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    Energy-optimal trajectory problems in relative motion solved via Theory of Functional Connections

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    Name:
    TFC_Relative_Motion_Journal.pdf
    Embargo:
    2023-02-04
    Size:
    987.0Kb
    Format:
    PDF
    Description:
    Final Accepted Manuscript
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    Author
    Drozd, Kristofer
    Furfaro, Roberto
    Schiassi, Enrico
    Johnston, Hunter
    Mortari, Daniele
    Affiliation
    Systems & Industrial Engineering, University of Arizona
    Aerospace & Mechanical Engineering, University of Arizona
    Issue Date
    2021-02-04
    Keywords
    Energy-optimal control
    Indirect method
    Least-squares
    Spacecraft relative motion
    Theory of functional connections
    
    Metadata
    Show full item record
    Publisher
    Elsevier Ltd
    Citation
    Drozd, K., Furfaro, R., Schiassi, E., Johnston, H., & Mortari, D. (2021). Energy-optimal trajectory problems in relative motion solved via Theory of Functional Connections. Acta Astronautica, 182, 361-382.
    Journal
    Acta Astronautica
    Rights
    © 2021 IAA. Published by Elsevier Ltd. All rights reserved.
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    Abstract
    In this paper, we present a new approach for solving a broad class of energy-optimal trajectory problems in relative motion using the recently developed Theory of Functional Connections (TFC). A total of four problem cases are considered and solved, i.e. rendezvous and intercept with fixed and free final time. Each problem is constrained and formulated using an indirect approach which casts the optimal trajectory problem as a system of linear or nonlinear two-point boundary value problems for the fixed and free final time cases, respectively. Using TFC, we convert each two-point boundary value problem into an unconstrained problem by analytically embedding the boundary constraints into a “constrained expression.” The latter includes a free-function that is expanded using Chebyshev polynomials with unknown coefficients. Regardless of the values of the unknown coefficients, the boundary constraints are satisfied and simple optimization schemes can be employed to numerically solve the problem (e.g. linear and nonlinear least-square methods). To validate the proposed approach, the TFC solutions are compared with solutions obtained via an analytical based method as well as direct and indirect numerical methods. In general, the proposed technique produces solutions to machine level accuracy. Additionally, for the cases tested, it is reported that computational run-time within the MATLAB implementation is lower than 28 and 300 ms for the fixed and free final time problems respectively. Consequently, the proposed methodology is potentially suitable for on-board generation of optimal trajectories in real-time.
    Note
    24 month embargo; first published online 4 February 2021
    ISSN
    0094-5765
    DOI
    10.1016/j.actaastro.2021.01.031
    Version
    Final accepted manuscript
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.actaastro.2021.01.031
    Scopus Count
    Collections
    UA Faculty Publications

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