Model Predictive Robustness of Signal Temporal Logic Predicates
This work addresses the challenge of precisely defining and computing robustness for complex predicates in signal temporal logic, with incremental improvements for autonomous driving applications.
The authors tackled the problem of evaluating the robustness of signal temporal logic predicates by proposing model predictive robustness, which incorporates system dynamics and uses Gaussian process regression for efficient online computation. Their approach, tested on an autonomous driving dataset, showed improved precision over traditional methods and enabled autonomous vehicles to obey traffic rules more robustly than human drivers.
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.