This project will develop mathematical foundations to safely and efficiently coordinate the Unmanned Aircraft Systems (UAS) traffic envisioned to routinely fly above urban centers. Per emerging UAS Traffic Management (UTM) standards, a dedicated transit airspace layer will assure UAS are separated from manned aircraft traffic allowing UAS to focus on coordinating with each other. The project is for a two-layer physics-based approach to route UAS as coordinated flow through high-density airspace transit channels. At the top "macroscopic" coordination layer, UAS will be assigned to traffic channels based on their destinations and physical ability to coordinate flight paths with each other. At the "microscopic" coordination layer, the existing continuum deformation cooperative control strategy will be extended to allow large-scale UAS groups to efficiently follow routes that respect airspace channel geometries backed by mathematical guarantees of collision avoidance. The project also defines an interface between macroscopic and microscopic layers to deal with unpredicted events and UAS failure in a resilient fashion. The theoretical achievements of the project will be supported by large-scale simulations and flight experiments. The project offers a physics-inspired traffic coordination approach for Unmanned Aircraft System (UAS) traffic management. The available physics-inspired approaches previously applied to highway traffic flow will be extended for low-altitude UAS traffic coordination in which no predefined paths exist. Airspace is considered a finite control volume in which coordinated UAS treated as a continuum deformation organize traffic flow within airspace channels prescribed by higher-level macroscopic coordination. Eulerian continuum mechanics efficiently defines macroscopic coordination as the solution of a parabolic partial differential equation (PDE) with spatiotemporal parameters. It is assumed vehicles operating in the planned airspace admit the nominal coordination, while unplanned airspace envelops no-fly zones and non-cooperative UAS. At the microscopic level, clustering vehicles is suggested based on vehicle performance limits. UAS clusters, with each UAS treated as a particle of a deformable body, use generalized leader-follower continuum deformation coordination to acquire the desired macroscopic coordination by local communication. This advances the existing theory by relaxing constraints on inter-agent communication topology and leaders' locations. The project's approach offers resilience to vehicle failures and rapid changes in airspace availability by formal safety analysis. Specifically, an adaptive boundary control algorithm will be developed to remove a non-cooperative or failed UAS from safely-coordinated channels in planned airspace. Large-scale simulations and flight tests will be used to refine models and validate coordination concepts. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.