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Dual-Based Method for Global Optimization of Impulsive Orbital Maneuvers

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Abstract

Optimization problems involving multiple impulsive maneuvers are, in general, nonlinear and nonconvex. This implies that their resolution is prone to local optimality and convergence issues. This work proposes an optimization method to exploit a specific structure of single-constraint nonlinear programming problems. The proposed algorithm is able to transform an optimization problem with an arbitrary number of variables into a root-finding problem of a univariate algebraic equation. Moreover, it can readily overcome the aforementioned local optimality and convergence issues. This methodology has been applied to three practical application examples. The first application involves the inclination optimization for change of plane maneuvers using drifting orbits with a relative nodal precession. The second application performs the semi-major axis optimization of phasing orbits, using a two-stage approach to solve it; specifically, the dual-based method yields a solution with phasing orbits that perform a fractional number of revolutions, which is then corrected to provide the appropriate integrality condition. The third application carries out the optimization of multi-impulse Hohmann-like transfers with an inclination change, relying on a conservation law that allows to compute a multi-impulse transfer from the solution of a two-impulse transfer. Finally, two highly relevant mission scenarios are described and numerically solved: the first scenario considers a geostationary transfer orbit with a phasing optimization to locate a satellite into a prescribed slot in geostationary orbit; the second scenario considers a multi-target rendezvous of a servicing spacecraft to visit several satellites of a constellation for debris removal or refueling operations.

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Acknowledgements

AB and HU wish to acknowledge funding from Grant PID2020-112576GB-C22 of the Spanish State Research Agency and the European Regional Development Fund. AB also wishes to acknowledge funding from Grant PREDOC20-003 of “Universidad Rey Juan Carlos”. LC wishes to acknowledge support from Project Grant F663—AAGNCS by the “Dirección General de Investigación e Innovación Tecnológica, Consejería de Ciencia, Universidades e Innovación, Comunidad de Madrid” and “Universidad Rey Juan Carlos”.

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Authors and Affiliations

  1. Aerospace Systems and Transport Research Group, Universidad Rey Juan Carlos, Camino del Molino 5, 28942, Fuenlabrada, Madrid, Spain

    Adrian Barea, Hodei Urrutxua & Luis Cadarso

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  1. Adrian Barea
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  2. Hodei Urrutxua
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  3. Luis Cadarso
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Correspondence to Adrian Barea.

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Barea, A., Urrutxua, H. & Cadarso, L. Dual-Based Method for Global Optimization of Impulsive Orbital Maneuvers. J Astronaut Sci 69, 1666–1690 (2022). https://doi.org/10.1007/s40295-022-00357-5

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