Completely Rational $\text{SO}(n)$ Orthonormalization
Jin Wu, Soheil Sarabandi, Jianhao Jiao, Huaiyang Huang, Bohuan Xue, Ruoyu Geng, Lujia Wang, Ming Liu
Abstract
The rotation orthonormalization on the special orthogonal group \text{SO}(n)\text{SO}(n), also known as the high dimensional nearest rotation problem, has been revisited. A new generalized simple iterative formula has been proposed that solves this problem in a completely rational manner. Rational operations allow for efficient implementation on various platforms and also significantly simplify the synthesis of large-scale circuitization. The developed scheme is also capable of designing efficient fundamental rational algorithms, for example, quaternion normalization, which outperforms long-exisiting solvers. Furthermore, an \text{SO}(n)\text{SO}(n) neural network has been developed for further learning purpose on the rotation group. Simulation results verify the effectiveness of the proposed scheme and show the superiority against existing representatives. Applications show that the proposed orthonormalizer is of potential in robotic pose estimation problems, e.g., hand-eye calibration.
BibTeX
@inproceedings{icra2023_completelyration,
title = {Completely Rational $\text{SO}(n)$ Orthonormalization},
author = {Jin Wu and Soheil Sarabandi and Jianhao Jiao and Huaiyang Huang and Bohuan Xue and Ruoyu Geng and Lujia Wang and Ming Liu},
booktitle = {ICRA 2023},
year = {2023}
}