Real-Time Spatiotemporal Tubes for Dynamic Unsafe Sets

2025-12-05

AI Summary

This paper addresses the prescribed-time arrival-avoidance-standby task for nonlinear pure-feedback systems operating in unknown dynamic environments. Method: We propose a real-time spatiotemporal tubular framework that online adjusts the center and radius of a time-varying sphere in the state space to dynamically characterize and avoid unsafe sets. It introduces, for the first time, an exact closed-form control law—without approximation—that integrates adaptive spatiotemporal modeling, predefined-time convergence, and state-constraint satisfaction. Contribution/Results: Rigorous theoretical analysis guarantees both obstacle-avoidance safety and task deadline compliance. Extensive simulations and hardware experiments on mobile robots and UAVs demonstrate millisecond-level online updates and timely, safe navigation in dense, dynamic obstacle fields—validating the framework’s strong real-time performance and scalability.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: State Estimation
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• Ensuring safety in dynamic environments with unknown dynamics
• Achieving reach-avoid-stay tasks within prescribed time constraints
• Providing formal guarantees for obstacle avoidance and task completion

Innovation

• Real-time spatiotemporal tube adapts online
• Closed-form control law ensures safety constraints
• Framework validated on mobile and aerial robots