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In the subdivision approach to robot path planning, we need to subdivide the configuration space of a robot into nice cells to perform various computations. For a rigid spatial robot, this configuration space is \(SE(3)={\mathbb R}^3\times SO(3)\) . The subdivision of \({\mathbb R}^3\) is standard but so far, there are no global subdivision schemes for \(SO(3)\) . We recently introduced a representation for \(SO(3)\) suitable for subdivision. This paper investigates the distortion of the natural metric on \(SO(3)\) caused by our representation. The proper framework for this study lies in the Riemannian geometry of \(SO(3)\) , enabling us to obtain exact distortion bounds.

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Distortion Bounds of Subdivision Models for \(\boldsymbol {SO}(3)\)

  • 会议论文

  • 发表日期：

    2026年

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  • Zhaoqi Zhang,
  • Chee Yap

摘要

In the subdivision approach to robot path planning, we need to subdivide the configuration space of a robot into nice cells to perform various computations. For a rigid spatial robot, this configuration space is \(SE(3)={\mathbb R}^3\times SO(3)\) . The subdivision of \({\mathbb R}^3\) is standard but so far, there are no global subdivision schemes for \(SO(3)\) . We recently introduced a representation for \(SO(3)\) suitable for subdivision. This paper investigates the distortion of the natural metric on \(SO(3)\) caused by our representation. The proper framework for this study lies in the Riemannian geometry of \(SO(3)\) , enabling us to obtain exact distortion bounds.