Lyapunov-Based Low-Thrust Control and Stabilization of a Tethered Satellite System in Arbitrary Attitude Configurations

This work investigates the control and stabilization of a tethered satellite system composed of two spacecraft of equal mass connected by a flexible tether, where the tether tension is actively generated and regulated through low-thrust propulsion. The objective is to stabilize the system in generic, non-radial configurations, including cross-track orientations, which are not naturally stable under gravity-gradient effects. To systematically design and validate the proposed control approach, two distinct dynamic models are developed, bridging analytical simplicity and physical realism. The first is a modified dumbbell model, which describes the tethered system dynamics in terms of two alternative attitude angles, γ and δ, representing the system orientation with respect to the crosstrack direction. A Lyapunov-based control law is analytically derived from this model, enabling the stabilization of arbitrary configurations while maintaining a desired tether tension through distributed low-thrust actuation at the spacecraft ends. The second model adopts a lumped-masses discretization of the tether, providing a higher-fidelity representation of its flexible dynamics. In this formulation, the relative dynamics of each lumped mass with respect to the system’s center of mass are described through an alternative state representation. The Lyapunov-based low-thrust control law derived from the dumbbell model is then implemented on the lumped-mass model to validate its performance through high-fidelity simulations. Results confirm that the proposed control enables stable operation of the tethered system in arbitrary orientations, including cross-track configurations, while maintaining the desired tension and ensuring bounded relative motion between the end bodies. Finally, a preliminary estimation of the mission duration is performed based on the propellant consumption required to sustain the low-thrust control effort, providing insights into the operational feasibility of such tethered formations. The proposed modeling and control framework opens new perspectives for the deployment of tethered multi-satellite systems in Earth observation missions, where maintaining precise relative configurations can enhance spatial coverage, imaging geometry, and revisit time.