Many space vehicles have been launched with large flexible components such as booms and solar arrays. These large space structures may require active shape control given the possibility of lightly damped vibrations. Such vibrations can be controlled using a collection of control moment gyros, which consist of a spinning wheel in gimbals and produce a torque when the orientation of the wheel is changed. This study investigates the optimal distribution of these control moment gyros on large space structures for vibration suppression. Initially, a continuum model is adopted that represents the distribution of control moment gyros by a continuous distribution of stored angular momentum (gyricity). The optimal control solution for the gimbal motions (for a given gyricity distribution) is then optimized with respect to the gyricity distribution. Further investigation considers discrete parameter models of beam and a plate structures with evenly placed discrete pointwise control moment gyros. Numerical optimization of a suitable cost function allocates the amount of stored angular momentum possessed by these control moment gyros.

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Extremum-seeking guidance endeavors to drive the output of a system to the extremum of an unknown objective function. This paper proposes an extremum-seeking guidance algorithm on SO3 for cases with and without inclusion and exclusion zones. The gradient of the unknown objective function is estimated via a Kalman filter so that the extremum of the objective function can be approximated. To satisfy inclusion and exclusion zone constraints, two different constrained Kalman filters are proposed. The first Kalman filter is a gain-projected Kalman filter, and the second is a novel linear matrix inequality based Kalman filter that is able to accommodate a larger class of constraints. The proposed extremum-seeking guidance algorithm is demonstrated using a performance objective that relates a spacecraft's attitude to received power of an unknown radiation source using a patch antenna.

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