Fast k-connectivity Restoration in Multi-Robot Systems for Robust Communication Maintenance (2404.03834v1)

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.

• The paper presents methods for Fast k-connectivity Restoration (FCR) in multi-robot systems to maintain robust communication networks after node failures with minimal robot movement.
• A scalable Edge Augmentation-Sequential Cascaded Relocation (EA-SCR) algorithm is introduced, featuring Graph Topology Optimization and Movement Minimization phases to efficiently restore connectivity.
• Empirical results show the EA-SCR algorithm is orders of magnitude faster than optimal solutions, performing within 10% of optimality and outperforming existing methods by approximately 30% in minimizing maximum robot movement.

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

The paper presents a notable contribution to the field of multi-robot systems by introducing solutions to the problem of Fast $k$-connectivity Restoration (FCR). This problem is critical for maintaining a robust communication network among a team of robots, particularly after the failure of some nodes. Within this context, a network is considered $k$-connected if it remains connected despite the removal of any $k-1$ nodes. The authors' primary objective is to restore such a connectivity level with minimal robot movement, ensuring that the overall communication topology is robust against failures.

Methodology

The authors propose two approaches to solve the FCR problem:

1. Quadratically Constrained Program (QCP) Formulation: The QCP formulation is aimed at providing an optimal solution leveraging multi-commodity flow concepts from network theory. Although this method can solve the problem optimally, it is computationally expensive and thus practical only for smaller networks. The formulation involves constructing binary variables to determine edge connectivity and ensuring that the movements maintain the $k$-connectivity requirement with minimal displacement.
2. Scalable EA-SCR Algorithm: To address the limitation regarding scalability in the QCP method, they introduce the EA-SCR (Edge Augmentation-Sequential Cascaded Relocation) algorithm. This heuristic approach offers a two-phase solution:
   • Graph Topology Optimization (GTO): The Edge Augmentation (EA) algorithm identifies additional edges required to achieve $k$-connectivity and ensures that these augmentations minimize robot movement.
   • Movement Minimization (MM): The Sequential Cascaded Relocation (SCR) component finds the minimal movement path for robots while establishing these new connections, ensuring no existing connections are lost.

Results

Empirical evaluation of the EA-SCR algorithm demonstrates that it performs within 10% of the optimal solutions provided by the QCP method in terms of minimizing the maximum robot movement, which is quantified as the "minmax distance.” Notably, the EA-SCR algorithm proves to be orders of magnitude faster, making it viable for larger network sizes. Furthermore, the algorithm outperforms existing solutions by approximately 30% concerning this key performance metric.

Implications and Future Directions

The proposed methods have significant implications for the deployment of multi-robot systems, especially in scenarios requiring robust communication under varying topology constraints, such as exploration or patrolling tasks in adversarial environments. While the QCP formulation provides a theoretical benchmark, the EA-SCR algorithm offers a practical solution capable of real-time applications due to its scalability.

Future work could explore extensions for environments with obstacles, which the current models assume away. Furthermore, developing distributed algorithms based on the presented concepts could greatly enhance the adaptability and resilience of robot teams in decentralized settings. The paper's methods could also be evaluated for applications beyond robotic communication maintenance, particularly in networks requiring similar robustness under constrained mobility. Overall, these contributions anchor promising advancements in the pragmatic deployment of resilient multi-robot networks.