Steering law design with perturbed Jacobian matrix for Single Gimbal Control Moment Gyroscopes

Steering law design for Single Gimbal Control Moment Gyroscopes (SGCMGs) can be transformed into a problem of nonlinear programming with nonsingular constraint. Although the suboptimal solution to the nonlinear programming has the closed form through the estimation of the Kuhn-Tucker multipliers without sophisticated numerical calculations, it is still often trapped in the elliptic singular points. In this paper, a modified steering law based on nonlinear programming is presented. In this algorithm, a proper gimbal perturbation is inserted into the Jacobian matrix actively when SGCMGs are approaching to or locked in the singular points. Thus, the algorithm can output feasible gimbal commands even near singularities and can force the gimbals leave singular configurations for the desired ones. Extensive simulation results demonstrate the effectiveness of the proposed method.