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Astrodynamics 2021, 5(4): 359-371 https://doi.org/10.1007/s42064-021-0114-0
Research Article | Issue | Published: 26 November 2021

Costate mapping for indirect trajectory optimization

Show Author's Information Ehsan Taheri1,  Vishala Arya2,  John L. Junkins2
Department of Aerospace Engineering, Auburn University, Auburn, AL 36849, USA
Department of Aerospace Engineering, Texas A & M University, College Station, TX 77843-3141, USA
Keywords:
trajectory optimization, low thrust, interplanetary, indirect optimization, spacecraft, optimal control theory, minimum time, minimum fuel, Earth-centered
Cite this article:
Taheri E, Arya V, Junkins JL. Costate mapping for indirect trajectory optimization. Astrodynamics, 2021, 5(4): 359-371. https://doi.org/10.1007/s42064-021-0114-0
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Abstract Full text About this article

Numerical solutions of optimal control problems are influenced by the appropriate choice of coordinates. The proposed method based on the variational approach to map costates between sets of coordinates and/or elements is suitable for solving optimal control problems using the indirect formalism of optimal control theory. The Jacobian of the nonlinear map between any two sets of coordinates and elements is a key component of costate vector mapping theory. A new solution for the class of planar, free-terminal-time, minimum-time, orbit rendezvous maneuvers is also presented. The accuracy of the costate mapping is verified, and its utility is demonstrated by solving minimum-time and minimum-fuel spacecraft trajectory optimization problems.


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About this article

Costate mapping for indirect trajectory optimization

Show Author's information Ehsan Taheri1, Vishala Arya2, John L. Junkins2
Department of Aerospace Engineering, Auburn University, Auburn, AL 36849, USA
Department of Aerospace Engineering, Texas A & M University, College Station, TX 77843-3141, USA

Abstract

Numerical solutions of optimal control problems are influenced by the appropriate choice of coordinates. The proposed method based on the variational approach to map costates between sets of coordinates and/or elements is suitable for solving optimal control problems using the indirect formalism of optimal control theory. The Jacobian of the nonlinear map between any two sets of coordinates and elements is a key component of costate vector mapping theory. A new solution for the class of planar, free-terminal-time, minimum-time, orbit rendezvous maneuvers is also presented. The accuracy of the costate mapping is verified, and its utility is demonstrated by solving minimum-time and minimum-fuel spacecraft trajectory optimization problems.

Keywords: trajectory optimization, low thrust, interplanetary, indirect optimization, spacecraft, optimal control theory, minimum time, minimum fuel, Earth-centered

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Publication history
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Publication history

Received: 11 July 2021
Accepted: 13 September 2021
Published: 26 November 2021
Issue date: December 2021

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© Tsinghua University Press 2021
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