Optimization Method For The Moon-Earth Abort Return Trajectories Based On Analytic Homotopic Technique

The manned lunar mission is complicated and charactered with advanced technologies, and the safety of astronauts becomes the most important concern in mission design. The ability to optimize abort return trajectories is especially critical, since the abort mission probably results in quite high cost. The major focus of this dissertation is the treatment of an indirect method and its application on the Moon-Earth transfers in the restricted three-body problem. The main work is summarized as follows.A general way of posing first order optimality necessary conditions for impulsive trajectories is studied and proposed. In order to simplify the establishment process of optimality conditions, the generic equations of optimality conditions for impulsive trajectories are derived, consisting of four equations described by Hamiltonian and adjoints. These generic equations proved to be equivalent to Lawden’s primer theory at interior points; moreover, they could also provide optimality conditions at initial and final points in the context of the same theoretical frame.An indirect optimization procedure based on an analytic homotopic method is developed and used in solving multi-point boundary value problem(MPBVP). An auxiliary optimal control problem(AOCP) with analytic solution is constructed; by means of the known initial adjoints of the AOCP, the optimal solution of the original optimal control problem can be obtained by following a homotopy map in N steps, by successively increasing the continuation parameters. The test results of classical orbit transfer and rendezvous problems are presented and compared with the existing results, which show the advantage of the aforementioned methods.The dynamic models of lunar return trajectories are studied and established, and a preliminary design method is presented. The dynamic equations using spherical frame are derived in the circular restricted three body problem(CR3BP) framework, which provides a fundamental model for the optimization of lunar return trajectories. In addition, a new double two-body model that suits to manage the preliminary design of lunar return trajectories developed. Based on two-body and double two-body models, the terminal reentry constrained parameters are analyzed, and the orbit characteristics of abort return without plane change are also obtained.The optimal control model and solving method for two-dimensional Moon-Earth transfers are studied and proposed. According to the simplified two-dimensional model, two different solving methods, analytic homotopic approach and adjoint-control transformation(ACT) approach, are developed and compared. Moreover, a hybrid performance index is introduced into the indirect method to analyze the trade-off characteristics between fuel consumption and flight time.The optimal control model and solving method for three-dimensional Moon-Earth abort transfers are studied and proposed. The two-dimensional optimal solution is utilized to provide a good initial guess for the first single-impulse three-dimensional transfer problem. The optimal solutions of three-impulse three-dimensional transfer problem are obtained by means of the aforementioned analytic homotopic approach. Also, the optimality conditions concerning the constraint of minimum distance with respect to the Moon are presented, and the optimal solutions are then found. Furthermore, the comparison between 1-impulse and 3-impulse trajectories will aid in determining the number of impulses to use, considering of the total impulsive cost under the influence of the departure initial orbit position.To sum up, the theory and techniques of indirect optimization for impulsive trajectories are systematically studied in this dissertation, which constitute a complete set of indirect methods for impulsive trajectories by means of the analytic homotopic approach. Other trajectories optimization problem could also benefit from the proposed methods in this work. In terms of the theoretical studies, the indirect method is applied in the optimization problem of Moon-Earth abort return trajectories in CR3 BP, and a set of orbit characteristics are revealed, which may have some application value for future manned lunar landing missions.