Relative control of an ion beam shepherd satellite in eccentric orbits

Abstract

The “ion-beam shepherd” is a contactless space debris removal concept, which implies that the shepherd satellite (SS) must be controlled to move at a certain small distance in front of a space debris object during the de-orbiting phase. As shown in recent studies, the strategy to control the relative motion of this formation using only one compensation thruster of the SS can significantly reduce propellant mass of the actuators. However, such a control system maintains a required relative position of the underactuated SS with a periodic error. The amplitude of this error is small for quasi-circular orbits, but it can be significant for eccentric orbits due to the time-varying behavior of the plant. Given that there are debris in non-circular orbits that need to be removed, this article investigates the feasibility of using only one compensation thruster to control relative position of the SS in eccentric orbits. Both time-invariant and periodic linear-quadratic regulators are examined for using as a controller of the SS. A periodic reference input of the regulator is designed to reduce the relative position errors and improve the efficiency of the ion beam impact on the space debris object.