Modern drones and robots are increasingly being used as intelligent agents in critical real-world tasks such as search and rescue operations, environmental monitoring, and disaster response. These agents often need to work together in fast-changing and uncertain environments. However, current systems often struggle with planning efficient air or ground paths and making safe, real-time decisions. This project addresses this challenge by developing a new framework called AERIAL (AI-Embedded Responsive Intelligent Agents with Trajectory-Induced Digital Twin Learning). AERIAL will enable drones and robots to collaborate intelligently by combining advanced mathematics with artificial intelligence. It also leverages a virtual simulation of the real world (a digital twin) to help the agents plan and adapt their paths as situations evolve. This project aims to improve the safety, speed, and efficiency of drone missions that support public safety and national resilience. The project also includes hands-on educational opportunities for both college and high school students. To achieve these goals, the research introduces a new AI-driven mathematical model called the "trajectory-induced graph," which captures how drone flight paths and communication networks evolve over time. These graphs support a new class of AI tools powered by graph neural networks, enabling drones to interpret and respond to their environment effectively. The project centers on two main thrusts: (1) developing the mathematical foundations for trajectory-induced graphs, (2) applying them to real-time missions using novel machine learning and reinforcement learning methods. In addition, the system will be optimized so that low-cost drones with limited battery life and computing power can operate efficiently. The approach will be deployed and validated through real-world scenarios, including drone-based search and rescue missions. The outcomes will advance fundamental areas of cyber-physical systems, including autonomy, machine learning, control, real-time systems, and networking. 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.