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Stationkeeping controllers for Earth–Moon L1 and L2 libration points halo orbits

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Abstract

This paper considers the dynamics of the circular restricted three-body problem (CRTBP) for the Earth–Moon system designing stationkeeping controllers at periodic orbits. Taking into account the \(L_1\) and \(L_2\) equilibrium points in this dynamics, it is constructed a family of periodic orbits in the vicinity of these libration points, called halo orbits. The orbits are constructed using an analytical approach as a first guess with a numerical method in addition, in order to correct the linear approximation procedure. Withal the stability of these libration points, trajectories are analyzed and proved to be unstable; a spacecraft moving near these points must use some correction maneuver to remain close to the nominal orbit. Two types of controllers are proposed for stationkeeping maneuvers performed by low-thrust power-limited propulsion system . The first controller is based on the linear quadratic regulator (LQR) and the second one is based on the nonlinear feedback control which uses the state-dependent Riccati equation control (SDRE). Finally, a parameters comparison analysis is performed taking into account different values of the weight matrices for both controllers at both halo orbits.

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Authors and Affiliations

  1. Technological Institute of Aeronautics, Praça Marechal Eduardo Gomes 50, São José dos Campos, SP, Brazil

    Thiago César Lousada Marsola & Sandro da Silva Fernandes

  2. State University of São Paulo—UNESP, Av. Eng. Luís Edmundo Carrijo Coube, Bauru, SP, Brazil

    José Manoel Balthazar

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  1. Thiago César Lousada Marsola
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  2. Sandro da Silva Fernandes
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  3. José Manoel Balthazar
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Correspondence to Thiago César Lousada Marsola.

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Technical editor: Monica Carvalho.

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Marsola, T.C.L., da Silva Fernandes, S. & Balthazar, J.M. Stationkeeping controllers for Earth–Moon L1 and L2 libration points halo orbits. J Braz. Soc. Mech. Sci. Eng. 43, 347 (2021). https://doi.org/10.1007/s40430-021-03071-9

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