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

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

TL;DR

The paper addresses real-time estimation of the 4-DOF relative transformation between two robots using odometry and UWB ranging data. It introduces a two-step maximum likelihood method: an unconstrained least squares initialization with projection, followed by a single Gauss-Newton refinement, achieving fast and accurate relative pose estimates under space constraints. It also provides path design and UWB configuration guidelines to guarantee identifiability and minimum operating time, demonstrated via simulations against SDP that show substantial reductions in computation time with maintained accuracy. The work enables practical real-time relative transformation estimation in constrained spaces and lays groundwork for extending to multi-robot scenarios and broader attitude estimation tasks.

Abstract

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.

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

TL;DR

The paper addresses real-time estimation of the 4-DOF relative transformation between two robots using odometry and UWB ranging data. It introduces a two-step maximum likelihood method: an unconstrained least squares initialization with projection, followed by a single Gauss-Newton refinement, achieving fast and accurate relative pose estimates under space constraints. It also provides path design and UWB configuration guidelines to guarantee identifiability and minimum operating time, demonstrated via simulations against SDP that show substantial reductions in computation time with maintained accuracy. The work enables practical real-time relative transformation estimation in constrained spaces and lays groundwork for extending to multi-robot scenarios and broader attitude estimation tasks.

Abstract

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.
Paper Structure (13 sections, 2 theorems, 26 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 13 sections, 2 theorems, 26 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. System Overview
  3. Problem Statement
  4. Range Measurement Model
  5. Proposed Approach
  6. Maximum Likelihood Formulation
  7. First step
  8. One Step of the Gauss-Newton Iteration
  9. Path Design and UWB Configuration
  10. Simulation
  11. Simulation Setup
  12. Simulation Results
  13. CONCLUSIONS AND FUTURE WORKS

Key Result

theorem thmcountertheorem

The estimate obtained through one step of Gauss-Newton iteration on the ML problem eqn_MJ_Problems converges in probability to the ML estimates as the number of measurements $n$ increases. Specifically, we have

Figures (4)

  • Figure 1: Overview of the proposed system.
  • Figure 2: Performance under repeated ranging in case $(i)$.
  • Figure 3: Estimation errors with varying $R_{max}$ and $\|\bf t\|$.
  • Figure 4: Estimation errors with varying speed.

Theorems & Definitions (4)

  • theorem thmcountertheorem
  • theorem thmcountertheorem
  • proof
  • remark thmcounterremark