Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fast Biconnectivity Restoration in Multi-Robot Systems for Robust Communication Maintenance

Md Ishat-E-Rabban, Guangyao Shi, Pratap Tokekar

TL;DR

From a connected initial network $G(X_0)$ of $n$ robots, the paper addresses Fast Biconnectivity Restoration by restoring to a $2$-connected topology $G(X^*)$ while minimizing the maximum movement $\max_i \|x_i^* - x_i\|$. It couples an exact Quadratically Constrained Program (OPT) with practical two-phase approximations: Graph Topology Optimization (GTO) to select augmentation edges and Movement Minimization (MM) to realize them, via algorithms EA-SCR and EA-OPT, with a QCP MM alternative. The authors introduce a BC-Tree–based augmentation strategy (EA) using MBSA to guarantee a $2$-connected augmentation, and SCR for cascaded relocations to preserve existing edges while achieving the augmented topology. Empirical results show EA-SCR/EA-OPT outperform baseline methods in minmax distance and that OPT provides a higher-fidelity solution at the cost of scalability, demonstrated on synthetic datasets and a persistent monitoring case study. Collectively, the work advances robust, fast restoration of communication in multi-robot teams, balancing optimality, computational efficiency, and practical applicability.

Abstract

Maintaining a robust communication network plays an important role in the success of a multi-robot team jointly performing an optimization task. A key characteristic of a robust multi-robot system is the ability to repair the communication topology itself in the case of robot failure. In this paper, we focus on the Fast Biconnectivity Restoration (FBR) problem, which aims to repair a connected network to make it biconnected as fast as possible, where a biconnected network is a communication topology that cannot be disconnected by removing one node. We develop a Quadratically Constrained Program (QCP) formulation of the FBR problem, which provides a way to optimally solve the problem. We also propose an approximation algorithm for the FBR problem based on graph theory. By conducting empirical studies, we demonstrate that our proposed approximation algorithm performs close to the optimal while significantly outperforming the existing solutions.

Fast Biconnectivity Restoration in Multi-Robot Systems for Robust Communication Maintenance

TL;DR

From a connected initial network of robots, the paper addresses Fast Biconnectivity Restoration by restoring to a -connected topology while minimizing the maximum movement . It couples an exact Quadratically Constrained Program (OPT) with practical two-phase approximations: Graph Topology Optimization (GTO) to select augmentation edges and Movement Minimization (MM) to realize them, via algorithms EA-SCR and EA-OPT, with a QCP MM alternative. The authors introduce a BC-Tree–based augmentation strategy (EA) using MBSA to guarantee a -connected augmentation, and SCR for cascaded relocations to preserve existing edges while achieving the augmented topology. Empirical results show EA-SCR/EA-OPT outperform baseline methods in minmax distance and that OPT provides a higher-fidelity solution at the cost of scalability, demonstrated on synthetic datasets and a persistent monitoring case study. Collectively, the work advances robust, fast restoration of communication in multi-robot teams, balancing optimality, computational efficiency, and practical applicability.

Abstract

Maintaining a robust communication network plays an important role in the success of a multi-robot team jointly performing an optimization task. A key characteristic of a robust multi-robot system is the ability to repair the communication topology itself in the case of robot failure. In this paper, we focus on the Fast Biconnectivity Restoration (FBR) problem, which aims to repair a connected network to make it biconnected as fast as possible, where a biconnected network is a communication topology that cannot be disconnected by removing one node. We develop a Quadratically Constrained Program (QCP) formulation of the FBR problem, which provides a way to optimally solve the problem. We also propose an approximation algorithm for the FBR problem based on graph theory. By conducting empirical studies, we demonstrate that our proposed approximation algorithm performs close to the optimal while significantly outperforming the existing solutions.

Paper Structure

This paper contains 16 sections, 1 theorem, 9 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. Heuristic Algorithms
  5. Graph Topology Optimization
  6. Block-Cut Tree
  7. Edge Augmentation Algorithm
  8. Movement Minimization
  9. Sequential Cascaded Relocation Algorithm
  10. QCP-based Formulation for MM
  11. Experiments
  12. Experimental Setup
  13. A Qualitative Example
  14. Empirical Results
  15. Case Study: Persistent Monitoring
  16. ...and 1 more sections

Key Result

Theorem 1

The augmentation set returned by Algorithm algorithm:biconnectivity_augmentation biconnects $G(X)$.

Figures (8)

  • Figure 1: (a) Solid lines show the communication network induced by the communication radius, $h$. Dashed lines show the edges to be augmented according to the GTO problem. (b) Hollow and solid circles refer to previous and new positions of the robots, respectively, according to the MM problem.
  • Figure 2: (a) Dotted ovals show the blocks. (b) The corresponding BC-Tree. Hollow squares and circles show blocks and cut vertices respectively.
  • Figure 3: (a) A barely connected graph created by removing vertex 12 from a biconnected graph. Dotted ovals show the blocks. (b), (c), and (d) show the outputs of the EA-SCR, BT, and CR algorithms respectively. The corresponding minmax distances are 0.1m, 0.3m, and 0.71m respectively.
  • Figure 4: Comparison with OPT algorithm using $n=8$ robots.
  • Figure 5: Comparison of minmax distance.
  • ...and 3 more figures

Theorems & Definitions (1)

  • Theorem 1