Distortion Bounds of Subdivision Models for SO(3)
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916739182231552 |
|---|---|
| author | Zhang, Zhaoqi Yap, Chee |
| author_facet | Zhang, Zhaoqi Yap, Chee |
| contents | 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 sharp distortion bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22961 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distortion Bounds of Subdivision Models for SO(3) Zhang, Zhaoqi Yap, Chee Robotics 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 sharp distortion bounds. |
| title | Distortion Bounds of Subdivision Models for SO(3) |
| topic | Robotics |
| url | https://arxiv.org/abs/2503.22961 |