A pseudoequinoctial shaping method with fourier approximation for low-thrust trajectory optimization

Shape-based methods are commonly used in solving the low-thrust trajectory optimization problem. Designing a shape trajectory by maximizing a given performance index has been widely researched in recent years. The main contribution of this paper is to present a new pseudoequinoctial shaping method with parameter optimization to solve general low-thrust spacecraft rendezvous problems. The shaping method can solve the rendezvous problem with a large inclination difference between the initial and target orbits and greatly improve the performance index of the trajectory while meeting the thrust constraints. At the same time, the shape can provide a better feasible solution for solving the low-thrust trajectory optimization problem by direct methods. Another contribution is to introduce a general adjoint estimation for indirect methods. By linearizing the equation of motion near the proposed shape-based trajectory and constructing the Hamiltonian function, the initial guess of the adjoint variables can be obtained in a closed form. The general linearization formulations applicable to all coordinate systems are presented, and three numerical examples are given, in which the first example verifies the superiority of the proposed shape-based method, the second example tests the feasibility of the shape as the initial value for a direct method, and the last example compares the convergence rates of the initial adjoint variables generated by the proposed method under different coordinate systems for an indirect method.(c) 2023 COSPAR. Published by Elsevier B.V. All rights reserved.