US Patent 7246776 Method and system for CMG array singularity avoidance

The present method provides a method for avoiding singularities in the movement of CMGs in an array of CMGs in a spacecraft. In a first step, a torque command representing a desired torque to produce an attitude adjustment for the spacecraft is received. Next, a range-space gimbal rate required to produce the desired torque based on the desired torque and a Jacobian matrix is calculated. Then, a null-space gimbal rate that assists in the avoidance of singularities is calculated. The total gimbal rate command is determined by summing the range-space gimbal rate and the null-space gimbal rate. Then, the total gimbal rate command is provided to the CMGs to produce the total gimbal rate.