# Temporal Reach-Avoid-Stay Control for Differential Drive Systems via Spatiotemporal Tubes

arXiv: https://arxiv.org/abs/2512.05495 · HTML: https://mlsanity.com/paper/2512.05495/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2025.

## Built on by (most cited first, 1 of 1)

- [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 computationally lightweight and robust control framework for differential-drive mobile robots with dynamic uncertainties and external disturbances, guaranteeing the satisfaction of Temporal Reach-Avoid-Stay (T-RAS) specifications. The approach employs circular spatiotemporal tubes (STTs), characterized by smoothly time-varying center and radius, to define dynamic safe corridors that guide the robot from the start region to the goal while avoiding obstacles. In particular, we first develop a sampling-based synthesis algorithm to construct a feasible STT that satisfies the prescribed timing and safety constraints with formal guarantees. To ensure that the robot remains confined within this tube, we then analytically design a closed-form control that is computationally efficient and robust to disturbances. The proposed framework is validated through simulation studies on a differential-drive robot and benchmarked against state-of-the-art methods, demonstrating superior robustness, accuracy, and computational efficiency.