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Concurrent-Learning Based Relative Localization in Shape Formation of Robot Swarms (Extended version)

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

TL;DR

This work tackles autonomous shape formation for large robot swarms in GPS-denied environments where external localization is unavailable. It introduces a concurrent-learning based relative-position estimator that relaxes the persistent-excitation requirement $PE$, a seed-robot driven finite-time shape localization protocol, and a behavior-based formation controller that scales to large swarms while improving observability of inter-robot localization. The main contributions are (i) PE-relaxing concurrent-learning localization, (ii) finite-time, seed-based shape localization without global coordinates, and (iii) a concise, four-command shape formation framework validated by simulations and outdoor experiments with up to six robots. The results enable robust, autonomous swarm formation in indoor and outdoor settings, reducing reliance on external localization systems and enabling practical deployment in GPS-denied scenarios.

Abstract

In this paper, we address the shape formation problem for massive robot swarms in environments where external localization systems are unavailable. Achieving this task effectively with solely onboard measurements is still scarcely explored and faces some practical challenges. To solve this challenging problem, we propose the following novel results. Firstly, to estimate the relative positions among neighboring robots, a concurrent-learning based estimator is proposed. It relaxes the persistent excitation condition required in the classical ones such as least-square estimator. Secondly, we introduce a finite-time agreement protocol to determine the shape location. This is achieved by estimating the relative position between each robot and a randomly assigned seed robot. The initial position of the seed one marks the shape location. Thirdly, based on the theoretical results of the relative localization, a novel behavior-based control strategy is devised. This strategy not only enables adaptive shape formation of large group of robots but also enhances the observability of inter-robot relative localization. Numerical simulation results are provided to verify the performance of our proposed strategy compared to the state-of-the-art ones. Additionally, outdoor experiments on real robots further demonstrate the practical effectiveness and robustness of our methods.

Concurrent-Learning Based Relative Localization in Shape Formation of Robot Swarms (Extended version)

TL;DR

This work tackles autonomous shape formation for large robot swarms in GPS-denied environments where external localization is unavailable. It introduces a concurrent-learning based relative-position estimator that relaxes the persistent-excitation requirement , a seed-robot driven finite-time shape localization protocol, and a behavior-based formation controller that scales to large swarms while improving observability of inter-robot localization. The main contributions are (i) PE-relaxing concurrent-learning localization, (ii) finite-time, seed-based shape localization without global coordinates, and (iii) a concise, four-command shape formation framework validated by simulations and outdoor experiments with up to six robots. The results enable robust, autonomous swarm formation in indoor and outdoor settings, reducing reliance on external localization systems and enabling practical deployment in GPS-denied scenarios.

Abstract

In this paper, we address the shape formation problem for massive robot swarms in environments where external localization systems are unavailable. Achieving this task effectively with solely onboard measurements is still scarcely explored and faces some practical challenges. To solve this challenging problem, we propose the following novel results. Firstly, to estimate the relative positions among neighboring robots, a concurrent-learning based estimator is proposed. It relaxes the persistent excitation condition required in the classical ones such as least-square estimator. Secondly, we introduce a finite-time agreement protocol to determine the shape location. This is achieved by estimating the relative position between each robot and a randomly assigned seed robot. The initial position of the seed one marks the shape location. Thirdly, based on the theoretical results of the relative localization, a novel behavior-based control strategy is devised. This strategy not only enables adaptive shape formation of large group of robots but also enhances the observability of inter-robot relative localization. Numerical simulation results are provided to verify the performance of our proposed strategy compared to the state-of-the-art ones. Additionally, outdoor experiments on real robots further demonstrate the practical effectiveness and robustness of our methods.
Paper Structure (43 sections, 9 theorems, 71 equations, 10 figures, 2 tables, 2 algorithms)

This paper contains 43 sections, 9 theorems, 71 equations, 10 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Distributed Shape Formation
  4. Relative Localization Estimation
  5. Local Measurement Based Shape Formation
  6. Preliminaries and System Overview
  7. Notions
  8. System Overview
  9. Adaptive Relative Localization
  10. Relative Localization Problem
  11. Data Collection Strategy
  12. Concurrent-Learning based Estimator
  13. Localization Enhancement Motion
  14. Behavior-Based Shape Formation
  15. Shape Definition and Parameterization
  16. ...and 28 more sections

Key Result

Theorem 1

Under Assumption A1, the estimation error $\tilde{p}_{ij,0}(t)$ is globally exponentially stable with the relative position estimator (Equ_observer). The convergence rate $\lambda_{ij}$ of $\tilde{p}_{ij,0}(t)$ can be calculated as

Figures (10)

  • Figure 1: Trajectories of a swarm of six robots forming an arrow shape in an external localization system denied environment. Each robot is equipped with an onboard light. This photo is obtained by long-exposure photography.
  • Figure 2: An illustration of the proposed shape formation strategy. A. Each robot in the swarms moves with the localization enhance control law and collects data to localize its neighboring robots. B. Each robot estimate the relative position to the initial position of the seed robot with the finite-time consensus method. C. Behavior-based localization enhance shape formation control scheme.
  • Figure 3: Geometric relationship between the displacements and distance measurements of the two robots. A. One sampling interval $\Delta t$ case. B. A sketch for $h$ sampling interval $\Delta t$ case
  • Figure 4: Comparision between the proposed relative localization method and the PE based one in Xie2019TCNS. A. Simulation results with the proposed method, from top to bottom are the trajectory, estimate error, tracking error and velocity norm of each robot. Here, tracking error and estimation error are defined as $e_{i}^{\mathrm{c}}(t) = \lVert {p}_{i}(t) - p_{0} - p_{i} \rVert$ and $e_{i}^{\mathrm{e}}(t) = \lVert \hat{p}_{i,0}(t) - p_{0} - p_{i} \rVert$, respectively. B. Simulation results with method in Xie2019TCNS.
  • Figure 5: Comparision between the proposed relative localization method and the PE based one in Xie2019TCNS with the sensor measurement noise. A. Simulation results with the proposed method, from top to bottom are the trajectory, estimate error, tracking error and velocity norm of each robot. B. Simulation results with method in Xie2019TCNS.
  • ...and 5 more figures

Theorems & Definitions (12)

  • Theorem 1
  • Remark 1
  • Theorem 2
  • Remark 2
  • Theorem 3
  • Remark 3
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • ...and 2 more