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arXiv · 2512.06151

Real-Time Spatiotemporal Tubes for Dynamic Unsafe Sets

Ratnangshu Das·Siddhartha Upadhyay·Pushpak Jagtap
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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.

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Ratnangshu Das, Siddhartha Upadhyay, Pushpak Jagtap. 2025-12-05. Real-Time Spatiotemporal Tubes for Dynamic Unsafe Sets. https://arxiv.org/abs/2512.06151

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