Uncrewed aerial vehicles (UAVs) are equipped with high-resolution cameras and a variety of sensors that can be used in different applications such as agriculture, environmental monitoring, disaster response, or infrastructure inspection. UAVs offer an excellent level of precision and adaptability, can be deployed easily, and provide access to remote regions. UAV-based sensing is a crucial asset in challenged settings, for example in remote regions with limited connectivity, during extreme events, and other similar situations. An optimized UAV trajectory ensures that data is collected in the most efficient and timely manner, from the most relevant locations, and at the most opportune times. This allows for real-time monitoring and quick response to dynamic environments or events of interest. This project develops the general mathematical framework that is needed to optimize UAV trajectories while incorporating practical operational constraints. To address the challenging problem of optimal UAV trajectory and deployment, various research communities have identified different objectives. For example, the communication community has focused on optimizing UAV trajectories to improve network capacity or data collection efficiency, often overlooking the UAV dynamics or the domain constraints. On the other hand, work from robotics and control communities tends to emphasize domain and maneuverability constraints with a focus on system dynamics. This project aims to develop a genera