421 Low Energy Transfer Trajectories of a Spacecraft from the Earth to the Moon

Low-energy transfer trajectory is of growing interest in the space community. It is important to choose the patch point of the unstable manifold of the Lyapunov orbit around Sun–Earth L2 and the stable manifold of the Lyapunov orbit around Earth–Moon L2. The main contributions of this study are two areas: (a) designing the optimization model and using evolutionary algorithms to optimize the initial condition and (b) developing effective algorithms for this problem. In this article, an improved differential evolution (DE) algorithm, named adaptive uniform design differential evolution (AUDE), is proposed to solve the Earth–Moon low-energy transfer optimization problem. It incorporates the uniform design technology and the self-adaptive parameter control method into standard DE to accelerate its convergence speed and improve the stability and calculation accuracy. To verify the performance of AUDE, the Earth–Moon low-energy transfer optimization problem and 15 benchmark functions with diverse complexities are employed. The experiment results indicate that the authors' approach is able to find the better one, or at least comparably, in terms of the quality and stability of the final solutions than the other three algorithms. Moreover, it proves that the application of DE algorithm in the Earth–Moon low-energy transfer optimization problem is effective.

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Enhanced Hybrid Differential Evolution for Earth-Moon Low-Energy Transfer Trajectory Optimization

International Journal of Aerospace Engineering ◽

10.1155/2018/4560173 ◽

2018 ◽

Vol 2018 ◽

pp. 1-17

Author(s):

Yanyun Zhang ◽

Lei Peng ◽

Guangming Dai ◽

Maocai Wang

Keyword(s):

Energy Transfer ◽

Differential Evolution ◽

Trajectory Optimization ◽

Transfer Problem ◽

Low Energy ◽

Initial Condition ◽

Transfer Trajectory ◽

De Algorithm ◽

The Earth ◽

Low Energy Transfer

It is known that the optimization of the Earth-Moon low-energy transfer trajectory is extremely sensitive with the initial condition chosen to search. In order to find the proper initial parameter values of Earth-Moon low-energy transfer trajectory faster and obtain more accurate solutions with high stability, in this paper, an efficient hybridized differential evolution (DE) algorithm with a mix reinitialization strategy (DEMR) is presented. The mix reinitialization strategy is implemented based on a set of archived superior solutions to ensure both the search efficiency and the reliability for the optimization problem. And by using DE as the global optimizer, DEMR can optimize the Earth-Moon low-energy transfer trajectory without knowing an exact initial condition. To further validate the performance of DEMR, experiments on benchmark functions have also been done. Compared with peer algorithms on both the Earth-Moon low-energy transfer problem and benchmark functions, DEMR can obtain relatively better results in terms of the quality of the final solutions, robustness, and convergence speed.

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Combining Two and Three-Body Dynamics for Low Energy Transfer Trajectories of Practical Interest

10.2514/6.iac-04-a.7.02 ◽

2004 ◽

Keyword(s):

Energy Transfer ◽

Practical Interest ◽

Low Energy ◽

Body Dynamics ◽

Low Energy Transfer ◽

Three Body ◽

Transfer Trajectories

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Trajectory Design for the Transfer from the Lissajous Orbit of Sun-Earth System to Asteroids

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.390.478 ◽

2013 ◽

Vol 390 ◽

pp. 478-484 ◽

Cited By ~ 5

Author(s):

Ya Min Wang ◽

Dong Qiao ◽

Ping Yuan Cui

Keyword(s):

Energy Transfer ◽

Perturbation Method ◽

Design Method ◽

Low Energy ◽

Trajectory Design ◽

Design Issue ◽

Lissajous Orbit ◽

Low Energy Transfer ◽

Three Body ◽

Transfer Trajectories

This paper investigates the trajectory design issue for the transfer from the Lissajous orbit of CHANGE 2 probe to asteroids. First, an intersection search method, which is a general design method of low-energy transfer trajectories by searching the intersection of unstable and stable manifolds in the circular restricted three-body problem (CRTBP), is applied to produce the zero-cost flyby trajectories for the asteroid flyby missions of CHANGE 2 probe, and the simulation result shows that this method is invalid. Then, for this trajectories design issue, a perturbation method, which consists of a process of searching initial trajectories by applying velocity perturbations in the direction of unstable eigenvectors of the Lissajous orbit and a trajectory correction process with two-level differential correction, is proposed. Finally, the transfer opportunities between the Lissajous orbit of CHANGE 2 and asteroids Toutatis and 2010 JK1 are searched by the perturbation method. The results show that the method proposed in this paper can identify low-energy transfer trajectories for asteroid flyby missions of CHANGE 2. Moreover, this method provides a global understanding of the trend of impulsive maneuvers over the transfer date.

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