Abstract
A geometric theory regarding singularity problems of single gimbal control moment gyrosystems is outlined. Most control moment gyrosystems have impassable and inescapable singular states that obstruct continuous changes of the total angular momentum vector. The remaining problem of the theory regarding degenerate singularity is described with an unproved conjecture. Based on the theory, various steering laws such as gradient methods and singularity robust methods for the pyramid-type control moment gyrosystem, and those for variable speed control moment gyros are surveyed and analyzed. Problems of the attitude control by these steering laws are examined by geometrical analyses without numerical simulation.
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