Model Predictive Robustness of Signal Temporal Logic Predicates

TL;DR

This paper introduces a model predictive approach to evaluate the robustness of Signal Temporal Logic predicates using Gaussian process regression, enhancing precision and system compliance in autonomous driving scenarios.

Contribution

It proposes a systematic, model-based robustness evaluation method for STL predicates, addressing limitations of model-free definitions and enabling efficient online computation.

Findings

Improved robustness evaluation accuracy in autonomous driving

Enhanced traffic rule compliance in trajectory planning

Efficient online robustness computation using Gaussian processes

Abstract

The robustness of signal temporal logic not only assesses whether a signal adheres to a specification but also provides a measure of how much a formula is fulfilled or violated. The calculation of robustness is based on evaluating the robustness of underlying predicates. However, the robustness of predicates is usually defined in a model-free way, i.e., without including the system dynamics. Moreover, it is often nontrivial to define the robustness of complicated predicates precisely. To address these issues, we propose a notion of model predictive robustness, which provides a more systematic way of evaluating robustness compared to previous approaches by considering model-based predictions. In particular, we use Gaussian process regression to learn the robustness based on precomputed predictions so that robustness values can be efficiently computed online. We evaluate our approach for the use case of autonomous driving with predicates used in formalized traffic rules on a recorded dataset, which highlights the advantage of our approach compared to traditional approaches in terms of precision. By incorporating our robustness definitions into a trajectory planner, autonomous vehicles obey traffic rules more robustly than human drivers in the dataset.