Optimal Control Of Spacecraft Rendezvous Using Elastic Tethers

This study is made to utilize a tether technology for the rendezvous and capture of payloads. A set of non-linear differential equations of tethered system with elastic tether is formulated based on Lagrange's equation. The correct positions at specified time are derived for an optimal rendezvous. A guidance scheme based on the direct Gauss pseudospectral method that can achieve rendezvous with a payload using a longitudinally flexible tether is demonstrated.Three case studies are considered in which the payload is inclined relative to the tether system by 0.5, 1.0 and 1.5 deg. The most rendezvous positions are distributed at the juncture of two orbits. As the inclination of the orbit increases, opportunities for rendezvous become rarer. This is a result of the constraint on maximum allowable tether length, which limits the excursion of the tether in the out-of-plane direction as the inclination increase.The optimal guidance law is determined by using the direct Gauss pseudospectral method, and the validity of solution is well demonstrated through case studies. It is shown that the rendezvous maneuver can be achieved by using only tension control and the out-of-plane thrust force. When the initial conditions of deployment are given, the trajectories of the capture seem like an"8". The trajectories become more complicated when the initial conditions are also taken as parameters for optimization. The results of numerical integration match the direct solutions obtained by using the method of nonlinear programming when the feedback terms of tether length and length rate are included in the tension control law. As indicated in the case studies, the proposed scheme not only gives a smooth trajectory of capture mechanism, but also guarantees the high precision for achieving the desired final states of rendezvous.