Optimal control for the attitude stabilization of a rigid body using non-redundant parameters

This paper introduces a new class of an optimal stabilizing feedback control law for the attitude of motion of a rotating rigid body using rotors system which rotate with the help of electrical motors that are mounted on this body. The control moments that can be generated by the rotors system are derived as non-linear terms of new parameterizations of the rotation group. The stabilizing properties of the proposed control law are proved by using the optimal Liapunov function. Some known results on the control of the rigid body motion are generalized and other new results are obtained. Finally, numerical examples demonstrate the theoretical results.