This paper presents a solution to the control allocation problem posed by four tip vanes with two degrees of freedom on a square solar sail. Instead of solving for the vane angles, the solution being sought is redefined as the vane torques. The estimated attainable moment sets, defined as general ellipses, constrain the solution within the feasible set. The resulting control allocation problem is much easier to solve via numerical algorithms due to the convex nature of the constraints. The vane angles are analytically derived from the vane torques to achieve the desired solution. Numerical examples are presented to demonstrate the efficacy of the solution.
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