scholarly journals Passivity-Based Attitude Control on the Special Orthogonal Group of Rigid-Body Rotations

2013 ◽  
Vol 36 (6) ◽  
pp. 1596-1605 ◽  
Author(s):  
James Richard Forbes
Keyword(s):  
Rigid Body ◽  
Attitude Control ◽  
Orthogonal Group ◽  
Special Orthogonal Group

General Identities for Parameterizations of SO(3) With Applications

2014 ◽  
Vol 81 (7) ◽  
Author(s):  
Anton H. J. de Ruiter ◽  
James Richard Forbes
Keyword(s):  
Rigid Body ◽  
Orthogonal Group ◽  
Attitude Determination ◽  
Unit Length ◽  
Spacecraft Attitude ◽  
Euler Angles ◽  
Motion Equations ◽  
Rotation Matrices ◽  
Special Orthogonal Group ◽  
Lagrange’S Equation

Rotation matrices, which are three-by-three orthonormal matrices with determinant equal to plus one, constitute the special orthogonal group of rigid-body rotations, denoted SO(3). Owing to the three-by-three nature of rotation matrices plus their orthonormality constraint, parameterizations are often used in favor of rotation matrices for computations and derivations. For example, Euler angles and Rodrigues parameters are common three-parameter unconstrained parameterizations, while unit-length quaternions are a popular four-parameter constrained parameterization. In this paper various identities associated with the parameterization of SO(3) are considered. In particular, we present six identities, three related to unconstrained parameterizations and three related to constrained parameterizations. We also discuss rotation matrix perturbations. The utility of these identities is highlighted when deriving the motion equations of a rigid body using Lagrange's equation. We also use them to examine some issues associated with spacecraft attitude determination.

Semiglobal Nonmemoryless Attitude Controls on the Special Orthogonal Group

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Taeyoung Lee ◽  
Dong Eui Chang ◽  
Yongsoon Eun
Keyword(s):  
Control Systems ◽  
Attitude Control ◽  
Orthogonal Group ◽  
Global Attractivity ◽  
Control Input ◽  
Attitude Dynamics ◽  
Region Of Attraction ◽  
Special Orthogonal Group ◽  
Topological Restriction ◽  
New Framework

This paper presents tracking strategies for the attitude dynamics of a rigid body that are global on the configuration space SO(3) and semiglobal over the phase space SO(3)×ℝ3. It is well known that global attractivity is prohibited for continuous attitude control systems on the special orthogonal group. Such topological restriction has been dealt with either by constructing smooth attitude control systems that exclude a set of zero measure in the region of attraction or by introducing discontinuities in the control input. This paper proposes nonmemoryless attitude control systems that are continuous in time, where the region of attraction guaranteeing exponential convergence completely covers the special orthogonal group. This provides a new framework to address the topological restriction in attitude controls. The efficacy of the proposed methods is illustrated by numerical simulations and an experiment.

scholarly journals Isometries of the special orthogonal group

2013 ◽  
Vol 439 (1) ◽  
pp. 174-188 ◽  
Author(s):  
Toshikazu Abe ◽  
Shigeki Akiyama ◽  
Osamu Hatori
Keyword(s):  
Orthogonal Group ◽  
Special Orthogonal Group
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