Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibration-Reference-Cited by-同舟云学术

Generating Uniform Incremental Grids on SO(3) Using the Hopf Fibration

Published:2009-11-13 Issue:7 Volume:29 Page:801-812
ISSN:0278-3649
Container-title:The International Journal of Robotics Research
language:en
Short-container-title:The International Journal of Robotics Research

Author:

Yershova Anna¹,Jain Swati²,LaValle Steven M.³,Mitchell Julie C.⁴

Affiliation:

1. Duke University, Durham, NC 27707, USA

2. Duke University, Durham, NC 27707, USA,

3. University of Illinois, Urbana, IL 61801, USA

4. University of Wisconsin-Madison, Madison, WI 53706, USA

Abstract

The problem of generating uniform deterministic samples over the rotation group, SO(3 ), is fundamental to computational biology, chemistry, physics, and numerous branches of computer science. We present the best-known method to date for constructing incremental, deterministic grids on SO(3 ); it provides: (1) the lowest metric distortion for grid neighbor edges, (2) optimal dispersion-reduction with each additional sample, (3) explicit neighborhood structure, and (4) equivolumetric partition of SO(3 ) by the grid cells. We also demonstrate the use of the sequence on motion planning problems.

Publisher

SAGE Publications

Subject

Applied Mathematics,Artificial Intelligence,Electrical and Electronic Engineering,Mechanical Engineering,Modeling and Simulation,Software

Link

http://journals.sagepub.com/doi/pdf/10.1177/0278364909352700

Reference33 articles.

1. RANDOM ROTATION MATRICES

2. FAST RANDOM ROTATION MATRICES

3. The Subgroup Algorithm for Generating Uniform Random Variables

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