Attitude Control of a Spacecraft with Single Variable-Speed Control Moment Gyroscope

Abstract

C ONTROL moment gyroscopes (CMGs) have been studied since they were used in the Skylab in the mid-1960s. There are several versions of CMGs: single-gimbal, double-gimbal, and variable-speed. Nowadays, variable-speed CMGs (VCMGs) are becoming an important research topic because of their advantages over the conventional CMGs: a VCMG generates two orthogonal torques and it operates like amechanical battery for energy storage.A cluster of VCMGs has less singular conditions than those of conventional constant-speed CMGs. Several control methods to use the advantages of VCMGs have been presented [1–3]. In this Note, we are interested in the attitude control problem of a spacecraft using only one single-gimbal, variable-speed CMG (SVCMG). If one SVCMG is able to control the attitude of a spacecraft, several benefits such as low cost and low weight are expected. However, since one SVCMGgenerates only two independent control inputs, one axis among three body axes is not controlled arbitrary. This is called an underactuated problem. Some notable papers and references therein are useful to understand this issue [4–7]. The control strategy depends on the amount of the angular momentum of a spacecraft. If the total angular momentum of a spacecraft is null, an arbitrary attitude can be reached by three consecutive rotations about two axes [5]. If not, an arbitrary attitude is not always possible due to the conservation of the angular momentum. For a spacecraft using one SVCMGwith nonnull angular momentum, a Lyapunov-based control methodwas presented to stabilize the angular speeds in [8]. The authors of [9] advanced a step further: a certain face of a spacecraft, on which important apparatus might be installed, was controlled to aim at a target point on the assumption that a line-of-sight control was sufficient for a given mission or communication. However, the method needs three different control laws acting consecutively. Transitions between controls could cause an undesirable transient response of the spacecraft. In this Note, we present an effective control law based on the backsteppingmethod to control the line-of-sight of a spacecraft or the direction of a target axis. Several improvements on the result of [9] are achieved: there is no bump phenomenon, a linear model about an equilibrium condition is not necessary, and a ramp input is followed by the proportional–integral (PI) control. The Note is organized as follows: Sec. II presents preliminaries and objectives of this study. The attitude is described by the quaternion and the direction of a target axis is represented by the directional cosines. In Sec. III, a new control law is proposed that is based on the backsteppingmethod and its stability is proved. The stability and the performance of the proposed control law are validated with illustrative numerical simulations in Sec. IV. Finally, Sec. V presents conclusions.