Global Distributed Attitude Tracking Control of Multiple Rigid Bodies via Quaternion-Based Hybrid Feedback

Abstract

This article investigates the leader-following attitude tracking control problem of multiple rigid body systems in the presence of uncertain parameters and disturbances. The communication constraint is considered that only a subset of followers have access to the leader, and a quaternion-based nonlinear hybrid distributed observer is first proposed to estimate the leader's trajectory for each follower. In particular, the proposed distributed attitude observer always evolves on the 3-D unit sphere $\mathbb {S}^{3}$ . This property guarantees the feasibility of the observer-based distributed control scheme, since the separation principle is satisfied. By incorporating a hysteresis-based switch of a binary logic variable for each pair of neighboring rigid bodies, the proposed hybrid distributed observer achieves the global asymptotic stability for any initial attitude and avoids the unwinding phenomenon. Next, an observer-based attitude tracking control law is developed by combining adaptive technique and hybrid theory, which does not require precise model information and has good robustness to the disturbances. In addition, it is shown that the attitude tracking errors converge to the origin globally asymptotically. Finally, simulation results are provided to validate the theoretical results.