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In this paper, we investigate the problem of estimating the 4-DOF (three-dimensional position and two-dimensional orientation) robot-robot relative frame transformation using odometers and distance measurements between robots. Firstly, we apply a two-step estimation approach based on maximum likelihood estimation. Concretely, 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.

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Fast Estimation of Relative Transformation Based on Fusion of Odometry and UWB Ranging Data

  • 会议论文

  • 发表日期：

    2025年

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  • Yuan Fu,
  • Zheng Zhang,
  • Guangyang Zeng,
  • Chun Liu,
  • Junfeng Wu,
  • Xiaoqiang Ren

摘要

In this paper, we investigate the problem of estimating the 4-DOF (three-dimensional position and two-dimensional orientation) robot-robot relative frame transformation using odometers and distance measurements between robots. Firstly, we apply a two-step estimation approach based on maximum likelihood estimation. Concretely, 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.