A new 3d shaping method for low-thrust trajectories between non-intersect orbits

This paper proposes a new shape-based method in spherical coordinates to solve three-dimensional rendezvous problems. Compared with the existing shape-based methods, the proposed method does not need parameter optimization. Moreover, it improves the flexibility of orbit fitting, greatly reduces the velocity increment and maximum thrust acceleration, and ensures the orbit safety to a certain extent. The shaping function can provide the initial estimate for numerical trajectory optimization and improve the convergence rate in a certain range when combined with the normalization method. The superiority of the proposed method over the existing methods is demonstrated by two numerical examples. Its effectiveness at initial estimation generation in the indirect optimization of a low-thrust trajectory is demonstrated by the third example.