The three-dimensional maneuver control of spinning tether system under a new Lagrangian model

This study explores the modeling and control of the spinning tether system (STS) for maneuvering between arbitrary spinning planes. The spinning tether system garners significant attention for good centrifugal stability and transportation ability. However, conventional STS models face challenges such as singularities and coupling when studying three-dimensional spinning motion. To tackle the aforementioned challenges, a new singularity-adjustable model and a maneuvering control strategy are proposed. Initially, a variable coordinate system is defined, which allows for relocating singularities to unattainable positions during three-dimensional motions. Based on this new coordinate system, the singularity-adjustable Lagrangian model is established. Subsequently, based on the new model, a three-dimensional maneuvering scheme for spatial spinning motions is introduced to define and describe STS maneuvering trajectories in a de-coupled way. Finally, based on the reference maneuvering scheme, a saturated radial basis function network-based controller is designed to attenuate potential disturbances and errors, as electric thrusters used in this work are limited in actuating magnitude. Numerical results demonstrate that, with the new singularity-adjustable Lagrangian model, singularity and coupling phenomena are avoided during the three-dimensional maneuver, and the proposed controller ensures a stable STS three-dimensional maneuvering motion.