Optimal Solution for Torque Capability of Control Moment Gyroscopes

This paper improves the generality and performance of constraint-based steering laws for control moment gyroscopes (CMGs). Specifically, the paper provides analytical, closed-form gimbal-angle constraint functions that maximize the torque capability for arrays with parallel gimbal axes. The analytical solutions define an optimal gimbal-angle set for a given angular-momentum state for any planar array with four or more CMGs. Proofs verify the global optimality of the provided gimbal-angle set constraints for nearly all angular-momentum states. For angular-momentum states where an analytical proof is not provided, a numerical assessment provides evidence of global optimality. The solutions can be applied to planar and non-planar arrays consisting of planar segments of CMGs, such as roof arrays and box arrays. The gimbal-angle constraint functions also enable fault-tolerant steering laws because the constraint functions apply to any number of planar CMGs greater than four. Thus, if one or more CMGs fail, the resulting steering law can still perform optimally. The gimbal-angle constraint functions are broadly applicable to aerospace and robotics problems. In their more general form, these constraints optimize velocity-tracking capability of planar serial manipulators, which benefits tasks requiring large velocities of the end effector, such as rapid mobile manipulation and intercepting fast-moving objects. Due to their generality, the constraint functions are applicable to hyper-redundant multi-degree-of-freedom systems, including elephant trunks and snakelike robots. Simulations comparing the performance of this approach to that of existing constraint-based methods illustrate the improvements.