# Model Predictive Robustness of Signal Temporal Logic Predicates

arXiv: https://arxiv.org/abs/2209.07881 · HTML: https://mlsanity.com/paper/2209.07881/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 52 references that are in the map.
- First posted on arXiv 16 Sep 2022.

## Builds on (most cited first, 14 of 14)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [The highD Dataset: A Drone Dataset of Naturalistic Vehicle Trajectories on German Highways for Validation of Highly Automated Driving Systems](https://mlsanity.com/paper/1810.05642/) (2018)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics](https://mlsanity.com/paper/1710.11040/) (2017)
- [On Robustness Metrics for Learning STL Tasks](https://mlsanity.com/paper/2003.06041/) (2020)
- [A Smooth Robustness Measure of Signal Temporal Logic for Symbolic Control](https://mlsanity.com/paper/2006.05239/) (2020)
- [Rule-based Optimal Control for Autonomous Driving](https://mlsanity.com/paper/2101.05709/) (2021)
- [Arithmetic-Geometric Mean Robustness for Control from Signal Temporal Logic Specifications](https://mlsanity.com/paper/1903.05186/) (2019)
- [Mixed-Integer Programming for Signal Temporal Logic with Fewer Binary Variables](https://mlsanity.com/paper/2204.06367/) (2022)
- [Variable selection for Gaussian processes via sensitivity analysis of the posterior predictive distribution](https://mlsanity.com/paper/1712.08048/) (2017)
- [Formalizing Traffic Rules for Machine Interpretability](https://mlsanity.com/paper/2007.00330/) (2020)
- [Formal Specification and Verification of Autonomous Robotic Systems: A Survey](https://mlsanity.com/paper/1807.00048/) (2018)
- [Control with Probabilistic Signal Temporal Logic](https://mlsanity.com/paper/1510.08474/) (2015)
- [Signal Temporal Logic Synthesis as Probabilistic Inference](https://mlsanity.com/paper/2105.06121/) (2021)

## Built on by (most cited first, 3 of 3)

- [Traffic-Rule-Compliant Trajectory Repair via Satisfiability Modulo Theories and Reachability Analysis](https://mlsanity.com/paper/2412.15837/) (2024)
- [Knowledge Integration Strategies in Autonomous Vehicle Prediction and Planning: A Comprehensive Survey](https://mlsanity.com/paper/2502.10477/) (2025)
- [Structural-Ambiguity-Aware Translation from Natural Language to Signal Temporal Logic](https://mlsanity.com/paper/2603.28426/) (2026)

## Abstract (arXiv)

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.