Partial Lyapunov Strictification: Smooth Angular Velocity Observers for Attitude Tracking Control

Abstract

A smooth angular velocity observer is proposed for the attitude tracking control of a rigid body in the absence of angular velocity measurements. The observer design ensures asymptotic convergence of angular velocity state estimation errors irrespective of the control torque or the initial attitude state of the spacecraft. Unlike existing rate observer formulations that attain estimation error convergence by imposing certain switching conditions or hybrid logic, the proposed observer has a smooth structure that ensures continuity of all estimated states. Furthermore, the combined implementation of the proposed observer with a proportional-derivative type of attitude control law leads to an important “separation property.” In particular, an independently designed proportional-derivative control law driven by angular velocity estimates generated from the smooth observer results in (almost) global asymptotic stability of the overall closed-loop tracking error dynamics. The main feature of this key technical result stems from our use of a Lyapunov “strictification” process that enables the closed-loop stability and convergence analysis to proceed along novel lines in a spiral logic fashion. A rigorous analysis of the proposed formulation is provided and numerical simulation studies are presented to help illustrate the effectiveness of the angular velocity observer for rigid-body attitude tracking control.