A Graph Theoretic Approach to the Robustness of k-Nearest Neighbor Vehicle Platoons

TL;DR

This paper uses graph theory to analyze the stability and robustness of vehicle platoons communicating with their k-nearest neighbors, revealing trade-offs between delay tolerance and disturbance robustness.

Contribution

It introduces a graph-theoretic framework to quantify platoon robustness and stability, analyzing both first- and second-order vehicle dynamics.

Findings

Robustness to disturbances increases with higher nodal degrees.

Delay tolerance decreases as robustness to disturbances improves.

Theoretical results are validated through simulations.

Abstract

We consider a graph theoretic approach to the performance and robustness of a platoon of vehicles, where each vehicle communicates with its $k$-nearest neighbors. In particular, we quantify the platoon's stability margin, robustness to disturbances (in terms of system $\mathcal{H}_{\infty}$ norm), and maximum delay tolerance via graph-theoretic notions such as nodal degrees and (grounded) Laplacian matrix eigenvalues. Our results show that there is a trade-off between robustness to time delay and robustness to disturbances. Both first-order dynamics (reference velocity tracking) and second-order dynamics (controlling inter-vehicular distance) are analyzed in this direction. Theoretical contributions are confirmed via simulation results.