Trajectory global optimization for spacecraft launched from the earth in the whole solar system

The global optimal 4-D trajectory (t, x, y, z) for a spacecraft controlled by low thrust and launched from the Earth to fly around the Sun is proposed in this paper. To optimize the 4-D trajectory of the spacecraft, a set of numerical algorithm, including a searching algorithm and a 4-D trajectory optimization algorithm is presented. The searching algorithm is used for finding as many as possible asteroids near the 4-D trajectory of the Earth chosen from all the 248997 asteroids in the whole Sun system. The performance index of optimal trajectory is to maximize the number of asteroids met with the spacecraft and the rendezvous times with them, and also maximize the final mass. The 4-D trajectory optimization algorithm is composed of improved dynamic programming algorithm, conjugate gradient algorithms based on optimal control theory and static parameter optimization algorithm. Based on a great deal of numerical flight simulation by using this combined algorithm, the 4-D optimal trajectory of the spacecraft is obtained, the spacecraft passes by 12 asteroids among the 248997 asteroids in the whole Sun system within one year.