Modeling

Microscopic LAAT Model

Our exploration of a cutting-edge model is designed to understand and navigate the complexities of air mobility. Our LAAT microscopic model is formulated to capture the essence of aircraft dynamics, routes, and collision avoidance. Visualize our microscopic LAAT model through this simplified representation:

Understanding LAAT Dynamics

In our model, we break down the LAAT dynamics into three main components:

We define the behavior of each aircraft using its position and velocity, controlled by velocity command. Maximum velocity and acceleration bounds are set to ensure safe operation.

The aircraft's journey is determined by a predefined route, from an origin point to a destination point. The original route is typically a direct line, but variations can be introduced based on specific needs.

Safety is paramount. Our model incorporates collision avoidance algorithms to ensure that aircraft can navigate around obstacles and, importantly, avoid collisions with other aircraft. Various proven algorithms contribute to this critical aspect of our model.

Microscopic LAAT Model with Waypoints

Our model extends to incorporate waypoints, offering a modified collision-avoidance strategy. A cooperative distributed control algorithm ensures conflict-free flight while guaranteeing convergence to desired waypoints.

Decentralized Control Strategies

To coordinate the movements of LAAT aircraft efficiently, we employ decentralized control strategies. These strategies focus on waypoint following and inter-agent collision avoidance, ensuring a harmonious flow of traffic.

Key Features:

Macroscopic Fundamental Diagram for LAAT Networks

Our exploration of deriving a Macroscopic Fundamental Diagram (MFD) for LAAT networks. We build upon the microscopic traffic flow model discussed earlier and present the approach to constructing an MFD for LAAT networks.

Generalizing Vehicular Traffic Theory to Aircraft Traffic Flow

We extend the concepts of vehicular traffic flow theory to aircraft traffic flow by adapting spatial dimensions. Similar to pedestrian flows, the principles of vehicular traffic are applied to two- or three-dimensional aircraft traffic flows.

In our approach, the airspace is divided into vertical latitudes and regions, as described in Haddad et al. 2021. The MFD shape can be determined per region or for the entire network, estimating essential macroscopic traffic flow variables.

Macroscopic Variables and Calculations

The key macroscopic traffic flow variables include flow, density, speed, outflow, and accumulation. These variables are calculated based on the general movement characteristics of aircraft in the network.

Summary

Our model offers a comprehensive framework that facilitates the understanding and management of air traffic. It provides valuable insights into the dynamics of individual aircraft, as well as ensuring safe interactions between multiple aircraft. We have discovered the Macroscopic Fundamental Diagrams (MFDs) for LAAT systems, which reveal the traffic dynamics of these low-altitude aircraft. Our innovative modeling framework combines microscopic and macroscopic levels, resulting in a real-time simulation of large-scale LAAT operations. By doing so, we aim to identify airspace conditions, detect congestion, and pioneer control strategies. As we strive to shape the future of urban mobility, airspace management, and cutting-edge control solutions, we invite you to explore our project and discover the next frontier in urban air transportation. 

For a more detailed understanding and discussion, we recommend exploring the original paper by Safadi et al. 2023.