This dissertation advances the field of momentum control systems, specifically control momentum gyroscopes (CMGs), with three main contributions. The first two contributions improve the generality and performance of constraint-based steering laws for CMGs, while the third focuses on a novel implementation of CMGs that exploits their torque efficiency. First, this work provides analytical, closed-form gimbal-angle constraint functions that maximize the performance for CMG 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. A numerical assessment provides evidence of global optimality for the remaining angular-momentum states. In conjunction with previously developed constraint implementations methods, the provided constraints offer a general, high-performance, and fault-tolerant steering law. Simulations comparing the performance of this approach to that of an existing constraint-based method illustrates its improvement. The resulting steering law is also broadly applicable to aerospace and robotics problems. These constraints optimize velocity-tracking capability of planar serial manipulators, resulting in a control method that enables robotic end effectors to track large velocities, benefiting many tasks such as rapid mobile manipulation. Due to their generality, the constraint functions are also applicable to hyper-redundant multi-degree-of-freedom systems, including snake-like robots, enabling high-performance singularity avoidance. Second, this work provides a closed-form constraint-based steering law for the four-CMG box-90 array, one of the most common arrays in practice. The steering law offers guaranteed avoidance of all internal singularities. Furthermore, performance guarantees dictate a maximum torque magnitude that the array is capable of producing in all directions, within the array’s mechanical limitations. These performance guarantees increase the robustness of the overall control architecture by enabling maneuvers to be designed such that the torque commands remain bounded by the available torque. They also enable the CMGs for a particular application to be sized without the need for inexact numerical methods, such as Monte Carlo simulations. The proposed steering law is compared to the local-gradient steering law, which highlights its benefits over this and other candidate laws for the four-CMG box-90 array. Finally, this dissertation focuses on a novel implementation of CMGs that exploits their torque efficiency. Specifically, it explores a polyhedral rover that uses a CMG for rolling locomotion. Unlike reaction wheels, which have been used in similar rovers to enable hopping and tumbling motions, CMGs have not been explored extensively. Nevertheless, their torque and energy efficiency make them well suited for rover applications, motivating the development of design principles and control architectures that use CMGs effectively. This dissertation explores how exploiting the interaction between the chassis and the ground through morphology and control design, enables the rover with just one CMG to locomote over extreme terrain more efficiently and predictably, compared to other contemporary rover architectures.