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A steering law design for single gimbal control moment gyros (CMGs) for spacecraft attitude control is addressed. The novel approach for the new steering law has a close relevance to the well-known singularity robustness method combined with the null motion approach. The proposed predicted singularity robustness (PSR) approach ultimately leads to an optimized solution of gimbal rates with performance improvement to avoid singularity by robust gradient null vectors. To apply it to practical systems, a singularity index, so-called inner-product index, is also introduced. The null vector induced from the suggested index provides a more reliable and robust way of escaping singular states than that of the well-known condition number index. Performance of the proposed algorithm is demonstrated by using a ground experimental hardware simulator equipped with four single gimbal CMGs floating on top of an air bearing.