes

Fingerprint

Moon
Earth (planet)
Trajectories
Orbits
Spacecraft
Parking
Nonlinear programming
Transcription
Propulsion
Coastal zones

Keywords

  • Direct transcription and collocation method
  • Homotopy continuation method
  • Mixed impulsive and continuous thrust
  • Planar circular restricted three-bodyproblem
  • Primer vector theory

ASJC Scopus subject areas

  • Aerospace Engineering

Cite this

Optimal interior Earth-Moon Lagrange point transfer trajectories using mixed impulsive and continuous thrust. / Lee, Daero; Butcher, Eric A.; Sanyal, Amit.

In: Aerospace Science and Technology, Vol. 39, 01.01.2014, p. 281-292.

Research output: Contribution to journalArticle

@article{81dc913df42b4b349d34d08d7c2f6563,
title = "Optimal interior Earth-Moon Lagrange point transfer trajectories using mixed impulsive and continuous thrust",
abstract = "Optimal interior Earth-Moon Lagrange point transfer trajectories results with fixed flight time using mixed impulsive and continuous thrust propulsion in the framework of the planar Circular Restricted Three-BodyProblem are presented. A virtual spacecraft departs geosynchronous or low-Earth orbit and enters a specified Lyapunov orbit around the interior Earth-Moon Lagrange point. For these transfer trajectory designs, a direct transcription and collocation method is employed to reformulate the continuous dynamic optimization problem into a discrete optimization problem, which then is solved using nonlinear programming software. As the design parameters, flight time and relative weighting factor between impulsive and continuous thrust are adjusted in the transfer trajectory design procedure. For practically implementable transfer trajectory designs, the constraints for coast arc and bounded control thrust are applied in the problem formulation as equality and inequality constraints, respectively. In addition, both quadratic performance index and minimum fuel performance index are used to show the relative comparison and analysis in the transfer trajectory design results. According to the relative weighting factor, the transfer trajectories are classified into direct and spiral departure trajectories whose virtual spacecraft directly departs the Earth parking orbit and departs after generating spirals around the Earth, respectively. The convergence of these transfer trajectory design methods are numerically verified by generating varying numbers of nodes and comparing their design results. Especially, the primer vector theory is utilized to analyze the transfer trajectory design results using minimum fuel performance index. Finally, the progressive homotopy continuation method is applied to design low-Earth departure transfer trajectories. These transfer trajectories show that they are numerically and theoretically valid results with the benefit of mixed impulsive and continuous thrust.",
keywords = "Direct transcription and collocation method, Homotopy continuation method, Mixed impulsive and continuous thrust, Planar circular restricted three-bodyproblem, Primer vector theory",
author = "Daero Lee and Butcher, {Eric A.} and Amit Sanyal",
year = "2014",
month = "1",
day = "1",
doi = "10.1007/s10569-004-0406-8",
language = "English (US)",
volume = "39",
pages = "281--292",
journal = "Aerospace Science and Technology",
issn = "1270-9638",
publisher = "Elsevier",

}

TY - JOUR

T1 - Optimal interior Earth-Moon Lagrange point transfer trajectories using mixed impulsive and continuous thrust

AU - Lee, Daero

AU - Butcher, Eric A.

AU - Sanyal, Amit

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Optimal interior Earth-Moon Lagrange point transfer trajectories results with fixed flight time using mixed impulsive and continuous thrust propulsion in the framework of the planar Circular Restricted Three-BodyProblem are presented. A virtual spacecraft departs geosynchronous or low-Earth orbit and enters a specified Lyapunov orbit around the interior Earth-Moon Lagrange point. For these transfer trajectory designs, a direct transcription and collocation method is employed to reformulate the continuous dynamic optimization problem into a discrete optimization problem, which then is solved using nonlinear programming software. As the design parameters, flight time and relative weighting factor between impulsive and continuous thrust are adjusted in the transfer trajectory design procedure. For practically implementable transfer trajectory designs, the constraints for coast arc and bounded control thrust are applied in the problem formulation as equality and inequality constraints, respectively. In addition, both quadratic performance index and minimum fuel performance index are used to show the relative comparison and analysis in the transfer trajectory design results. According to the relative weighting factor, the transfer trajectories are classified into direct and spiral departure trajectories whose virtual spacecraft directly departs the Earth parking orbit and departs after generating spirals around the Earth, respectively. The convergence of these transfer trajectory design methods are numerically verified by generating varying numbers of nodes and comparing their design results. Especially, the primer vector theory is utilized to analyze the transfer trajectory design results using minimum fuel performance index. Finally, the progressive homotopy continuation method is applied to design low-Earth departure transfer trajectories. These transfer trajectories show that they are numerically and theoretically valid results with the benefit of mixed impulsive and continuous thrust.

AB - Optimal interior Earth-Moon Lagrange point transfer trajectories results with fixed flight time using mixed impulsive and continuous thrust propulsion in the framework of the planar Circular Restricted Three-BodyProblem are presented. A virtual spacecraft departs geosynchronous or low-Earth orbit and enters a specified Lyapunov orbit around the interior Earth-Moon Lagrange point. For these transfer trajectory designs, a direct transcription and collocation method is employed to reformulate the continuous dynamic optimization problem into a discrete optimization problem, which then is solved using nonlinear programming software. As the design parameters, flight time and relative weighting factor between impulsive and continuous thrust are adjusted in the transfer trajectory design procedure. For practically implementable transfer trajectory designs, the constraints for coast arc and bounded control thrust are applied in the problem formulation as equality and inequality constraints, respectively. In addition, both quadratic performance index and minimum fuel performance index are used to show the relative comparison and analysis in the transfer trajectory design results. According to the relative weighting factor, the transfer trajectories are classified into direct and spiral departure trajectories whose virtual spacecraft directly departs the Earth parking orbit and departs after generating spirals around the Earth, respectively. The convergence of these transfer trajectory design methods are numerically verified by generating varying numbers of nodes and comparing their design results. Especially, the primer vector theory is utilized to analyze the transfer trajectory design results using minimum fuel performance index. Finally, the progressive homotopy continuation method is applied to design low-Earth departure transfer trajectories. These transfer trajectories show that they are numerically and theoretically valid results with the benefit of mixed impulsive and continuous thrust.

KW - Direct transcription and collocation method

KW - Homotopy continuation method

KW - Mixed impulsive and continuous thrust

KW - Planar circular restricted three-bodyproblem

KW - Primer vector theory

UR - http://www.scopus.com/inward/record.url?scp=84908403446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908403446&partnerID=8YFLogxK

U2 - 10.1007/s10569-004-0406-8

DO - 10.1007/s10569-004-0406-8

M3 - Article

AN - SCOPUS:84908403446

VL - 39

SP - 281

EP - 292

JO - Aerospace Science and Technology

JF - Aerospace Science and Technology

SN - 1270-9638

ER -