Robust global asymptotic attitude stabilization of a rigid body by quaternion-based hybrid feedback

Global asymptotic stabilization of the attitude of a rigid body is hindered by major topological obstructions. In fact, this task is impossible to accomplish with continuous state feedback. Moreover, when the attitude is parametrized with unit quaternions, it becomes impossible to design a globally...

Full description

Saved in:
Bibliographic Details
Main Authors: Mayhew, C.G., Sanfelice, R.G., Teel, A.R.
Format: Conference Proceeding
Language:English
Subjects:
Backstepping
Hysteresis
Kinematics
Logic
Lyapunov method
Noise measurement
Noise robustness
Quaternions
Robust control
State feedback
Online Access:Request full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Global asymptotic stabilization of the attitude of a rigid body is hindered by major topological obstructions. In fact, this task is impossible to accomplish with continuous state feedback. Moreover, when the attitude is parametrized 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 an energy-based Lyapunov function and another based on backstepping. Analyzing the change in these Lyapunov functions due to switching of a logic variable yields a straightforward form for state-based hysteresis. A simulation study demonstrates how hysteresis provides robustness to measurement noise and highlights differences between the energy-based and backstepping control laws.
ISSN:0191-2216
DOI:10.1109/CDC.2009.5400431