Distributed almost global finite-time attitude consensus of multiple spacecraft without velocity measurements

This paper addresses the attitude consensus problem of multiple rigid bodies in terms of the unit quaternion parameterization. By employing Lyapunov theory and homogeneous techniques, distributed finite-time attitude consensus laws are proposed for leader-following and leaderless multi-agent systems, with full-state (i.e., attitude plus angular velocity) or attitude-only measurements. Specifically, sliding mode observers are used to estimate the leader's information in finite time for followers without direct access to the leader. The so-called “separation principle” is then established between the observers and the consensus controllers. In addition, quaternion filtering systems are constructed to inject the necessary damping into the closed-loop system when angular velocity measurements are absent. In all scenarios, the proposed methods ensure almost global finite-time convergence, avoid the unwinding problem, and yield continuous control torques with a priori known bounds. Numerical examples demonstrate the effectiveness of the proposed methods.