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Relative Pose Estimation for Nonholonomic Robot Formation with UWB-IO Measurements (Extended version)

Kunrui Ze, Wei Wang, Shuoyu Yue, Guibin Sun, Kexin Liu, Jinhu Lü

TL;DR

This work tackles distributed formation control for groups of nonholonomic robots in GPS-denied environments by exploiting onboard UWB distance measurements and inertial odometry. It introduces a concurrent-learning based relative pose estimator to infer interrobot poses in local frames, a cooperative DAG‑based strategy to estimate each follower’s pose to the leader, and a two-stage distributed formation controller that relies only on UWB and IO data. The approach relaxes the need for a persistently exciting external input, achieves global exponential convergence of localization errors under SE conditions, and demonstrates compelling 2D and 3D experiments with ground and aerial platforms. The results show accurate relative localization, robust formation tracking, and practical viability for scalable swarm operations in complex environments.

Abstract

This article studies the problem of distributed formation control for multiple robots by using onboard ultra wide band (UWB) distance and inertial odometer (IO) measurements. Although this problem has been widely studied, a fundamental limitation of most works is that they require each robot's pose and sensor measurements are expressed in a common reference frame. However, it is inapplicable for nonholonomic robot formations due to the practical difficulty of aligning IO measurements of individual robot in a common frame. To address this problem, firstly, a concurrent-learning based estimator is firstly proposed to achieve relative localization between neighboring robots in a local frame. Different from most relative localization methods in a global frame, both relative position and orientation in a local frame are estimated with only UWB ranging and IO measurements. Secondly, to deal with information loss caused by directed communication topology, a cooperative localization algorithm is introduced to estimate the relative pose to the leader robot. Thirdly, based on the theoretical results on relative pose estimation, a distributed formation tracking controller is proposed for nonholonomic robots. Both 3D and 2D real-world experiments conducted on aerial robots and grounded robots are provided to demonstrate the effectiveness of the proposed method.

Relative Pose Estimation for Nonholonomic Robot Formation with UWB-IO Measurements (Extended version)

TL;DR

This work tackles distributed formation control for groups of nonholonomic robots in GPS-denied environments by exploiting onboard UWB distance measurements and inertial odometry. It introduces a concurrent-learning based relative pose estimator to infer interrobot poses in local frames, a cooperative DAG‑based strategy to estimate each follower’s pose to the leader, and a two-stage distributed formation controller that relies only on UWB and IO data. The approach relaxes the need for a persistently exciting external input, achieves global exponential convergence of localization errors under SE conditions, and demonstrates compelling 2D and 3D experiments with ground and aerial platforms. The results show accurate relative localization, robust formation tracking, and practical viability for scalable swarm operations in complex environments.

Abstract

This article studies the problem of distributed formation control for multiple robots by using onboard ultra wide band (UWB) distance and inertial odometer (IO) measurements. Although this problem has been widely studied, a fundamental limitation of most works is that they require each robot's pose and sensor measurements are expressed in a common reference frame. However, it is inapplicable for nonholonomic robot formations due to the practical difficulty of aligning IO measurements of individual robot in a common frame. To address this problem, firstly, a concurrent-learning based estimator is firstly proposed to achieve relative localization between neighboring robots in a local frame. Different from most relative localization methods in a global frame, both relative position and orientation in a local frame are estimated with only UWB ranging and IO measurements. Secondly, to deal with information loss caused by directed communication topology, a cooperative localization algorithm is introduced to estimate the relative pose to the leader robot. Thirdly, based on the theoretical results on relative pose estimation, a distributed formation tracking controller is proposed for nonholonomic robots. Both 3D and 2D real-world experiments conducted on aerial robots and grounded robots are provided to demonstrate the effectiveness of the proposed method.

Paper Structure

This paper contains 36 sections, 4 theorems, 46 equations, 26 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and problem formulation
  3. Robot Models
  4. UWB Measurement and Communication Topology
  5. Control Objective
  6. Methods
  7. Problem Formulation of Relative Localization
  8. Relative Localization to Neighboring Robot
  9. Relative Localization to Leader Robot
  10. Distributed Formation tracking Controller
  11. Simulation Results
  12. Performance of the PE-free relative localization method
  13. Outlier measurement value detection
  14. Experiment results
  15. Experiment Setup
  16. ...and 21 more sections

Key Result

Lemma 1

Zhao2023TM Consider a perturbed system where $\textbf{x} \in \mathbb{R}^{n_{x}}$ is the state and $\delta \in \mathbb{R}^{n_{\delta}}$ is an exogenous signal. $f(t,\textbf{x})$ and $g(t,\textbf{x},\bm{\delta})$ are piecewise continues in $t$ and locally Lipschitz in $\textbf{x}$ and $(\textbf{x},\bm{\delta})$, respectively. Normal system

Figures (26)

  • Figure 1: Geometric relationship between the displacement and UWB distance measurements of the two robots. A. All the robot have a global orientation Xie2019TCNSdong2025tmechLiu2023Autoxiong2025adaptiveChen2023TIELiu2023RAL. B. Each robot is in its local frame.
  • Figure 2: An example directed acyclic graph, the leader robot and follower robots are denoted in the orange and blue dots.
  • Figure 3: Pose estimation error defined in (\ref{['estimate_error']}) under different noise level.
  • Figure 4: Convergence time (time required for the relative error of the estimated value to be less than 5%) of the two algorithm under different swarm scales.
  • Figure 5: Smoothness indicator defined in Eq.(\ref{['smoothness']}) under different swarm scale.
  • ...and 21 more figures

Theorems & Definitions (8)

  • Lemma 1
  • Theorem 1
  • proof
  • Remark 1
  • Theorem 2
  • proof
  • Theorem 3
  • proof