# Approximation-free Control for Signal Temporal Logic Specifications using Spatiotemporal Tubes

arXiv: https://arxiv.org/abs/2505.05323 · HTML: https://mlsanity.com/paper/2505.05323/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2025.

## Built on by (most cited first, 2 of 2)

- [Reward Machines for Signal Temporal Logic](https://mlsanity.com/paper/2608.13625/) (2026)
- [Tractable Reinforcement Learning for Full Class of Signal Temporal Logic Specifications Using Spatiotemporal Tube Reward](https://mlsanity.com/paper/2609.28396/) (2026)

## Abstract (arXiv)

This paper presents a spatiotemporal tube (STT)-based control framework for satisfying Signal Temporal Logic (STL) specifications in unknown control-affine systems. We formulate STL constraints as a robust optimization problem (ROP) and recast it as a scenario optimization program (SOP) to construct STTs with formal correctness guarantees. We also propose a closed-form control law that operates independently of the system dynamics, and ensures the system trajectory evolves within the STTs, thereby satisfying the STL specifications. The proposed approach is validated through case studies and comparisons with state-of-the-art methods, demonstrating superior computational efficiency, trajectory quality, and applicability to complex STL tasks.