In space missions, numerical techniques for minimizing the fuel consumption of spacecraft using low-thrust propulsion are desirable. Among various nonlinear optimization methods, convex optimization has been attracting attention because it allows optimal solutions to emerge robustly and requires short computation times. In particular, trajectory design in the three-body problem near the Lagrange points involves instability and nonlinearity. Hence, this study considers the application of convex optimization to trajectory design with low-thrust propulsion in cislunar space and verifies that this technique performs well, even for sensitive and highly nonlinear dynamics. Specifically, the convex optimization scheme is applied in the transfer from a halo orbit to a near-rectilinear halo orbit where both are periodic as defined in the circular restricted three-body problem. As a further step, the transfer problem is transitioned to an ephemeris model. In addition, extensive investigations of the dependence on various parameters used in convex optimization are conducted, and a trajectory corrections maneuver method is constructed combined with the convex optimization process. This investigation provides valuable insight into the convex optimization technique in the three-body problem and facilitates the estimation of low-thrust trajectory designs for complex space missions.
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