Generating uniform incremental grids on SO(3) using the hopf fibration

Anna Yershova; Swati Jain; Steven M. Lavalle; Julie C. Mitchell

doi:10.1177/0278364909352700

Generating uniform incremental grids on SO(3) using the hopf fibration

Anna Yershova, Swati Jain, Steven M. Lavalle, Julie C. Mitchell

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	801-812
Number of pages	12
Journal	International Journal of Robotics Research
Volume	29
Issue number	7
DOIs	https://doi.org/10.1177/0278364909352700
State	Published - Jun 2010

Keywords

Grids
Haar measure
Motion planning
Orthogonal group
Uniform sampling

ASJC Scopus subject areas

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

Online availability

10.1177/0278364909352700

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Generating uniform incremental grids on SO(3) using the hopf fibration

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Keywords

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