# Signal Temporal Logic Neural Predictive Control

arXiv: https://arxiv.org/abs/2309.05131 · HTML: https://mlsanity.com/paper/2309.05131/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 41 references that are in the map.
- First posted on arXiv 10 Sep 2023.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Reinforcement Learning With Temporal Logic Rewards](https://mlsanity.com/paper/1612.03471/) (2016)
- [Q-Learning for Robust Satisfaction of Signal Temporal Logic Specifications](https://mlsanity.com/paper/1609.07409/) (2016)
- [STyLuS*: A Temporal Logic Optimal Control Synthesis Algorithm for Large-Scale Multi-Robot Systems](https://mlsanity.com/paper/1809.08345/) (2018)
- [Multi-agent Motion Planning from Signal Temporal Logic Specifications](https://mlsanity.com/paper/2201.05247/) (2022)
- [Recurrent Neural Network Controllers for Signal Temporal Logic Specifications Subject to Safety Constraints](https://mlsanity.com/paper/2009.11468/) (2020)
- [Model-based Reinforcement Learning from Signal Temporal Logic Specifications](https://mlsanity.com/paper/2011.04950/) (2020)
- [Robust Counterexample-guided Optimization for Planning from Differentiable Temporal Logic](https://mlsanity.com/paper/2203.02038/) (2022)
- [STL2vec: Signal Temporal Logic Embeddings for Control Synthesis With Recurrent Neural Networks](https://mlsanity.com/paper/2109.04636/) (2021)
- [Model-Based Reinforcement Learning for Approximate Optimal Control with Temporal Logic Specifications](https://mlsanity.com/paper/2101.07156/) (2021)
- [Modularized Control Synthesis for Complex Signal Temporal Logic Specifications](https://mlsanity.com/paper/2303.17086/) (2023)

## Built on by (most cited first, 13 of 13)

- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [TeLoGraF: Temporal Logic Planning via Graph-encoded Flow Matching](https://mlsanity.com/paper/2505.00562/) (2025)
- [Diverse Controllable Diffusion Policy with Signal Temporal Logic](https://mlsanity.com/paper/2503.02924/) (2025)
- [TGPO: Temporal Grounded Policy Optimization for Signal Temporal Logic Tasks](https://mlsanity.com/paper/2510.00225/) (2025)
- [STeP: Signal Temporal Logic for Precise Specifications for Action Generation with Vision Language Models](https://mlsanity.com/paper/2607.18580/) (2026)
- [Accelerated Learning with Linear Temporal Logic using Differentiable Simulation](https://mlsanity.com/paper/2506.01167/) (2025)
- [SUN: Agentic Robot Policy Learning with Persistent Task Programs](https://mlsanity.com/paper/2608.31167/) (2026)
- [GraSP-STL: A Graph-Based Framework for Zero-Shot Signal Temporal Logic Planning via Offline Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2603.29533/) (2026)
- [Zero-Shot Signal Temporal Logic Planning with Disjunctive Branch Selection in Dynamic Semantic Maps](https://mlsanity.com/paper/2605.01222/) (2026)
- [Robustness of Robotic Manipulation: Foundations and Frontiers](https://mlsanity.com/paper/2606.31494/) (2026)
- [Learning-enabled Parameter Synthesis for Nonlinear Systems from Signal Temporal Logic](https://mlsanity.com/paper/2607.08899/) (2026)
- [Reward Machines for Signal Temporal Logic](https://mlsanity.com/paper/2608.13625/) (2026)
- [Learning Robot Policies from Sparse Success Signals via STL-Guided Stein Variational Policy Gradient](https://mlsanity.com/paper/2609.31606/) (2026)

## Abstract (arXiv)

Ensuring safety and meeting temporal specifications are critical challenges for long-term robotic tasks. Signal temporal logic (STL) has been widely used to systematically and rigorously specify these requirements. However, traditional methods of finding the control policy under those STL requirements are computationally complex and not scalable to high-dimensional or systems with complex nonlinear dynamics. Reinforcement learning (RL) methods can learn the policy to satisfy the STL specifications via hand-crafted or STL-inspired rewards, but might encounter unexpected behaviors due to ambiguity and sparsity in the reward. In this paper, we propose a method to directly learn a neural network controller to satisfy the requirements specified in STL. Our controller learns to roll out trajectories to maximize the STL robustness score in training. In testing, similar to Model Predictive Control (MPC), the learned controller predicts a trajectory within a planning horizon to ensure the satisfaction of the STL requirement in deployment. A backup policy is designed to ensure safety when our controller fails. Our approach can adapt to various initial conditions and environmental parameters. We conduct experiments on six tasks, where our method with the backup policy outperforms the classical methods (MPC, STL-solver), model-free and model-based RL methods in STL satisfaction rate, especially on tasks with complex STL specifications while being 10X-100X faster than the classical methods.