Unit Quaternion-Based Output Feedback for the Attitude Tracking Problem

Abstract

In this note, we propose a quaternion-based dynamic output feedback for the attitude tracking problem of a rigid body without velocity measurement. Our approach consists of introducing an auxiliary dynamical system whose output (which is also a unit quaternion) is used in the control law together with the unit quaternion representing the attitude tracking error. Roughly speaking, the necessary damping that would have been achieved by the direct use of the angular velocity can be achieved, in our approach, by the vector part \mathtilde <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> of the error signal between the output of the auxiliary system and the unit quaternion tracking error. The resulting velocity-free control scheme guarantees <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">almost</i> global asymptotic stability which is as strong as the topology of the motion space can permit. In the regulation case, our control law is a pure quaternion feedback (i.e., consisting of two terms that are vector parts of unit-quaternion), and hence, the control torques are naturally bounded by the control gains. Simulation results are provided to show the effectiveness of the proposed control scheme.