Almost global finite-time stabilization of rigid body attitude dynamics using rotation matrices

Summary This work considers continuous finite‐time stabilization of rigid body attitude dynamics using a coordinate‐free representation of attitude on the Lie group of rigid body rotations in three dimensions, SO(3). Using a Hölder continuous Morse–Lyapunov function, a finite‐time feedback stabiliza...

Full description

Saved in:
Bibliographic Details
Published in:International journal of robust and nonlinear control 2016-06, Vol.26 (9), p.2008-2022
Main Authors: Bohn, Jan, Sanyal, Amit K.
Format: Article
Language:English
Subjects:
continuous feedback
Control theory
Feedback
Feedback control
finite-time stabilization
Mathematical analysis
Morse-Lyapunov function
Quaternions
Representations
rigid body attitude dynamics
Rigid-body dynamics
Stabilization
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Summary This work considers continuous finite‐time stabilization of rigid body attitude dynamics using a coordinate‐free representation of attitude on the Lie group of rigid body rotations in three dimensions, SO(3). Using a Hölder continuous Morse–Lyapunov function, a finite‐time feedback stabilization scheme for rigid body attitude motion to a desired attitude with continuous state feedback is obtained. Attitude feedback control with finite‐time convergence has been considered in the past using the unit quaternion representation. However, it is known that the unit quaternion representation of attitude is ambiguous, with two antipodal unit quaternions representing a single rigid body attitude. Continuous feedback control using unit quaternions may therefore lead to the unstable unwinding phenomenon if this ambiguity is not resolved in the control design, and this has adverse effects on actuators, settling time, and control effort expended. The feedback control law designed here leads to almost global finite‐time stabilization of the attitude motion of a rigid body with Hölder continuous feedback to the desired attitude. As a result, this control scheme avoids chattering in the presence of measurement noise, does not excite unmodeled high‐frequency structural dynamics, and can be implemented with actuators that can only provide continuous control inputs. Numerical simulation results for a spacecraft in low Earth orbit, obtained using a Lie group variational integrator, confirm the theoretically obtained stability and robustness properties of this attitude feedback stabilization scheme. Copyright © 2015 John Wiley & Sons, Ltd.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.3399