Unit Quaternion-Based Output Feedback for the Attitude Tracking Problem

摘要

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 ${mathtilde {q}}$ of the error signal between the output of the auxiliary system and the unit quaternion tracking error. The resulting velocity-free control scheme guarantees almost globalIn this paper we use the term almost global (see, for instance, ) to indicate that the boundedness of the states is guaranteed over $BBQ _{u},times, BBQ _{u} ,times, BBR ^{3}$ , where $BBQ _{u}$ is the set of unit-quaternion. Furthermore, the closed-loop system has four equilibrium points (three repeller equilibria and one attractor) that are mathematically different but represent the same physical attitude of the rigid body. All trajectories starting in $BBQ _{u} ,times, BBQ _{u} ,times, BBR ^{3}$–except the three repeller equilibria— will converge to the unique attractor equilibrium. For more details about the topological obstruction to continuous global stabilization of rotational motion, the reader is referred to .- - 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.