The attitude control problem

A general framework for the analysis of the attitude tracking control problem for a rigid body is presented. A large family of globally stable control laws is obtained by using the globally nonsingular unit quaternion representation in a Lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body. The controllers share the common structure of a proportional-derivative feedback plus some feedforward which can be zero (the model-independent case), the Coriolis torque compensation, or an adaptive compensation. These controller structures are compared in terms of the requirement on the a priori model information, guaranteed transient performance, and robustness. The global stability of the Luh-Walker-Paul robot end-effector controller is also analyzed in this framework.