Feed-forward control of total retrieval of the space tether from vertical position

This paper presents the results of studies of the feasibility of total and safe retrieval of a space tether of two bodies connected by an elastic, massless cable. The purpose of the research is to build up the control for the mode of the total and safe retrieval of the tether, which is one of the basic modes of its functioning. It allowed the development of the feed-forward control of the tether length or tension that provides demanded change of the angular momentum of the tether under the effect of the gravitational torque. The novelty of the research results consists also in the novel approach to the control of underactuated mechanical systems, which have the number of the control channels less than their degrees of freedom. Here the constraints on the tether angular motion relative to the pitch axis are introduced. They reduce the number of the system degrees of freedom and allow realizing the necessary mode of motion. For this control, only the remaining degree of freedom is used. The numerical simulation of the effect of the mode parameters on the tether motion is carried out for the tether in the chosen ranges of the parameters. The numerical example demonstrates the simplicity of the application of the method in practice. Plots illustrate the analysis of the results.