Advances in sensing, artificial intelligence, computation and communication are enabling the deployment of large networks of autonomous systems, such as drones, ground robots, and other mobile agents, across diverse applications including search and rescue, environmental monitoring, precision agriculture, and transportation. The research funded by this grant aims to create new mathematical tools and algorithms that allow large groups of autonomous agents to operate safely, efficiently, and collaboratively, even under physical constraints, communication limitations, and local decision-making. The central idea of this research is to model large groups of autonomous agents not individually, but as evolving spatial distributions like densities or concentrations over a region. This macroscopic perspective looks to enable the design of scalable, tractable algorithms that guide the collective behavior of many agents, while still accounting for each agent’s physical limitations, local interactions, asynchronous timing, and safety constraints. By linking these global objectives with local decision-making through new optimization techniques, the project seeks to create algorithms that are both theoretically grounded and practically applicable. The research will be complemented by educational and outreach activities that include the development of new curriculum for undergraduate and graduate education, research experiences for students through high-fidelity simulations, and opportunit