# A Planar-Symmetric SO(3) Representation for Learning Grasp Detection

arXiv: https://arxiv.org/abs/2410.04826 · HTML: https://mlsanity.com/paper/2410.04826/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2024.

## Built on by (most cited first, 1 of 1)

- [Simultaneous Pick and Place Detection by Combining SE(3) Diffusion Models with Differential Kinematics](https://mlsanity.com/paper/2504.19502/) (2025)

## Abstract (arXiv)

Planar-symmetric hands, such as parallel grippers, are widely adopted in both research and industrial fields. Their symmetry, however, introduces ambiguity and discontinuity in the SO(3) representation, which hinders both the training and inference of neural-network-based grasp detectors. We propose a novel SO(3) representation that can parametrize a pair of planar-symmetric poses with a single parameter set by leveraging the 2D Bingham distribution. We also detail a grasp detector based on our representation, which provides a more consistent rotation output. An intensive evaluation with multiple grippers and objects in both the simulation and the real world quantitatively shows our approach's contribution.