TY - GEN
T1 - Generating uniform incremental grids on SO(3) Using the Hopf fibration
AU - Yershova, Anna
AU - LaValle, Steven M.
AU - Mitchell, Julie C.
PY - 2010
Y1 - 2010
N2 - 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 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.
AB - 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 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.
UR - http://www.scopus.com/inward/record.url?scp=77949805513&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-00312-7_24
DO - 10.1007/978-3-642-00312-7_24
M3 - Conference contribution
AN - SCOPUS:77949805513
SN - 9783642003110
T3 - Springer Tracts in Advanced Robotics
SP - 385
EP - 399
BT - Algorithmic Foundations of Robotics VIII - Selected Contributions of the Eighth International Workshop on the Algorithmic Foundations of Robotics
T2 - 8th International Workshop on the Algorithmic Foundations of Robotics, WAFR
Y2 - 7 December 2008 through 9 December 2008
ER -