Real-Time Spatiotemporal Tubes for Dynamic Unsafe Sets
Abstract
This paper presents a real-time control framework for nonlinear pure-feedback systems with unknown dynamics to satisfy reach-avoid-stay tasks within a prescribed time in dynamic environments. To achieve this, we introduce a real-time spatiotemporal tube (STT) framework. An STT is defined as a time-varying ball in the state space whose center and radius adapt online using only real-time sensory input. A closed-form, approximation-free control law is then derived to constrain the system output within the STT, ensuring safety and task satisfaction. We provide formal guarantees for obstacle avoidance and on-time task completion. The effectiveness and scalability of the framework are demonstrated through simulations and hardware experiments on a mobile robot and an aerial vehicle, navigating in cluttered dynamic environments.
Cite
@article{arxiv.2512.06151,
title = {Real-Time Spatiotemporal Tubes for Dynamic Unsafe Sets},
author = {Ratnangshu Das and Siddhartha Upadhyay and Pushpak Jagtap},
journal= {arXiv preprint arXiv:2512.06151},
year = {2025}
}