The Earth-Mars Transfer Trajectory Optimization of Solar Sail Based on hp-Adaptive Pseudospectral Method

Solar sails have many advantages over traditional chemical propulsion spacecraft, such as needlessness of fuel, high payload ratio, long service life, and great application potential in deep space exploration, interstellar voyage, and other aerospace application fields. However, the period of solar sail transfer from the initial orbit to the desired orbit is relatively long. Thus, it is necessary to optimize the transfer trajectory of solar sail according to specific tasks. The hp-adaptive pseudospectral method combines the global pseudospectral method with the finite element method, which adopts double layer optimization strategy to solve the optimal control problem and has higher computational efficiency and accuracy than the traditional global pseudospectral method. In this paper, the pressure of solar light acting on the solar sail is analyzed, and the kinematic equation of the solar sail is established in polar coordinate system first; then the basic principle of the hp-adaptive pseudospectral method is introduced, and the steps of solving the transfer trajectory optimization problem by hp-adaptive pseudospectral method are proposed; finally, the trajectory optimization of the solar sail from Earth orbit to Sun-centered Mars orbit is simulated as an example to demonstrate the effectiveness of hp-adaptive pseudospectral method in the orbit transfer optimization problem of solar sail. The simulation results show that the adopted method is not sensitive to the initial values and has more reasonable distribution and less computational cost than the Gauss pseudospectral method.