3D traffic flow model for UAVs

TL;DR

This paper introduces a novel 3D traffic flow model for UAVs that replaces lane-based notions with a density and capacity framework, enabling analysis of formation and stability in aerial traffic.

Contribution

The paper presents the Scalar Capacity Model (SCM), a new 3D traffic flow model for UAVs that captures passing and blocking regimes without relying on lanes.

Findings

Model exhibits linear local and string stability.

Numerical simulations show evidence of non-linear stability.

Analytically solvable in certain regimes.

Abstract

In this work, we introduce a microscopic traffic flow model called Scalar Capacity Model (SCM) which can be used to study the formation of traffic on an airway link for autonomous Unmanned Aerial Vehicles (UAV) as well as for the ground vehicles on the road. Given the 3D nature of UAV flights, the main novelty in our model is to eliminate the commonly used notion of lanes and replace it with a notion of density and capacity of flow, but in such a way that individual vehicle motions can still be modeled. We name this a Density/Capacity View (DCV) of the link capacity and how vehicles utilize it versus the traditional One/Multi-Lane View (OMV). An interesting feature of this model is exhibiting both passing and blocking regimes (analogous to multi-lane or single-lane) depending on the set scalar parameter for capacity. We show the model has linear local (platoon) and string stability. Also, we perform numerical simulations and show evidence for non-linear stability. Our traffic flow model is represented by a nonlinear differential equation which we transform into a linear form. This makes our model analytically solvable in the blocking regime and piece-wise analytically solvable in the passing regime.