Mars exploring trajectory optimization using Gauss Pseudo-spectral Method

In this paper, we propose a method for Mars exploring trajectory optimization by the Gauss Pseudo-spectral Method (GPM). The Gauss Pseudo-spectral Method has advantages for solving the optimal control problems because it is not necessary to guess the initial value of the co-states and the method has relatively large radii of convergence. Therefore, it is robust to the initial value for iteration. The Mars exploring orbit is divided into two sections, the Earth escaping section and the Earth-Mars transferring section, and the two sections can be optimized respectively. During the optimization of the Gauss Pseudo-spectral Method, we choose the initial states, the terminal states of the Mars probe and the vector of the thrust at each Legendre-Gauss point (LG point) as the optimal variables. With an appropriate quantity of LG points computed in the GPM, we can get optimal trajectory from the circular orbit around Earth to Mars. According to the simulation results we could see that the optimization converges well and a rough guess can satisfy the convergence.