Modified Singular-Direction Avoidance Steering for Control Moment Gyros

Abstract

T HE geometric singularity problem is one of the most serious difficulties when using single-gimbal control moment gyros (SGCMGs) as spacecraft attitude control devices. Singularities preclude SGCMGs from generating torque in a certain direction, called the singular direction, and lead to loss of three-axis control of the spacecraft. Operating near these singularities may result in unreasonably high gimbal-rate commands and undesirable system response if one wishes to generate torque in the singular direction. This paper presents a simple modified singular-direction avoidance steering (SDA) method while achieving similar performance with current, more complicated, methods. Various approaches have been explored so far to solve the singularity problem [1–10]. These approaches include null motion [3], preferred gimbal-angle setting [4], constrained steering laws [5], offline planning [6], the singular robust inverse (SRI) method, etc. The most feasible and successfully applied technique is the SRI method, such as singularity robust (SR) steering law [7], generalized SR steering law (GSR) [8], offdiagonal SR steering law (o-DSR) [9], and SDA steering law [10], etc. These techniques lead to a practical solution to avoid or escape from singularities by allowing torque error, and they do not require any extra time-consuming planning process, initial gimbal-angle configuration, or constrained workspace. Though transient CMG torque errors are inevitable while escaping or passing through elliptic singularities, the resulting attitude transient dynamics are often acceptable, because precision pointing is not required during large-angle slew maneuvers [9]. In this Technical Note, the so-called SDA steering law proposed by Ford and Hall [10] is further examined. It is confirmed that the SDA steering law cannot escape the singular points effectively, since the gimbal-rate command along the singular direction is zero at singular points [9]. Based on the principle of singular-value decomposition (SVD), the SDA steering logic is augmented with a geometric principal rotation of singular vectors. This rotation introduces additional torque direction error to prevent zero gimbal-rate output when commanded torque is nonzero. Moreover, the singularity avoidance parameter is modified to allow gimbal movement in the null direction as the singularity approaches. The numerical simulations are adopted to evaluate the effectiveness of the proposed steering law. This modified SDA steering has a clearer geometric meaning, yet it shares a similar ability to escape any singularitieswith the existing methods.