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The paper introduces EigenSafe, a novel operator-theoretic framework for learning-enabled safety-critical control of stochastic systems by deriving a linear operator governing the dynamic programming principle for safety probability. EigenSafe addresses the limitations of conventional methods like Hamilton-Jacobi reachability and control barrier functions in providing a holistic measure of safety for stochastic robotic systems. They demonstrate that jointly learning the dominant eigenpair of this operator and a safe backup policy offline allows for the construction of a safety filter that detects potentially unsafe situations and reverts to the backup policy, validated across three simulated tasks.
Escape stochastic robotic systems' safety limitations with EigenSafe, a spectral method that learns a safety filter from the dominant eigenpair of a dynamic programming operator.
We present EigenSafe, an operator-theoretic framework for learning-enabled safety-critical control for stochastic systems. In many robotic systems where dynamics are best modeled as stochastic systems due to factors such as sensing noise and environmental disturbances, it is challenging for conventional methods such as Hamilton-Jacobi reachability and control barrier functions to provide a holistic measure of safety. We derive a linear operator governing the dynamic programming principle for safety probability, and find that its dominant eigenpair provides information about safety for both individual states and the overall closed-loop system. The proposed learning framework, called EigenSafe, jointly learns this dominant eigenpair and a safe backup policy in an offline manner. The learned eigenfunction is then used to construct a safety filter that detects potentially unsafe situations and falls back to the backup policy. The framework is validated in three simulated stochastic safety-critical control tasks.
BAIR