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.

翻译：信号时序逻辑的鲁棒性不仅评估信号是否满足规范，还提供了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，即不包含系统动态。此外，精确定义复杂谓词的鲁棒性往往具有挑战性。为解决这些问题，我们提出了一种模型预测鲁棒性的概念，通过考虑基于模型的预测，为鲁棒性评估提供了一种比先前方法更系统的方式。特别地，我们利用高斯过程回归基于预计算预测来学习鲁棒性，从而能够在线上高效计算鲁棒性值。我们在一个记录数据集上对自动驾驶用例进行评估，该用例涉及形式化交通规则中的谓词，突出了我们的方法在精确性方面相比传统方法的优势。通过将我们的鲁棒性定义融入轨迹规划器，自动驾驶车辆比数据集中的人类驾驶员更鲁棒地遵守交通规则。