PROGRAMMED CONTROL OF ADDITIONAL DEPLOYMENT OF A SPACE TETHER WITH RECOVERY OF ITS INITIAL VERTICAL ORIENTATION

The additional deployment of a two-body space tether with a massless cable is studied to develop a feed-forward control by the mode of increasing the length of a previously deployed space tether with the recovery of its initial vertical orientation. The motion equations of the variable length tether, written in spherical coordinates, are used for it. The developed feed-forward control by the length of the tether provides the necessary change of its angular momentum under the effect of the gravitational torque. The novelty of the results consists of developing a new approach to creating control for underactuated mechanical systems, which have a number of control channels less than the number of degrees of freedom. Here, a tether length control is developed, which allows for the control of its motion about the pitch axis, using only one tether length control channel. The passive but controlled effect of the gravitational torque on the tether is used for this purpose. To achieve this effect, it is proposed to impose restrictions on the motion of the tether about the pitch axis, which formally reduces the number of system degrees of freedom. This allows the implementation of the set motion mode with control only on the remained degree of freedom. The type of such restrictions is defined based on physical reasons. By accounting for all requirements for the mode of additional deployment, it is possible to develop the law of varying the pitch angle over time, which is described by a seventh-order polynomial. Detailed numerical research on the effect of mode parameters, such as the duration of deployment and expected shape of the pitch angle law vs. time, on the length of the unrolled tether and the character of its behavior during deployment is conducted. An example is provided numerically for the application of the developed method. Numerical simulation of the mode is carried out within the integration of the initial value problem for the Hill-Clohessy-Wiltshire equations. Quantitative estimation of errors of numerical simulation is conducted. The results of the calculations are illustrated graphically.