Investigation of the Retrieval Dynamics of the Tethered Satellites Using ANCF-ALE Variable-Length Element

Tether satellite system (TSS) comprises two satellites connected by a flexible tether and has wide applications, such as orbital transferring, deep space exploration, and so on. In this article, a variable-length element, based on the absolute nodal coordinate formulation (ANCF) in the framework of arbitrary Lagrangian–Eulerian (ALE) description, is used to predict the characteristics of length variation and flexibility of the tether in the phases of retrieval and station-keeping. Then, to achieve a stable retrieval implementation and take the underactuation property of the TSS into account, an optimal retrieval trajectory is programmed using the Gauss pseudospectral method-based dynamic optimization. Three different retrieval schemes are implemented using the developed ANCF-ALE model. Numerical studies show that, compared with the dumbbell model, the ANCF-ALE-based model can predict the tension of the tether in the phase of retrieval. Results indicate that the tether tension is sensitive to the ratio of change of the tether retrieval velocity. Improper retrieval scheme may induce the intensive oscillation in the tether tension, or a switched state of the tether between pseudoslack and tensile. In the optimization for optima trajectory programming, weight of ratio of tether velocity in the objective function should be considered carefully to realize a robust retrieval implementation.