Adaptive Spacecraft Attitude Control Using Single-Gimbal Control Moment Gyroscopes Without Singularity Avoidance

This paper applies retrospective cost adaptive control (RCAC) to spacecraft attitude control with a rotation-matrix attitude parameterization using constant-speed single-gimbal control moment gyroscopes. Unlike control laws that use torque-steering laws to synthesize torque requests while avoiding gimbal singularities, the adaptive control law requests the rate of each gimbal. Because no torque request is provided, there is no need to invert the mapping from the gimbal rates to the control torque, and thus no attempt is made to avoid gimbal singularities. The RCAC implementation is based on a target model involving a single Markov parameter corresponding to the initial gimbal configuration. The parameters and weights for RCAC are based on nominal-model tuning, which uses no explicit knowledge of the nonlinear equations of motion. This paper investigates the robustness of RCAC to off-nominal conditions of commands, noise, and unknown bus inertia; and it examines the performance of RCAC in the case where an approximately singular gimbal configuration occurs during attitude command, following as well as the case of an initial gimbal-lock singularity. The performance of the adaptive controller in the presence of sensor/actuator misalignment is also investigated.