Abstract Cyber-physical systems (CPS) with reinforcement learning (RL)-based controllers are increasingly being deployed in complex physical environments such as autonomous vehicles, the Internet-of-Things (IoT), and smart cities. An important property of a CPS is tolerance; i.e., its ability to function safely under possible disturbances and uncertainties in the actual operation. In this paper, we introduce a new, expressive notion of tolerance that describes how well a controller is capable of satisfying a desired system requirement, specified using Signal Temporal Logic (STL), under possible deviations in the system. Based on this definition, we propose a novel analysis problem, called the tolerance falsification problem, which involves finding small deviations that result in a violation of the given requirement. We present a novel, two-layer simulation-based analysis framework and a novel search heuristic for finding small tolerance violations. To evaluate our approach, we construct a set of benchmark problems where system parameters can be configured to represent different types of uncertainties and disturbances in the system. Our evaluation shows that our falsification approach and heuristic can effectively find small tolerance violations.

This paper presents the design and control of a novel quadrotor with a variable geometry to physically interact with cluttered environments and fly through narrow gaps and passageways. This compliant quadrotor with passive morphing capabilities is designed using torsional springs at every arm hinge to allow for rotation driven by external forces. We derive the dynamic model of this variable geometry quadrotor (SQUEEZE), and develop an adaptive controller for trajectory tracking. The corresponding Lyapunov stability proof of attitude tracking is also presented. Further, an admittance controller is designed to account for changes in yaw due to physical interactions with the environment. Finally, the proposed design is validated in flight tests with two setups: a small gap and a passageway. The experimental results demonstrate the unique capability of the SQUEEZE in navigating through constrained narrow spaces.