Adaptive singularity-free control moment gyroscopes

Design considerations of agile, precise, and reliable attitude control for a class of small spacecraft and satellites using adaptive singularity-free control moment gyroscopes (ASCMG) are presented. An ASCMG differs from that of a conventional controlmoment gyroscopes (CMG) because it is intrinsically free fromkinematic singularities and so does not require a separate singularity avoidance control scheme.Furthermore,ASCMGs are adaptive to the asymmetries in the structuralmembers (gimbal and rotor) as well as misalignments between the center ofmass of the gimbal and rotors. Moreover, ASCMG clusters are highly redundant to failure and can function as variable and constant-speed CMGs without encountering singularities. A generalized multibody dynamics model of the spacecraft-ASCMG system is derived using the variational principles ofmechanics, relaxing the standardset of simplifying assumptionsmade in prior literatureonCMG.The dynamicsmodel so obtainedshows the complex nonlinear coupling betweenthe internal degrees of freedomassociatedwithanASCMGand the spacecraft attitudemotion.The generaldynamicsmodel is then extended to include the effects of multiple ASCMG, called the ASCMG cluster, and the sufficient conditions for nonsingular cluster configurations are obtained.The adverse effects of the simplifying assumptions that lead to the intricate design of the conventional CMG, and how they lead to singularities, become apparent in this development. A bare-minimum hardware prototype of anASCMGusing low-cost commercial off-the-shelf components is developed to showthe design simplicity and scalability. A geometric variational integration scheme is obtained for this multibody spacecraft- ASCMG system for numerical and embedded implementation. Attitude pointing control of a CubeSat with three ASCMGs in the absence of external torques is numerically simulated to demonstrate the singularity-free characteristics and redundancy of the ASCMG cluster.