Shape-based analytic safe trajectory design for spacecraft equipped with low-thrust engines

To rapidly design three dimensional low-thrust safe trajectories for spacecraft orbit transfer and rendezvous problems, an analytic shape-based approach is proposed. Unlike some existing analytic methods, in which a fixed shape of the trajectory is assumed, the proposed trajectory model in this paper is based on the initial and target orbit elements, through which the fitting ability for the trajectory shape is effectively improved. Additionally, the trajectory safety is guaranteed by using the shaping function. Moreover, the proposed approach can avoid computationally intensive numerical integration of the motion equations. The low-thrust trajectories designed by the proposed method can be also used to provide initial guess for more-accurate numerical trajectory optimization. Extensive numerical simulations are presented to show the effectiveness of the proposed approach.