Low-Thrust Lunar Trajectory Optimization Using Canonical Transformation

It is well known that the optimal low-thrust transfer between Earth and lunar orbit passes through the vicinity of libration point EML1 of the Earth-Moon system. In this regard, the libration point EML1 has been used as a junction point for the geocentric and selenocentric segments of trajectory in several studies. This technique allows us to obtain the results of near-optimal trajectory with insignificant losses in the cost function (transfer duration or fuel consumption). However, the degrees of non-optimality of solution using the libration point as a junction point and the degrees of difference between the trajectory with an optimal junction point are not known exactly. The aim of this research is to analyze the trajectories to the Moon with the optimal junction point of geocentric and selenocentric segments to figure out how much the trajectories obtained by optimizing the junction point can improve the value of cost function. The proposed method is based on the application of maximum principle and continuation method to solve the end-to-end trajectory optimization problem. To transform costate variables between geocentric and selenocentric coordinate systems, it is proposed to use the canonical transformation of costate variables. The possibility of using obtained canonical transformations to solve the optimization problem of low-thrust trajectories to the Moon with the optimal junction points of geocentric and selenocentric segments is demonstrated. For the initial guess, the libration point EML1 is used as a junction point and the transformation to the optimal junction point of these segments, which ensures the continuity of the dependence of costate variables on the independent variable, is carried out using the continuation method and canonical transformations. Numerical examples of low-thrust transfer from elliptical Earth orbit to circular lunar orbit taking into account the full ephemeris model are given and comparison is made between the trajectories with optimal junction point and the trajectories with intermediate EML1 rendezvous. Copyright © 2022 by Mr. Sung Wook Yoon, Dr. Viacheslav G. Petukhov, Dr. Alexey V. Ivanyukhin. Published by the IAF, with permission and released to the IAF to publish in all forms.