# Spatiotemporal Tubes for Temporal Reach-Avoid-Stay Tasks in Unknown Systems

arXiv: https://arxiv.org/abs/2411.13834 · HTML: https://mlsanity.com/paper/2411.13834/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2024.

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

- [Learning from Demonstration via Spatiotemporal Tubes for Unknown Euler-Lagrange Systems](https://mlsanity.com/paper/2607.00534/) (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)

The paper considers the controller synthesis problem for general MIMO systems with unknown dynamics, aiming to fulfill the temporal reach-avoid-stay task, where the unsafe regions are time-dependent, and the target must be reached within a specified time frame. The primary aim of the paper is to construct the spatiotemporal tube (STT) using a sampling-based approach and thereby devise a closed-form approximation-free control strategy to ensure that system trajectory reaches the target set while avoiding time-dependent unsafe sets. The proposed scheme utilizes a novel method involving STTs to provide controllers that guarantee both system safety and reachability. In our sampling-based framework, we translate the requirements of STTs into a Robust optimization program (ROP). To address the infeasibility of ROP caused by infinite constraints, we utilize the sampling-based Scenario optimization program (SOP). Subsequently, we solve the SOP to generate the tube and closed-form controller for an unknown system, ensuring the temporal reach-avoid-stay specification. Finally, the effectiveness of the proposed approach is demonstrated through three case studies: an omnidirectional robot, a SCARA manipulator, and a magnetic levitation system.