Real-Time Spatiotemporal Tubes for Dynamic Unsafe Sets

TL;DR

This paper introduces a real-time control framework using spatiotemporal tubes to ensure safety and task completion for nonlinear systems in dynamic environments, demonstrated through simulations and hardware tests.

Contribution

We propose a novel real-time spatiotemporal tube framework with an approximation-free control law for nonlinear systems in dynamic settings.

Findings

Effective obstacle avoidance demonstrated in simulations and experiments

Guarantees on safety and on-time task completion

Scalable approach applicable to mobile robots and aerial vehicles

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.