Control strategies of formation flying using solar sail propulsion in the vicinity of collinear points

Realization of formation flying using solar sail propulsion will offer great benefits for future space exploration missions. The use of solar sail, which will significantly reduce the use of the chemical propulsions, allows missions to be more flexible in term of mass and life cycle of the missions. Missions which require long baselines, potentially is solved by flying spacecrafts in a formation. Collinear points of the Sun-Earth system, L ₁ and L₂ have lower pseudo gravity potential compared to other Lagrangian points hence these points are potentially exploited for space missions. A formation flying consists of two spacecrafts are introduced as Mirror Spacecraft (MSC) and Detector Spacecraft (DSC). The relative distance between the spacecraft are ought to be kept constant. A formation keeping strategy is adopted and the equations of relative motion are derived by linearization at the MSC position and consequently a linear-time varying system is obtained. The formation is controlled to a piece constant and the optimal feedback control for this system is achieved by using Linear Quadratic Regulator method (LQR).