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Shape-based methods are becoming popular in low-thrust trajectory optimization due to their fast computation speeds. In existing shape-based methods constraints are treated at the acceleration level but not at the thrust level. These two constraint types are not equivalent since spacecraft mass decreases over time as fuel is expended. This paper develops a shape-based method based on a Fourier series approximation that is capable of representing trajectories defined in spherical coordinates and that enforces thrust constraints. An objective function can be incorporated to minimize overall mission cost, i.e., achieve minimum Δ V . A representative mission from Earth to Mars is studied. The proposed Fourier series technique is demonstrated capable of generating feasible and near-optimal trajectories. These attributes can facilitate future low-thrust mission designs where different trajectory alternatives must be rapidly constructed and evaluated. [ABSTRACT FROM AUTHOR]

In the circular restricted three-body problem (CR3BP), transit orbit is a class of orbit which can pass through the bottleneck region of the zero velocity curve and escapes from the vicinity of the primary or the secondary. This kind of orbit plays a very important role in the design of space exploration missions. A kind of low-energy interplanetary transfer, which is called Interplanetary Superhighway (IPS), can be realized by utilizing transit orbits. To use the transit orbit in actual mission design, a key issue is to find an algorithm which can separate the states corresponding to transit orbits from the states corresponding to other types of orbits rapidly. In fact, the distribution of transit orbit in the phase space has been investigated by numerical method, and a Fourier series approximation method has been introduced to describe the boundary of transit orbits. However, the Fourier series approximation method needs several hundred sets of Fourier series. The coefficients of these Fourier series are neither easy to be computed nor convenient to be stored, which makes the method can hardly be used in actual mission design. In this paper, the support vector machine (SVM) is used to classify the trajectories in the CR3BP. Using the Gaussian kernel, the 6-dimensional states in the CR3BP are mapped into an infinite-dimensional space, and the bound of the transit orbits is described by a hyperplane. A training data generation method is introduced, which reduces the size of training data by generating the states near the hyperplane. The numerical results show that the proposed algorithm gives the good correct rate of classification, and its computing speed is much faster than that of the Fourier series approximation method. [ABSTRACT FROM AUTHOR]