Elliptical Slice Sampling for Probabilistic Verification of Stochastic Systems with Signal Temporal Logic Specifications

TL;DR

This paper introduces an efficient probabilistic verification method for stochastic systems with STL specifications, utilizing elliptical slice sampling to accurately estimate task satisfaction probabilities without over-approximation.

Contribution

It presents a novel sampling-based verification approach that avoids over-approximations and efficiently computes satisfaction probabilities for systems with Gaussian noise.

Findings

The method accurately estimates task satisfaction probabilities.

It avoids over-approximations and double-counting of failures.

Illustrative robot motion planning examples demonstrate effectiveness.

Abstract

Autonomous robots typically incorporate complex sensors in their decision-making and control loops. These sensors, such as cameras and Lidars, have imperfections in their sensing and are influenced by environmental conditions. In this paper, we present a method for probabilistic verification of linearizable systems with Gaussian and Gaussian mixture noise models (e.g. from perception modules, machine learning components). We compute the probabilities of task satisfaction under Signal Temporal Logic (STL) specifications, using its robustness semantics, with a Markov Chain Monte-Carlo slice sampler. As opposed to other techniques, our method avoids over-approximations and double-counting of failure events. Central to our approach is a method for efficient and rejection-free sampling of signals from a Gaussian distribution such that satisfy or violate a given STL formula. We show illustrative examples from applications in robot motion planning.