Retrieval control of a three-body tethered formation in orbital plane

A tethered satellite formation system can take various configurations, among which three configurations are most popular, namely, the hub-and-spoke configuration, the closed-hub-and-spoke configuration and the series configuration. In this paper, the dynamic control is studied for a three-body tethered satellite formation system in hub-and-spoke configuration. A combination of the quasi-linearization method and the Legendre pseudo-spectral algorithm is introduced to convert the original nonlinear optimal control problem into a series of linear algebraic equations that can be solved iteratively. Finally, the effectiveness of the presented control scheme is demonstrated through three case studies.