  Providing guarantees on the safe operation of robots against edge cases is
challenging as testing methods such as traditional Monte-Carlo require too many
samples to provide reasonable statistics. Built upon recent advancements in
rare-event sampling, we present a model-based method to verify if a robotic
system satisfies a Signal Temporal Logic (STL) specification in the face of
environment variations and sensor/actuator noises. Our method is efficient and
applicable to both linear and nonlinear and even black-box systems with
arbitrary, but known, uncertainty distributions. For linear systems with
Gaussian uncertainties, we exploit a feature to find optimal parameters that
minimize the probability of failure. We demonstrate illustrative examples on
applying our approach to real-world autonomous robotic systems.
