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dc.contributor.authorDrozd, Kristofer
dc.contributor.authorFurfaro, Roberto
dc.contributor.authorSchiassi, Enrico
dc.contributor.authorJohnston, Hunter
dc.contributor.authorMortari, Daniele
dc.date.accessioned2021-03-24T21:02:55Z
dc.date.available2021-03-24T21:02:55Z
dc.date.issued2021-02-04
dc.identifier.citationDrozd, 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.en_US
dc.identifier.issn0094-5765
dc.identifier.doi10.1016/j.actaastro.2021.01.031
dc.identifier.urihttp://hdl.handle.net/10150/657192
dc.description.abstractIn 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.en_US
dc.language.isoenen_US
dc.publisherElsevier Ltden_US
dc.rights© 2021 IAA. Published by Elsevier Ltd. All rights reserved.en_US
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en_US
dc.subjectEnergy-optimal controlen_US
dc.subjectIndirect methoden_US
dc.subjectLeast-squaresen_US
dc.subjectSpacecraft relative motionen_US
dc.subjectTheory of functional connectionsen_US
dc.titleEnergy-optimal trajectory problems in relative motion solved via Theory of Functional Connectionsen_US
dc.typeArticleen_US
dc.contributor.departmentSystems & Industrial Engineering, University of Arizonaen_US
dc.contributor.departmentAerospace & Mechanical Engineering, University of Arizonaen_US
dc.identifier.journalActa Astronauticaen_US
dc.description.note24 month embargo; first published online 4 February 2021en_US
dc.description.collectioninformationThis 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.en_US
dc.eprint.versionFinal accepted manuscripten_US
dc.source.journaltitleActa Astronautica
dc.source.volume182
dc.source.beginpage361
dc.source.endpage382


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