Abstract
The shape-based method can provide suitable initial guesses for trajectory optimization, which are useful for quickly converging a more accurate trajectory. Combined with the optimal control theory, an optimized shape-based method using the finite Fourier series is proposed in this paper. Taking the flight time-fixed case and the time-free case into account, respectively, the optimized shape-based method, which considers the first-order optimal necessary conditions, can guarantee that not only an orbit designed during the preliminary phase is optimal, but also the thrust direction is not constrained to be tangential. Besides, the traditional shape-based method using the finite Fourier series, in which the thrust direction is constrained to be tangential, is developed for the time-free case in this paper. The Earth-Mars case and the LEO-GEO case are used to verify the optimized shape-based method’s feasibility for time-fixed and time-free continuous low-thrust trajectory design between circular coplanar orbits, respectively. The optimized shaped-based method can design a lower cost trajectory.
Highlights
Continuous low-thrust trajectory design and optimization are becoming increasingly popular [1, 2], they are very challenging and time-consuming
Cui et al [7] proposed a new search approach algorithm for the launch window of low-thrust gravity-assist missions based on the exponential sinusoid (ES) method, which has fewer searching variables and is more efficient than the traditional SB methods
All recent SB methods design spacecraft trajectories based on the tangential thrust assumption and cannot guarantee that the designed trajectory is optimal without the first-order optimal necessary conditions
Summary
Continuous low-thrust trajectory design and optimization are becoming increasingly popular [1, 2], they are very challenging and time-consuming. Shang et al [11] proposed a semianalytical Lambert algorithm based on the N-degree IP method in order to improve the precision of preliminary design for an interplanetary low-thrust transfer trajectory. Gondelach et al [16] proposed a novel low-thrust trajectory design method called hodographic-shaping (HS) method These velocity functions are assumed to be some sets of simple base functions. All recent SB methods (except the HS method) design spacecraft trajectories based on the tangential thrust assumption and cannot guarantee that the designed trajectory is optimal without the first-order optimal necessary conditions.
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