Abstract
A new form of the equations of motion for a spacecraft with Single Gimbal Control Moment Gyros is developed using a momentum approach. This set of four vector equations describing the rotational motion of the system is of order 2N + 7 where N is the number of CMGs. The control input is an N x I column vector of torques applied to the gimbal axes. A modification to the singularity robust Lyapunov control law presented by Oh and Vadali is examined and compared to their control law. Specifically, the attempt to avoid singular gimbal configurations is abandoned in favor of simply avoiding movement in the singular direction. The singular value decomposition is used to compute a pseudoinverse which prevents large gimbal rate commands near or at actual singularities.
Published Version
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