Climber motion optimization for the tethered space elevator

The tethered space elevator could provide a revolutionary means for enabling cheap transportation to geostationary altitude and beyond. Assuming that such a system can be built, one of the dynamic design problems is determining a means of moving the elevator along the tether so as to minimize the residual in-plane librational motion of the elevator ribbon and counterweight. In particular, this paper studies the problem from the point of view of dynamic optimization. A simplified dynamic model of the elevator system is derived that accounts for the fundamental libration modes and the motion of the elevator. The model is used to solve an optimal control problem that results in zero final in-plane librational motion of the ribbon. The results show that it is possible to eliminate the in-plane librational oscillations by reversing the direction of the elevator for a short time. It is also shown that it is possible to remove excess librational energy by controlled movement of the elevator on the ribbon. The effects of out-of-plane librations are also considered, but the climber motion does not have enough control authority to damp the out-of-plane motion over short time scales.