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Fast k-connectivity Restoration in Multi-Robot Systems for Robust Communication Maintenance

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

TL;DR

The paper addresses maintaining robust communication in multi-robot systems by restoring network $k$-connectivity while minimizing individual robot movement. It introduces a Quadratically Constrained Program (QCP) formulation for optimal FCR and a scalable two-phase algorithm, EA-SCR, that decomposes the problem into Graph Topology Optimization and Movement Minimization. Empirical results show EA-SCR achieves solutions within about 10% of the optimal and offers roughly 30% improvements in the minmax movement metric over existing methods, with successful hardware validation on six drones. The work enables scalable, robust communication maintenance for larger robot teams and suggests future directions for obstacle-aware and distributed FCR extensions.

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 cooperative multi-robot system is the ability to repair the communication topology in the case of robot failure. In this paper, we focus on the Fast k-connectivity Restoration (FCR) problem, which aims to repair a network to make it k-connected with minimum robot movement. We develop a Quadratically Constrained Program (QCP) formulation of the FCR problem, which provides a way to optimally solve the problem, but cannot handle large instances due to high computational overhead. We therefore present a scalable algorithm, called EA-SCR, for the FCR problem using graph theoretic concepts. By conducting empirical studies, we demonstrate that the EA-SCR algorithm performs within 10 percent of the optimal while being orders of magnitude faster. We also show that EA-SCR outperforms existing solutions by 30 percent in terms of the FCR distance metric.

Fast k-connectivity Restoration in Multi-Robot Systems for Robust Communication Maintenance

TL;DR

The paper addresses maintaining robust communication in multi-robot systems by restoring network -connectivity while minimizing individual robot movement. It introduces a Quadratically Constrained Program (QCP) formulation for optimal FCR and a scalable two-phase algorithm, EA-SCR, that decomposes the problem into Graph Topology Optimization and Movement Minimization. Empirical results show EA-SCR achieves solutions within about 10% of the optimal and offers roughly 30% improvements in the minmax movement metric over existing methods, with successful hardware validation on six drones. The work enables scalable, robust communication maintenance for larger robot teams and suggests future directions for obstacle-aware and distributed FCR extensions.

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 cooperative multi-robot system is the ability to repair the communication topology in the case of robot failure. In this paper, we focus on the Fast k-connectivity Restoration (FCR) problem, which aims to repair a network to make it k-connected with minimum robot movement. We develop a Quadratically Constrained Program (QCP) formulation of the FCR problem, which provides a way to optimally solve the problem, but cannot handle large instances due to high computational overhead. We therefore present a scalable algorithm, called EA-SCR, for the FCR problem using graph theoretic concepts. By conducting empirical studies, we demonstrate that the EA-SCR algorithm performs within 10 percent of the optimal while being orders of magnitude faster. We also show that EA-SCR outperforms existing solutions by 30 percent in terms of the FCR distance metric.
Paper Structure (14 sections, 8 equations, 6 figures, 3 algorithms)

This paper contains 14 sections, 8 equations, 6 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Formulation
  4. QCP Formulation
  5. Scalable Algorithm: EA-SCR
  6. Graph Topology Optimization
  7. Edge Augmentation Algorithm
  8. Movement Minimization
  9. Sequential Cascaded Relocation Algorithm
  10. Experiments
  11. Experimental Setup
  12. Empirical Results
  13. Hardware Experiments
  14. Conclusion

Figures (6)

  • Figure 1: (a) Initial 1-connected configuration. (b) Robot positions for $k=2$. (c) Robot positions for $k=3$. Dashed gray arrows show robot movements from initial positions.
  • Figure 2: Before (a) and after (b) connecting edge (1,2). First, $r_1$ moves towards $r_2$ by distance $\frac{d}{2}$, where $d=\left\lVert x_1 - x_2\right\rVert-h$. This movement disconnects edge (1,4), hence $r_4$ moves minimally towards $r_1$ to reconnect the edge. Subsequently edge (4,5) gets disconnected and $r_5$ moves minimally towards $r_4$ to reconnect the edge. Finally, $r_2$ moves towards $r_1$ by distance $\frac{d}{2}$ connecting (1,2). This disconnects edge (2,6), hence $r_6$ moves towards $r_2$ to reconnect the edge. Gray arrows in (b) show robot movements.
  • Figure 3: Comparison with OPT algorithm using $n=8$ and $k=2$.
  • Figure 4: Comparison of EA-SCR, NB, and BT algorithms for $k=2$ in terms of (a) minmax distance, (b) total distance, and (c) running time.
  • Figure 5: Comparison of EA-SCR and NB algorithms. (a) $k=3$. metric: minmax distance. (b) $k=3$. metric: running time. (c) $k=4$. metric: minmax distance. (d) $k=4$. metric: running time.
  • ...and 1 more figures