In this paper, we investigate the problem of estimating the 4-DOF (three-dimensional position and orientation) robot-robot relative frame transformation using odometers and distance measurements between robots. Firstly, we apply a two-step estimation method based on maximum likelihood estimation. Specifically, a good initial value is obtained through unconstrained least squares and projection, followed by a more accurate estimate achieved through one-step Gauss-Newton iteration. Additionally, the optimal installation positions of Ultra-Wideband (UWB) are provided, and the minimum operating time under different quantities of UWB devices is determined. Simulation demonstrates that the two-step approach offers faster computation with guaranteed accuracy while effectively addressing the relative transformation estimation problem within limited space constraints. Furthermore, this method can be applied to real-time relative transformation estimation when a specific number of UWB devices are installed.
@article{arxiv.2405.12577,
title = {Fast Estimation of Relative Transformation Based on Fusion of Odometry and UWB Ranging Data},
author = {Yuan Fu and Zheng Zhang and Guangyang Zeng and Chun Liu and Junfeng Wu and Xiaoqiang Ren},
journal= {arXiv preprint arXiv:2405.12577},
year = {2024}
}