This paper studies how global dynamics can inform path planning and decision-making for robots. Specifically, we investigate how coherent sets, an environmental feature found in flow-like environments, informs robot awareness within these scenarios. We compute coherent sets online with techniques from machine learning, and design a framework for robot behavior that uses coherent sets. We demonstrate the effectiveness of online methods over offline methods. Notably, we apply these online methods for robot monitoring of urban environments and robot navigation through water. Environmental features such as coherent sets provide rich context to robots for smarter, more efficient behavior.