Steering Law for Control Moment Gyroscopes with Online Torque Capacity Maximization

While single-gimbal control moment gyroscopes (CMGs) remain the actuators of choice for agile spacecraft, using over-redundant or overdesigned CMG arrays will cease to be a viable approach as agility requirements increase. The torque envelope of a CMG array under gimbal rate constraints is a zonotope, whose geometrical characteristics can be used to systematically increase the torque capacity around an arbitrarily given axis. For a four-CMG roof array, which consists of two coplanar CMG pairs, the torque capacity is a function of the allocation of angular momentum between the pairs. Based on the latter, a gimbal angle steering law is developed that maximizes the CMG array's torque capacity around a preferred axis defined by the current slew maneuver. A main feature of the proposed steering law is that this maximization does not require offline computations for any given preferred axis. In addition, an angular-momentum-based attitude tracking control law is formulated. As verified in numerical simulations, the developed steering and attitude control algorithms are able to follow a typical agile reference profile with adequate time domain performance while satisfying actuator constraints.