Decentralized Biconnectivity Conditions in Multi-robot Systems

TL;DR

This paper introduces a decentralized method to ensure biconnectivity in multi-robot networks, enhancing robustness against single-robot failures by relating network conditions to the third smallest Laplacian eigenvalue.

Contribution

It provides a novel decentralized approach with sufficient conditions for biconnectivity based on spectral properties of the Laplacian matrix.

Findings

Conditions related to the third smallest Laplacian eigenvalue ensure biconnectivity.

The approach is decentralized, relying on neighbor-to-neighbor data exchange.

Proven robustness against single-robot failures in network connectivity.

Abstract

The network connectivity in a group of cooperative robots can be easily broken if one of them loses its connectivity with the rest of the group. In case of having robustness with respect to one-robot-fail, the communication network is termed biconnected. In simple words, to have a biconnected network graph, we need to prove that there exists no articulation point. We propose a decentralized approach that provides sufficient conditions for biconnectivity of the network, and we prove that these conditions are related to the third smallest eigenvalue of the Laplacian matrix. Data exchange among the robots is supposed to be neighbor-to-neighbor.