Optimal control scheme of the tethered system for orbital transfer under a constant thrust

The tethered system with a long tether has its unique advantages in space environment exploration. With the development of requirement, the orbital transfer of the tethered system under a constant thrust and its related optimal control become significant and challenging. Three different optimal control schemes of the tethered system are proposed, including the tension control, the thrust vector control, and the mixed control. In the tension control, in order to ensure the smoothness of pendular motion of the tethered system, different cost functions are adopted and compared. In the thrust vector control, the constraint of thrust direction angle is fully considered. In the mixed control, equivalent conditions to other control schemes are investigated. The advantages and disadvantages of three optimal control schemes are compared and analyzed, which provides a reference for research on the optimal control problem of the tethered system under a constant thrust.