New optimal control laws for attitude of a rigid body motion without angular velocity measurements

In this paper we shall use the passive properties of Euler dynamic equations as well as the structural properties of kinematic equations in terms of Cayley–Rodrigues and Modified Rodrigues parameters to derive optimal control laws without any information about the angular velocity of the rigid body. The interesting difference in the current study is the assumption that only the kinematics attitude parameters are available for the control process. The optimal control laws ensure the optimal asymptotic stability of the rigid body motion and minimize a selecting performance are obtained in terms of the kinematics attitude parameters and their estimates. Numerical examples are presented to demonstrate the theoretical results.