# Stability Conditions for Coupled Autonomous Vehicles Formations

## TL;DR

This paper derives necessary stability conditions for linear arrays of coupled autonomous vehicles with mixed types, revealing that previous conditions do not generalize and introducing a nonlinear correction term.

## Contribution

It provides explicit necessary stability conditions for mixed vehicle configurations, extending prior results to more complex arrangements with nonlinear corrections.

## Key findings

- Necessary conditions involve a nonlinear correction term.
- Previous zero-moment condition does not generalize to mixed types.
- Explicit expressions for stability conditions in specific configurations.

## Abstract

In this paper, we give necessary conditions for stability of coupled autonomous vehicles in 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 that 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 that does not generalize. Instead, the (necessary) condition in the cases considered is that the first moment plus a nonlinear correction term must be zero.