On the use of Euler's theorem on rotations for the synthesis of attitude control systems

The problem of controlling the rotational position (attitude) of a rigid body in three dimensions is discussed. Several control laws are synthesized for this six-dimensional nonlinear control problem by means of some well-known techniques of classical mechanics. The system input, output, and error are represented by 3x3 orthogonal matrices. Euler's theorem on rotations is employed to express the error matrix in terms of the angle of rotation and the direction cosines of the real eigen­ vector of the error matrix. It is noted that the angle of rotation is a con­ venient scalar representation of the system error. which the control is a of the the angular of are The results are illustrated with three examples: reaction jet control, reaction wheel control, and reaction wheel control with bounded motor torque and speed.