Finite-time angular velocity observers for rigid-body attitude tracking with bounded inputs

The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite-time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion-based nonlinear proportional-derivative controller using full-state feedback is designed first, yielding uniformly almost globally finite-time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional-derivative controller ensures finite-time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high-gain injection, as opposed to the semi-global results, but also overcome the unwinding problem associated with some quaternion-based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods.