Deployment/retraction of the rotating Hub-Spoke Tethered Formation System

The Hub-Spoke Tethered Formation System (HS-TFS) is now a hot issue in many space applications, such as multi-point measurements, providing flexible frame for solar sail and other membrane or net structures. To achieve the valuable advantages, such as reduction of fuel consumption, promotion of the formation stability, the HS-TFS is usually in the rotating state. In addition, it is necessary to change the length of the tethers to obtain a variable coverage of the entire plane of the rotating HS-TFS in some applications, that is, the deployment and retraction problems of the rotating HS-TFS. However, the rotating motion will increase the complexity of the deployment and retraction of the rotating HS-TFS. In this paper, the deployment and retraction of a rotating HS-TFS is investigated. Firstly, a mathematical model is derived to describe the dynamics of the rotating HS-TFS. Then, the Gauss pseudospectral method is employed to solve the optimal deployment and retraction problems of the rotating HS-TFS. Finally, numerical simulations for deployment and retraction of the rotating HS-TFS are performed. Numerical simulation results reveal that it is necessary to apply active control on the deployment and retraction phases of the rotating HS-TFS, and after employing the optimal control (Gauss pseudospectral method), the HS-TFS can reach the desired configuration.