Robust Global Asymptotic Attitude Stabilization of a Rigid Body by Quaternion-based Hybrid Feedback

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URL:

https://hybrid.soe.ucsc.edu/files/preprints/38.pdf

Keywords:

attitude control

Abstract:

Global asymptotic stabilization of the attitude of a rigid body is made difficult by several topological obstructions. In fact, this task is impossible to accomplish with discontinuous state feedback. Moreover, when the attitude is parameterized with unit quaternions, it becomes impossible to design a globally stabilizing state feedback (even discontinuous) that is robust to measurement noise. In this paper, we present a quaternion-based hysteretic hybrid feedback that robustly globally asymptotically stabilizes the attitude of a rigid body. The hybrid control laws are derived through Lyapunov analysis in kinematic and dynamic settings. In the dynamic setting, we provide two control laws: one derived from a simple Lyapunov function, and another based on backstepping. Analyzing the change in these Lyapunov functions due to jumps of the hysteretic logic variable yields a straightforward form for state-based hysteretic switching points. A simulation study demonstrates robustness to measurement noise in the proposed control laws and differences between the non-backstepping and backstepping control laws.

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