Optimal in-orbit repositioning of Sun-pointing Smart Dust

A Smart Dust is a femto-spacecraft with an external surface coated with electrochromic material, which exploits the solar radiation pressure to produce a propulsive acceleration. As the optical properties of the electrochromic material change upon application of a suitable electric voltage, its propulsive acceleration may be modulated, within some limits, without the use of any propellant. This paper analyzes the optimal trajectories of a Sun-pointing Smart Dust, which provides a propulsive acceleration aligned with the Sun-spacecraft direction. In particular, the paper describes the relative motion of a Smart Dust with respect to a conventional spacecraft (the Mother Ship) that covers a heliocentric circular orbit of given radius. The Smart Dust is required to vary periodically its angular position with respect to the Mother Ship using an optimal (minimum time) strategy. This problem is addressed using an indirect approach and the optimal control law is obtained in a closed-form solution. The results discussed in this paper ensure interesting improvements over existing models from the recent literature, including the possibility of obtaining a generic phasing angle of the Smart Dust and to take into account an optimal number of on-off switchings of the electrochromic control system.