Deployment Dynamics and Control of a Hub-Spoke Tethered Satellite Formation Using Combined Arbitrary Lagrange-Euler and Referenced Nodal Coordinate Formulation

A novel modeling framework combining arbitrary Lagrange-Euler and referenced nodal coordinate formulation (ALE-RNCF) is proposed for deployment dynamics and control of a hub-spoke tethered satellite formation. The ALE-RNCF approach allows for an accurate analysis of the intricate coupling effect between the orbit, attitude, and deployment dynamics, and its strengths lie in overcoming the accuracy loss and low-efficiency issues when dealing with spatial and temporal multiscale problems. Specifically, the orbital and attitude motions are separated with vibrations of the variable-length ALE tethers through the RNCF, which is the main distinguishing feature over the widely-used absolute nodal coordinate formulation. To achieve stable deployment, the control torque is added to the central satellite by employing the proportional-differential algorithm, where the maximum tension of tethers or the spinning angular velocity is selected as the control object. Various cases with different deployment velocities, target tensions, and orbital heights are simulated and corresponding effects on the deployment performance are analyzed. The proposed ALE-RNCF approach provides a comprehensive understanding of the orbit-attitude-structure coupled behavior during the deployment of the hub-spoke tethered satellite formation and contributes to the development of effective control strategies.