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

Abstract The problem of generating uniform deterministic samples over the rotation group, SO(3), is fundamental to many fields, such as computational structural biology, robotics, computer graphics, astrophysics. We present the best-known method to date for constructing incremental, deterministic grids on SO(3); it provides the: 1) lowest metric distortion for grid neighbor edges, 2) optimal dispersionreduction 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.

• Type: Journal
• Year: 2010
• Where: IJRR
• Authors: Anna Yershova, Swati Jain, Steven M. LaValle, Julie C. Mitchell
• Keywords: Grid Neighbor Edges, IJRR 2010, Lowest Metric Distortion, Uniform Deterministic Samples