Introduce a Novel Approach to Orbital Maintenance in CRTBP

This paper presents a novel approach to designing an orbital maintenance strategy for the periodic Lyapunov orbits in the Circular Restricted Three-Body Problem. Since the position and velocity vector change simultaneously in the moment of non-periodic behavior, a short low-thrust maneuver must be established to return the satellite to the periodic orbit. The low-thrust trajectory is a Two-Boundary Value Problem (TBVP) and requires a particular solving approach. Previous investigations exploited numerical optimal control methods such as Non-Linear Programming (NLP). NLP implementation was hard, and the run time was too long. Hence the current paper utilizes Multi-Objective Particle Swarm Optimization (MOPSO) to design orbital maintenance missions. The following are three sequential steps for implementing the proposed method. It is first necessary to identify the first non-periodic moment of the satellite in the periodic Lyapunov orbit and its state vector. This step determines the criteria for non-periodic behavior through sensitivity analysis. As a groundbreaking idea, the desired state vector (the state vector to which the satellite needs to transfer to continue its periodic behavior) is considered as the corresponding point of the non-periodic starting point at the first period. Due to the characteristics of the Lyapunov orbits, this selection allows the satellite to continue its periodic motion. In the third step, the thruster components and their duration of working time are nominated as design variables. Two objective functions are suggested in this step and minimized by applying MOPSO to recognize the design variables: The first objective function is guaranteed that the state vector is converted from the first non-periodic moment state vector to the desired state vector by applying thruster components. Since the fuel consumption in the deep space mission is vital, the second objective function minimizes fuel consumption by minimizing the thrust magnitude. The Sun-Earth system is regarded as a system of interest, and the proposed method is simulated. The obtained result indicates that the proposed method, in addition to the significant reduction of calculations, will lead to the minimization of fuel consumption in orbital maintenance missions in the CRTBP.