A layered initial design method for interplanetary low-thrust transfer trajectories

To implement the interplanetary low-thrust transfer trajectory, a layered initial design method is proposed based on the Chebyshev polynomial theory and the multiple impulse design strategy. First, the Chebyshev polynomial is used to approach the orbital states of low-thrust orbit by fitting curve and the relationship between the states and time in three-dimensional space is established, accordingly avoiding the calculation of time constraint and having no assumption on the direction of velocity. Then, to reduce the difficulty of initial guess, low-level Chebyshev polynomial is used to solve boundary constraints in the global search. On this basis, the order of the Chebyshev polynomials is increased to improve the solution space dimension and the sequential quadratic programming is used for optimization of initial search results. Finally, adopting impulse discretization to process the consequence of the curve fitting, the low-thrust transfer trajectory design is described as a multi-variable optimization problem for solving the low-thrust orbit involving path constraint. The proposed layered method is demonstrated for an earth-Mars transfer trajectory and an earth-Mars-Jupiter transfer trajectory. Numerical results show that the method could be applied effectively to the rapid global initial design of low-thrust trajectories.