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Maintaining Strong r-Robustness in Reconfigurable Multi-Robot Networks using Control Barrier Functions

Haejoon Lee, Dimitra Panagou

TL;DR

This work tackles resilient leader-follower consensus under misbehaving agents by removing the need for fixed, topology-based robustness guarantees. It introduces a hierarchical Control Barrier Function (CBF) framework built from high-order CBFs (HOCBFs) and Bootstrap Percolation to directly enforce strong $r$-robustness in reconfigurable multi-robot networks, while keeping deviations from the desired control small. The authors derive a continuous, differentiable representation of activation states, compose multiple HOCBFs into a single CBF, and prove the resulting CBF's validity and robustness-maintenance properties. The approach is validated through comprehensive simulations and hardware experiments, including obstacle-rich environments, demonstrating practical resilience and improved convergence times relative to fixed-topology baselines.

Abstract

In leader-follower consensus, strong r-robustness of the communication graph provides a sufficient condition for followers to achieve consensus in the presence of misbehaving agents. Previous studies have assumed that robots can form and/or switch between predetermined network topologies with known robustness properties. However, robots with distance-based communication models may not be able to achieve these topologies while moving through spatially constrained environments, such as narrow corridors, to complete their objectives. This paper introduces a Control Barrier Function (CBF) that ensures robots maintain strong r-robustness of their communication graph above a certain threshold without maintaining any fixed topologies. Our CBF directly addresses robustness, allowing robots to have flexible reconfigurable network structure while navigating to achieve their objectives. The efficacy of our method is tested through various simulation and hardware experiments.

Maintaining Strong r-Robustness in Reconfigurable Multi-Robot Networks using Control Barrier Functions

TL;DR

This work tackles resilient leader-follower consensus under misbehaving agents by removing the need for fixed, topology-based robustness guarantees. It introduces a hierarchical Control Barrier Function (CBF) framework built from high-order CBFs (HOCBFs) and Bootstrap Percolation to directly enforce strong -robustness in reconfigurable multi-robot networks, while keeping deviations from the desired control small. The authors derive a continuous, differentiable representation of activation states, compose multiple HOCBFs into a single CBF, and prove the resulting CBF's validity and robustness-maintenance properties. The approach is validated through comprehensive simulations and hardware experiments, including obstacle-rich environments, demonstrating practical resilience and improved convergence times relative to fixed-topology baselines.

Abstract

In leader-follower consensus, strong r-robustness of the communication graph provides a sufficient condition for followers to achieve consensus in the presence of misbehaving agents. Previous studies have assumed that robots can form and/or switch between predetermined network topologies with known robustness properties. However, robots with distance-based communication models may not be able to achieve these topologies while moving through spatially constrained environments, such as narrow corridors, to complete their objectives. This paper introduces a Control Barrier Function (CBF) that ensures robots maintain strong r-robustness of their communication graph above a certain threshold without maintaining any fixed topologies. Our CBF directly addresses robustness, allowing robots to have flexible reconfigurable network structure while navigating to achieve their objectives. The efficacy of our method is tested through various simulation and hardware experiments.
Paper Structure (17 sections, 8 theorems, 30 equations, 3 figures, 1 table)

This paper contains 17 sections, 8 theorems, 30 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Notation
  3. Preliminaries and Problem Statement
  4. System Dynamics
  5. Fundamentals of Strong $r$-robustness and W-MSR
  6. Problem Statement
  7. High-Order Control Barrier Function
  8. Bootstrap Percolation
  9. HOCBFs for Strong $r$-Robustness
  10. Continuous Representation of the Activation States
  11. HOCBF for Robustness Maintenance
  12. CBF Composition
  13. Composition of Multiple HOCBFs
  14. Experimental Results
  15. Simulation
  16. ...and 2 more sections

Key Result

Theorem 1

Given the HOCBF $h$ and its safety set $\mathcal{C}$, if $x(t_0)\in \mathcal{C}$, any Lipschitz continuous controller $\mathbf u(\mathbf x) \in K_{\text{hocbf}}(\mathbf x)=\{\mathbf u\in U\mid \psi_{d}(\mathbf x)\geq0\}$ renders $\mathcal{C}$ forward invariant for system eq:combined_dynamicsxiao2022

Figures (3)

  • Figure 1: (a) and (b) display the evolutions of robots' trajectories in their LED colors and $h_{5}(\mathbf x)$\ref{['eq:all_h']} from the first simulation, respectively.
  • Figure 2: (a) and (b) show the snapshots of the simulations with our controller and dynamics \ref{['eq:combined_dynamics']} in Env. 1 and 2, respectively.
  • Figure 3: (a) and (b) show the evolutions of robots' consensus values for the simulations visualized in Fig. \ref{['fig:env']} (a) and (b), respectively.

Theorems & Definitions (19)

  • Definition 1: malicious agent
  • Definition 2: $\mathbf F$-local
  • Definition 3: $\mathbf r$-reachable LeBlanc13
  • Definition 4: strongly $\mathbf r$-robust mitra2019
  • Definition 5: HOCBF xiao2022
  • Theorem 1
  • Lemma 1
  • Corollary 1
  • Lemma 2
  • proof
  • ...and 9 more