Open AccessThe paper considers a maneuver for deorbiting the large space debris using an active spacecraft connected with the debris by an elastic tether. Tether slacking during the maneuver can lead to the tether rupture, kinking, and winding on the descending object. Therefore it is important to prevent slacking. The objective of this work is to find the law of thrust force control of the active spacecraft to ensure a continuously strained tether during the maneuver.
Using Lagrange formalism a mathematical model to describe the system plane motion is developed. This model considers the active spacecraft as a mass point, the space debris as a rigid body, and the tether as a weightless elastic rod. A thrust force is directed along the local horizon of the spacecraft. Linearization of nonlinear differential equation describing longitudinal oscillations of the tether length is performed. Its phase portrait is analyzed. An approximate expression describing the position of the center on the phase portrait is obtained. A time-optimal control with full feedback to ensure that the tether is in the strained state is found by solving the Bellman equation. To use the obtained optimal law it is necessary to set the measuring equipment on the spacecraft, which is capable of accurate measuring a distance to the space debris and its relative velocity. An alternative control law, which is simpler in terms of the practical implementation, is proposed. As an example, the descent from an orbit of nonfunctioning Soviet satellite Meteor-2 is considered. It is shown that both proposed laws provide continuous strain of the tether during deorbiting of the satellite. Moreover, slack does not occur even at the first period of oscillation of the tether length. It is shown that the use of the proposed control laws leads to slight increase of deorbiting time as compared to the case of using the constant thrust.
The results can be used to develop the control systems of small spacecrafts designed for deorbiting of space debris.