Moment error minimized direct control allocation for redundant reaction wheel configurations

Direct control allocation, which solves moment error minimization problem, for redundant reaction wheel configurations in spacecraft attitude control is considered. Based on the position of given command moment with respect to the moment envelope, the proposed direct control allocation strategy is performed in three successive steps. Firstly, a modified generalized inverse, which provides the greatest volume of moments, is calculated to help produce analytical solutions when the magnitude of command moment is relatively small. If some elements of these solutions break predefined moment limits, lx norm optimal solutions are then obtained on the premise that command moment still lies within the moment envelope. Finally, if the preceding steps failed in generating desired results, l2 norm optimal solutions that meet the requirement for moment error minimization are retrieved by utilizing the geometrical relationship between the command moment and the convex hull of moment space. Numerical simulations illustrate the presented control allocation strategy and show its advantages over other methods in acquiring optimal solutions.