# Physics-Based Freely Scalable Continuum Deformation for UAS Traffic Coordination

## TL;DR

This paper introduces a physics-inspired continuum deformation method for UAS traffic management, extending 1-D traffic models to 2-D airspace, with boundary control and vehicle clustering for resilient coordination.

## Contribution

It presents a novel higher-dimensional traffic coordination framework for UAS, incorporating boundary control, resilience to failures, and vehicle clustering techniques.

## Key findings

- Effective boundary control algorithm enhances resilience.
- Model successfully extends to 2-D airspace without predefined paths.
- Clustering improves microscopic coordination of UAS.

## Abstract

This paper develops a novel physics-inspired traffic coordination approach and applies it to Unmanned Aircraft System (UAS) traffic management. We extend available physics-inspired approaches previously applied to 1-D traffic flow on highways and urban streets to support models of traffic coordination in higher dimension airspace for cases where no predefined paths exist. The paper considers airspace as a finite control volume while UAS coordination, treated as continuum deformation, is controlled at the airspace boundaries. By partitioning airspace into planned and unplanned spaces, the paper models nominal coordination in the planned airspace as the solution of a partial differential equation with spatiotemporal parameters. This paper also improves resilience to vehicle failures with a resilient boundary control algorithm to update the geometry of the planned space when UAS problems threaten safe coordination in existing navigable airspace channels. To support UAS coordination at the microscopic level, we propose clustering vehicles based on vehicle performance limits. UAS clusters, with each UAS treated as a particle of a virtual rigid body, use leader-follower containment to acquire the macroscopic desired trajectory.