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In this article, we consider the problem of reachable set computation of a closed-loop system with anytime sensor and a neural network controller. We provide a star set data structure-based forward propagation algorithm that uses existing efficient operations on star-sets and a novel convex hull construction. We present rigorous analysis of the space-complexity of the star sets generated during the propagation. Our experimental results show significant improvement with respect to existing methods that use vertex-based representation of polyhedral sets for propagation through closed-loop systems with anytime sensing, as well as the feasibility of the approach on different types of dynamics, control and sensors. 

Urban Air Mobility (UAM) applications, such as air taxis, will rely heavily on perception for situational awareness and safe operation. With recent advances in AI/ML, state-of-the-art perception systems can provide the high-fidelity information necessary for UAM systems. However, due to size, weight, power, and cost (SWaP-C) constraints, the available computing resources of the on-board computing platform in such UAM systems are limited. Therefore, real-time processing of sophisticated perception algorithms, along with guidance, navigation, and control (GNC) functions in a UAM system, is challenging and requires the careful allocation of computing resources. Furthermore, the optimal allocation of computing resources may change over time depending on the speed of the vehicle, environmental complexities, and other factors. For instance, a fast-moving air vehicle at low altitude would need a low-latency perception system, as a long delay in perception can negatively affect safety. Conversely, a slowly landing air vehicle in a complex urban environment would prefer a highly accurate perception system, even if it takes a little longer. However, most perception and control systems are not designed to support such dynamic reconfigurations necessary to maximize performance and safety. We advocate for developing “anytime” perception and control capabilities that can dynamically reconfigure the capabilities of perception and GNC algorithms at runtime to enable safe and intelligent UAM applications. The anytime approach will efficiently allocate the limited computing resources in ways that maximize mission success and ensure safety. The anytime capability is also valuable in the context of distributed sensing, enabling the efficient sharing of perception information across multiple sensor modalities between the nodes.