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Sense-react systems (e.g. robotics and AR/VR) have to take highly responsive real-time actions, driven by complex decisions involving a pipeline of sensing, perception, planning, and reaction tasks. These tasks must be scheduled on resource-constrained devices such that the performance goals and the requirements of the application are met. This is a difficult scheduling problem that requires handling multiple scheduling dimensions, and variations in resource usage and availability. In practice, system designers manually tune parameters for their specific hardware and application, which results in poor generalization and increases the development burden. In this work, we highlight the emerging need for scheduling CPU resources at runtime in sense-react systems. We study three canonical applications (face tracking, robot navigation, and VR) to first understand the key scheduling requirements for such systems. Armed with this understanding, we develop a scheduling framework, Catan, that dynamically schedules compute resources across different components of an app so as to meet the specified application requirements. Through experiments with a prototype implemented on a widely-used robotics framework (ROS) and an open-source AR/VR platform, we show the impact of system scheduling on meeting the performance goals for the three applications, how Catan is able to achieve better application performance than hand-tuned configurations, and how it dynamically adapts to runtime variations.