# A Smooth Robustness Measure of Signal Temporal Logic for Symbolic Control

arXiv: https://arxiv.org/abs/2006.05239 · HTML: https://mlsanity.com/paper/2006.05239/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

## Built on by (most cited first, 21 of 21)

- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Learning Robust and Correct Controllers from Signal Temporal Logic Specifications Using BarrierNet](https://mlsanity.com/paper/2304.06160/) (2023)
- [Zero-Shot Trajectory Planning for Signal Temporal Logic Tasks](https://mlsanity.com/paper/2501.13457/) (2025)
- [Interpretable Fault Diagnosis of Rolling Element Bearings with Temporal Logic Neural Network](https://mlsanity.com/paper/2204.07579/) (2022)
- [Safe Model-based Control from Signal Temporal Logic Specifications Using Recurrent Neural Networks](https://mlsanity.com/paper/2103.15938/) (2021)
- [Reinforcement Learning with Formal Performance Metrics for Quadcopter Attitude Control under Non-nominal Contexts](https://mlsanity.com/paper/2107.12942/) (2021)
- [Model Predictive Robustness of Signal Temporal Logic Predicates](https://mlsanity.com/paper/2209.07881/) (2022)
- [Requirement falsification for cyber-physical systems using generative models](https://mlsanity.com/paper/2310.20493/) (2023)
- [Interpretable Imitation Learning via Generative Adversarial STL Inference and Control](https://mlsanity.com/paper/2402.10310/) (2024)
- [Neural Network-based Control for Multi-Agent Systems from Spatio-Temporal Specifications](https://mlsanity.com/paper/2104.02737/) (2021)
- [Co-learning Planning and Control Policies Constrained by Differentiable Logic Specifications](https://mlsanity.com/paper/2303.01346/) (2023)
- [ClarifySTL: An Interactive LLM Agent Framework for STL Transformation through Requirements Clarification](https://mlsanity.com/paper/2605.01209/) (2026)
- [Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning](https://mlsanity.com/paper/2603.29868/) (2026)
- [Reinforcement Learning Agent Training with Goals for Real World Tasks](https://mlsanity.com/paper/2107.10390/) (2021)
- [CatlNet: Learning Communication and Coordination Policies from CaTL+ Specifications](https://mlsanity.com/paper/2212.11792/) (2022)
- [Scaling Learning based Policy Optimization for Temporal Logic Tasks by Controller Network Dropout](https://mlsanity.com/paper/2403.15826/) (2024)
- [Feasibility-aware Learning of Robust Temporal Logic Controllers using BarrierNet](https://mlsanity.com/paper/2512.06973/) (2025)
- [Zero-Shot Signal Temporal Logic Planning with Disjunctive Branch Selection in Dynamic Semantic Maps](https://mlsanity.com/paper/2605.01222/) (2026)
- [Reward Machines for Signal Temporal Logic](https://mlsanity.com/paper/2608.13625/) (2026)
- [Backward through Time, Algebraically](https://mlsanity.com/paper/2608.17087/) (2026)
- [From LLM-Generated Specifications to Learned Quadruped Locomotion](https://mlsanity.com/paper/2609.07111/) (2026)

## Abstract (arXiv)

Recent years have seen an increasing use of Signal Temporal Logic (STL) as a formal specification language for symbolic control, due to its expressiveness and closeness to natural language. Furthermore, STL specifications can be encoded as cost functions using STL's robust semantics, transforming the synthesis problem into an optimization problem. Unfortunately, these cost functions are non-smooth and non-convex, and exact solutions using mixed-integer programming do not scale well. Recent work has focused on using smooth approximations of robustness, which enable faster gradient-based methods to find local maxima, at the expense of soundness and/or completeness. We propose a novel robustness approximation that is smooth everywhere, sound, and asymptotically complete. Our approach combines the benefits of existing approximations, while enabling an explicit tradeoff between conservativeness and completeness.