Minimum Fuel-Consumption Stabilization of a Spacecraft at the Lagrangian Points


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Abstract

We consider the motion of a spacecraft described by the differential equations of the three-body problem in the Earth-Moon system. The goal is to stabilize the spacecraft in the neighborhood of the collinear Lagrangian points (which are know to be unstable equilibria) via use of minimum fuel-consumption control. The adopted approach is based on l1-optimization of linearized and discretized equations with terminal conditions being the target Lagrangian point. Therefore, the problem reduces to a linear program, and its solution defines pulse controls for the original three-body equations. Upon reaching the desired neighborhood, the spacecraft performs control-free flight until its deviation from the Lagrangian point exceeds certain prespecified threshold. The correction is then applied repeatedly, so that the spacecraft is kept within a small neighborhood of the unstable equilibrium point.

About the authors

B. T. Polyak

Trapeznikov Institute of Control Sciences

Author for correspondence.
Email: boris@ipu.ru
Russian Federation, Moscow

L. A. Shalby

Moscow Institute of Physics and Technology

Author for correspondence.
Email: lina.khamis@gmail.com
Russian Federation, Moscow

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