Finite-time saturated control of spinning tether system for varying its spinning orientations based on a nonsingular model

This paper mainly studies the dynamic and control of a Spinning Tether System (STS) during its maneuver between arbitrary spinning orientations. The main challenge of the maneuvering process is that, due to the singularity caused by the commonly used attitude representations, it is complicated to develop a controller with conventional models for changing and maintaining STS spinning motion out of the orbital plane. Besides, spinning motion outside the orbital plane requires continuous maintaining force, while the most suitable electrical thrust is limited in actuating force. To deal with the problems above, first, a virtual spinning coordinate system capable of artificially manipulating singularity position is defined to describe STS spatial motion, and the generalized coordinates are chosen accordingly to derive the new model, which avoids singularity in the practical sense. Second, based on the new nonsingular model, an open-loop strategy is developed for maneuvering and maintaining the spinning motions of STS. Last, a finite-time saturated control controller is designed for tracking reference maneuvering trajectories considering the explicit limit of electrical thrust. Numerical results indicate that the new nonsingular model can describe the three-dimensional spin without singularity, and the finite-time saturated controller can ensure a stable maneuvering process under the limit of electrical thrusters.