Stability Conditions for Coupled Autonomous Vehicles Formations

Abstract

In this article, we give necessary conditions for the stability of coupled autonomous vehicles in $\mathbb {R}$ . We focus on linear arrays with decentralized vehicles, where each vehicle interacts with only a few of its neighbors. We obtain explicit expressions for necessary conditions for stability in the cases where a system consists of a periodic arrangement of two or three different types of vehicles, i.e., configurations as follows:... 2-1-2-1 or... 3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single vehicle type (...1-1-1) held that the first moment of certain coefficients of the interactions between vehicles has to be zero. Here, we show that this does not generalize. Instead, the condition (necessary) in the cases considered is that the first moment plus a nonlinear correction term must be zero.