Abstract
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.
Highlights
The continuous low-thrust propulsion system has attracted great attention because of its higher specific impulse and less fuel consumption compared with impulsive propulsion systems
The shape-based methods can be divided into two categories according to whether their shape functions consist of free optimization parameters: one has no parameter optimization, and the other has to resort to the help from parameter optimization
This paper proposed a new shape-based method to solve 3D rendezvous problems, keeping the advantages of Novak’s method and Zeng’s method
Summary
The continuous low-thrust propulsion system has attracted great attention because of its higher specific impulse and less fuel consumption compared with impulsive propulsion systems. Petropoulos and Longuski [11] proposed the first shape-based method without optimization, which uses an exponential sinusoid to describe a coplanar trajectory It is simple in form but cannot meet the boundary conditions of position and velocity at the same time, so it cannot solve rendezvous problems. Xie’s method [17] designs the in-plane and out-of-plane shapes separately and selects the polynomial as the shaping function, while Zeng’s method [18] does not design the shape separately in three dimensions and uses a Fourier series as the shaping function Both of these approaches can provide solutions for transfer and rendezvous problems with large elevation angles. A new shape-based 3D method is proposed for rendezvous problems, which considers the advantages of Novak’s method [15] and Zeng’s method [18] in the design and improves some deficiencies existing in these two methods.
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