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This paper addresses the leader-following attitude consensus problem for a group of spacecraft when at least one follower can access the leader's attitude and velocity relative to the inertial space. A nonlinear distributed observer is designed to estimate the leader's states for each follower. The observer possesses one important and novel feature of keeping attitude and angular velocity estimation errors on second-order sliding modes, and thus provides finite-time convergent estimates for each follower. Further, quaternion-based hybrid homogeneous controllers recently developed for single spacecraft are extended and then applied, by establishing a separation principle with the proposed observer, to track the leader's attitude motion. As a result, global finite-time attitude consensus is achieved on the entire attitude manifold, with either full-state measurements or attitude-only measurements, as long as the network topology among the followers is undirected and connected. Numerical simulations are presented to demonstrate the performance of the proposed methods.

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. If z≡0, system (40) coincides with the closed-loop system resulting from the full-state feedback controller (34), and according to Proposition 1, the equilibria x∈Z 0 are UAGAS. In addition, 26H. GUI AND G. VUKOVICH

This paper addresses the attitude tracking of a rigid body using a quaternion description. Global finite-time attitude controllers are designed with three types of measurements, namely, full states, attitude plus constant-biased angular velocity, and attitude only. In all three scenarios hybrid control techniques are utilized to overcome the well-known topological constraint on the attitude manifold, while coupled nonsmooth feedback inputs are designed via homogeneous theory to achieve finitetime stability. Specially, a finite-time bias observer is derived in the second scenario and a quaternion filter is constructed to provide damping in the absence of velocity feedback. The proposed methods ensure bounded control torques a priori and, in particular, include several existing attitude controllers as special cases.