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.

翻译：信号时序逻辑的鲁棒性不仅评估信号是否符合规范，还提供公式满足或违反程度的度量。鲁棒性的计算基于对底层谓词鲁棒性的评估。然而，谓词的鲁棒性通常以无模型方式定义，即不包含系统动力学。此外，精确定义复杂谓词的鲁棒性往往具有挑战性。针对这些问题，我们提出了一种模型预测鲁棒性的概念，该方法通过考虑基于模型的预测，相较于传统方法提供了一种更系统的鲁棒性评估方式。具体而言，我们利用高斯过程回归基于预计算的预测来学习鲁棒性，从而实现在线高效计算。我们基于记录数据集，在形式化交通规则中使用的谓词下，针对自动驾驶应用场景评估了该方法，凸显了本方法在表达能力上相较传统方法的优势。通过将我们的鲁棒性定义融入轨迹规划器，自动驾驶车辆在遵守交通规则方面比数据集中的人类驾驶员更具鲁棒性。