Optimal Control Method for Deployment and Retrieval of Transverse Formation Satellite-Sail Systems

One of the crucial applications of tether systems is formation flying. In recent research endeavors aimed at meeting the requirements of remote sensing satellites for interferometric measurements of ground targets, a new type of tethered solar sail spacecraft has been proposed. This spacecraft replaces the subsatellites of traditional tethered satellites with solar sail spacecraft, forming a distinctive formation configuration. Specifically, the main satellite is positioned in a sun-synchronous orbit, while the sub solar sail is in a suspended orbit. If the solar sail assumes an appropriate orientation, the main satellite and the solar sail spacecraft, linked by a metallic tether, can move side by side. Consequently, this formation system is termed the "transverse formation." The inter-satellite baseline in this transverse formation system is perpendicular to the satellite’s ground track, effectively addressing the periodic trigonometric variations observed in the inter-satellite baseline of traditional flyby formations. This paper delves into the control laws for the deployment and retrieval of tethered solar sails by constructing and resolving an optimal control problem.