Optimal Control of Flexible Tethers
Paul A. Williams · 54th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law · 2003
A method for determining optimal trajectories for tethered systems is presented based on a parameterization of the tension control input. Three separate models of the tether system are used to compare the effects of different cost functions on optimal trajectories. The parameterization of the control is based on a rigid tether model, while the optimal trajectories are determined using a model that discretizes the tether into 4 point masses connected by massless inextensible strings. The effect of various cost functions and terminal times are compared for deployment and retrieval. The effect of various cost functions are also studied for a tether-assisted sample return problem. It is shown that a cost function that minimizes the tether reel acceleration maintains the tether essentially straight when simulated in a fully flexible model of the system, whereas several other cost functions result in significant bending of the tether.