Optimal orbit transfer of spacecraft under constant thrust

This paper considers the optimal orbit transfer problem of spacecraft under constant thrust. The main purpose is to design the optimal control law to ensure the orbit transfer of the spacecraft with the least time consumption. It is formulated as a constrained optimal control problem, where specific requirements of this orbit transfer problem are all incorporated in the problem formulation. Then, by utilizing the specific features of the problem, this optimal orbit transfer problem is transformed into an equivalent standard optimal control problem subject to continuous state inequality constraints. A computational method is developed, based on the control parameterization in conjunction with a time scaling transform and the constraint transcription method, to design the optimal controller for this new constrained optimal control problem. The simulation results are presented in the illustrations. It shows the feasibility and effectiveness of the proposed method.