Abstract
This paper addresses the problem of singularity avoidance in a cluster of four Single-Gimbal Control Moment Gyroscopes (SGCMGs) in a pyramid configuration when used for the attitude control of a satellite by introducing a new gimballed control moment gyroscope (GCMG) cluster scheme. Four SGCMGs were used in a pyramid configuration, along with an additional small and simple stepper motor that was used to gimbal the full cluster around its vertical (z) axis. Contrary to the use of four variable-speed control moment gyroscopes (VSCMGs), where eight degrees of freedom are available for singularity avoidance, the proposed GCMG design uses only five degrees of freedom (DoFs), and a modified steering law was designed for the new setup. The proposed design offers the advantages of SGCMGs, such as a low weight, size, and reduced complexity, with the additional benefit of overcoming the internal elliptic singularities, which create a minor attitude error. A comparison with the four-VSCMG cluster was conducted through numerical simulations, and the results indicated that the GCMG design was considerably more efficient in terms of power while achieving a better gimbal configuration at the end of the simulation, which is essential when it is desired for different manoeuvres to be consecutively executed. Additionally, for a nano-satellite of a few kilograms, the results prove that it is feasible to manufacture the GCMG concept by using affordable and lightweight commercial off-the-shelf (COTS) stepper motors.
Highlights
Single-gimbal control moment gyroscopes (SGCMGs) have become popular actuators for satellites that have an agility requirement [1,2]
The steering law of Equation (26) is applied and the null motion guides the system to follow only the desired Ωdes set because the gimballed control moment gyroscope (GCMG) equals zero
Both the variable-speed control moment gyroscopes (VSCMGs) and GCMG cluster are capable of avoiding the internal singularity exploiting the redundant degrees of freedom (DoF) while maintaining a high manipulability index through the whole manoeuvre and similar settling time
Summary
Single-gimbal control moment gyroscopes (SGCMGs) have become popular actuators for satellites that have an agility requirement [1,2]. In cases where the angular speed of the flywheel is equal for all SGCMGs in the cluster, it is not possible to re-orient a symmetric gimbal set to a non-symmetric set through null-space motion in order to get a singularity-free path Such an action would result in a momentum change, and attitude error would be added into the system. A trajectory-planning approach was described in [18] to reduce the possibility of CMG saturation while the system followed a reference trajectory Another novel deterministic allocation algorithm for computing the angular rates of the gimbal was proposed in [19] instead of the well-known pseudo-inverse technique in order to keep the keep a four-CMG cluster in a roof configuration away from singularities. The details of the proposed GCMG, along with the advantages and the shortcomings of the proposed method, are presented in this paper
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