Hierarchical Trajectory Optimization under Multi-Segment Continuous-Thrust Considering Propulsion System Constraints

In this study, an efficient hierarchical trajectory optimization framework is proposed for orbital transfer under multi-segment continuous-thrust considering constraints on the propulsion system. In contrast to conventional continuous-thrust methods, the proposed approach effectively reduces the adjustment frequency of thrust magnitude and direction, making it more attractive for engineering applications. Considering constraints on the propulsion system in real scenarios, a variable-dimension multi-segment continuous-thrust trajectory optimization problem is first established. Then, a fixed-dimension mixed integer optimization problem is introduced utilizing variable reduction and equivalent transformation. In the first stage, a diversity-based adaptive genetic algorithm is proposed to search for a multi-impulse solution, which is converted into a feasible initial guess for the next stage using a rapid transformation algorithm. In the second stage, the original problem is relaxed into a nonlinear programming problem involving only continuous variables using variable relaxation and an integer-penalty function. Finally, a mixed-integer sequential quadratic programming method is employed to obtain a converged solution to the multi-segment continuous thrust trajectory optimization problem. Furthermore, numerical results indicate that the proposed framework can effectively transfers spacecraft to target orbits with lower fuel consumption and orbit injection accuracy than the standard SQP method.