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

TL;DR

This paper presents a fast, two-step maximum likelihood method for estimating 4-DOF relative transformations between robots using odometry and UWB ranging, optimizing UWB placement for real-time applications.

Contribution

It introduces a novel two-step estimation approach combining least squares and Gauss-Newton iteration for efficient relative transformation estimation.

Findings

Two-step method achieves faster computation with guaranteed accuracy.

Optimal UWB placement enhances real-time estimation capabilities.

Simulation confirms effectiveness in limited space scenarios.

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.