Rolling Stiefel manifolds

Authors:
K. Huper;M. Kleinsteuber;F. Silva Leite
Affiliations:
NICTA, Canberra, ACT, Australia,Department of Information Engineering, Research School of Information Sciences and Engineering, The Australian National University, Canberra, ACT, Australia;NICTA, Canberra, ACT, Australia,Department of Information Engineering, Research School of Information Sciences and Engineering, The Australian National University, Canberra, ACT, Australia;Institute of Systems and Robotics, University of Coimbra, Coimbra, Portugal,Department of Mathematics, University of Coimbra, Coimbra, Portugal
Venue:
International Journal of Systems Science - The Seventh Portuguese Conference on Automatic Control (Controlo'2006)
Year:
2008

Citing 8
Cited 2

The Geometry of Algorithms with Orthogonality Constraints

SIAM Journal on Matrix Analysis and Applications
Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation

International Journal of Computer Vision
A Grassmann--Rayleigh Quotient Iteration for Computing Invariant Subspaces

SIAM Review
The De Casteljau Algorithm on Lie Groups and Spheres

Journal of Dynamical and Control Systems
Essential Matrix Estimation Using Gauss-Newton Iterations on a Manifold

International Journal of Computer Vision
On the Geometry of Rolling and Interpolation Curves on Sn, SOn, and Grassmann Manifolds

Journal of Dynamical and Control Systems
Consistent independent component analysis and prewhitening

IEEE Transactions on Signal Processing - Part I
Covariance, subspace, and intrinsic Crame´r-Rao bounds

IEEE Transactions on Signal Processing

On the Geometry of Rolling and Interpolation Curves on Sn, SOn, and Grassmann Manifolds

Journal of Dynamical and Control Systems
An intrinsic formulation of the problem on rolling manifolds

Journal of Dynamical and Control Systems

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this article, rolling maps for real Stiefel manifolds are studied. Real Stiefel manifolds being the set of all orthonormal k-frames of an n-dimensional real Euclidean space are compact manifolds. They are considered here as rigid bodies embedded in a suitable Euclidean space such that the corresponding Euclidean group acts on the rigid body by rotations and translations in the usual way. We derive the kinematic equations describing this rolling motion.