A new mathematical model for the attitude control of a solar sail with spar-tip vanes

Solar sailing is a promising means of propulsion for space probes and satellites in the near future. Various methods for the control of the attitude and orbital motion of a solar sail have been proposed and thoroughly studied. One such method of control of a solar sail´s attitude is through the means of spar-tip articulated vanes. The energy consumption of a solar sail´s collective attitude control system is a major concern, and must be minimized for the better performance of the sail. A mathematical model has been developed and presented in this paper for vanes which are both sides reflective, and thus allow for continuous, uninhibited rotations. A novel optimization procedure (HypoTan) for the minimization of the energy expenditure of a maneuver for a solar sail whose attitude is controlled by four spar-tip vanes is also presented, and is applied to the mathematical model that is developed. Results are compared with the best existing technique of optimization proposed for a solar sail and the method presented in this paper gives consistently better results than the existing technique on the energy expenditure metric while providing equally satisfactory results as the existing technique in all other metrics.