Probabilistic Rare-Event Verification for Temporal Logic Robot Tasks

We present a method for calculating the probability that a robot successfully performs a task described using Signal Temporal Logic (STL). We focus on cases where the failure probability is very small, hence a traditional Monte-Carlo method becomes inefficient due to the large number of samples required to observe failures. Using elliptical sliced sampling, normalizing flows, and Bayesian optimization, we develop an algorithm that, under mild assumptions, is applicable to black-box systems, and can be applied to uncertainty sources with non-Gaussian probabilities. We demonstrate the application of our method on three different simulated robots.