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 expressiveness. By incorporating our
robustness definitions into a trajectory planner, autonomous vehicles obey
traffic rules more robustly than human drivers in the dataset.Comment: 7 pages, 6 figures, conference paper in submissio