Starshade Formation Flying II: Formation Control

Several Starshade concepts for imaging exo-Earths would operate at the 2nd Earth-Sun Lagrange point (L2) and consist of a Starshade flying in formation tens to hundreds of thousands of kilometers from a telescope. The Starshade would need to maintain meter-level lateral alignment with the line of sight from telescope to target star. A companion paper describes an optical sensing scheme using a pupil imaging camera in the telescope that can sense the relative lateral position to a few centimeters. In this article, a full flight-traceable formation flying framework that leverages this sensor is presented. In particular, a two-dimensional “disk deadbanding” algorithm is introduced for lateral control. The framework also maximizes the drift time between thruster burns to reduce interruption to science observations. The main sources of uncertainty affecting the control performance are compared and it is found that spacecraft mass uncertainty is a driving factor. The formation flying environment is also analyzed to identify conditions that lead to worst-case differential gravity and solar radiation pressure (SRP) disturbances. Finally, for a representative observation scenario with the Wide Field InfraRed Space Telescope (WFIRST), this control system is tested through Monte Carlo simulations. The results show robust meter-level control with essentially optimal drift time between thruster burns.