Spatiotemporal Tubes for Probabilistic Temporal Reach-Avoid-Stay Task in Uncertain Dynamic Environment

2025-12-24

AI Summary

Addressing the challenge of probabilistic time-bounded reach-avoid-stay (PrT-RAS) tasks in dynamic uncertain environments, this paper introduces a time-varying state-space spherical spatio-temporal tube (STT) modeling framework—the first to extend STTs to PrT-RAS problems. By online fusing uncertainty-aware information, it derives an exact, model-free, optimization-free closed-form real-time feedback control law, accompanied by formal guarantees on probabilistic collision avoidance and finite-time convergence. The method integrates spatio-temporal tube modeling, uncertainty propagation analysis, and probabilistic safety verification to jointly enforce safety constraints and task objectives. Experimental validation on mobile robots, quadcopters, and a 7-DOF manipulator demonstrates high real-time performance, strong safety assurance, and superior task success rates—enabling robust navigation and manipulation under high-density dynamic obstacles.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

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

Abstract

In this work, we extend the Spatiotemporal Tube (STT) framework to address Probabilistic Temporal Reach-Avoid-Stay (PrT-RAS) tasks in dynamic environments with uncertain obstacles. We develop a real-time tube synthesis procedure that explicitly accounts for time-varying uncertain obstacles and provides formal probabilistic safety guarantees. The STT is formulated as a time-varying ball in the state space whose center and radius evolve online based on uncertain sensory information. We derive a closed-form, approximation-free control law that confines the system trajectory within the tube, ensuring both probabilistic safety and task satisfaction. Our method offers a formal guarantee for probabilistic avoidance and finite-time task completion. The resulting controller is model-free, approximation-free, and optimization-free, enabling efficient real-time execution while guaranteeing convergence to the target. The effectiveness and scalability of the framework are demonstrated through simulation studies and hardware experiments on mobile robots, a UAV, and a 7-DOF manipulator navigating in cluttered and uncertain environments.

Problem

• Extending Spatiotemporal Tube framework for probabilistic reach-avoid-stay tasks
• Developing real-time tube synthesis with probabilistic safety guarantees
• Creating model-free control for uncertain dynamic environments

Innovation

• Real-time tube synthesis with probabilistic safety guarantees
• Closed-form control law without approximations or optimization
• Model-free framework ensuring convergence in uncertain environments