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Costate mapping for indirect trajectory optimization

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A Correction to this article was published on 11 February 2022

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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.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Auburn University, Auburn, AL, 36849, USA

    Ehsan Taheri

  2. Department of Aerospace Engineering, Texas A&M University, College Station, TX, 77843-3141, USA

    Vishala Arya & John L. Junkins

Authors
  1. Ehsan Taheri
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  2. Vishala Arya
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  3. John L. Junkins
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Correspondence to Ehsan Taheri.

Additional information

Ehsan Taheri is an assistant professor at the Department of Aerospace Engineering in Auburn University. His research is focused on developing dependable algorithms for solving optimal control problems associated with complex dynamical systems, including spacecraft equipped with low-thrust electric propulsion systems, entry, decent and landing vehicles, and multi-rotor unmanned aerial vehicles. E-mail: etaheri@auburn.edu.

Vishala Arya is a Ph.D. candidate at the Aerospace Department of Texas A&M University working under the supervision of Dr. John Junkins. Her research interests are direct and indirect-based methods for co-optimization of spacecraft, trajectory, and propulsion parameters of multi-mode solar propulsion systems, autonomous and fault-tolerant guidance of spacecraft for low thrust interplanetary maneuvers, and control principles for non-linear systems for both spacecraft and robotic applications.

John L. Junkins is University Distinguished Professor of Aerospace Engineering and holder of the Royce E. Wisenbaker Chair in Innovation at Texas A&M University. He is the founding director of the Hagler Institute for Advanced Study. Junkins was recently interim president of Texas A&M University for 6 months ending in June 2021. Junkins is a prolific scholar and has advised to completion 55 Ph.D. students. He is the author of over four-hundred papers and seven widely used technical books. His co-authored Analytical Mechanics of Aerospace Systems is now in its 4th edition and won the 2014 Martin Summerfield Best Book Award, given annually by AIAA. He is a member of the National Academy of Engineering, the National Academy of Inventors, the International Academy of Astronautics, and an Honorary Fellow of the American Institute for Aeronautics and Astronautics (AIAA). He recently received the highest honor in his field, the AIAA Robert H. Goddard Astronautics Award (2019).

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Taheri, E., Arya, V. & Junkins, J.L. Costate mapping for indirect trajectory optimization. Astrodyn 5, 359–371 (2021). https://doi.org/10.1007/s42064-021-0114-0

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