Trajectory Design of Solar Sail Spacecraft for Interplanetary Rendezvous Missions

This paper deals with in-plane motion of a solar sail spacecraft to rendezvous with a planet. In the interplanetary rendezvous problem, the spacecraft's velocity must coincide with the orbital velocity of the planet when it reaches the planet's orbit. Thus, the spacecraft's radial and tangential velocities as well as its orbital radius are controlled by one control input, i.e. the spacecraft's pitch angle. In this paper, we propose a trajectory design method which can reduce the amount of computational iterations considerably. This is applied to a rendezvous mission to a planet in a circular orbit and is achieved by utilizing locally optimal control techniques. A hidden problem in the method is pointed out, and a countermeasure is proposed. Then, numerical results of the proposed method are shown and compared with the results obtained by a fully numerical iteration method. Finally, some mathematical properties of a sailcraft's governing equations are discussed in the framework of nonlinear control theory. We show analytically that a solar sail spacecraft can rendezvous with any planet in any elliptical orbit by using only pitch angle control.