Spatiotemporal Tubes for Temporal Reach-Avoid-Stay Tasks in Unknown Systems

2024-11-21

arXiv.org

AI Summary

This paper addresses the spatiotemporal safety control problem for MIMO systems with unknown dynamics, requiring guaranteed “reach–avoid–dwell” performance within a prescribed time horizon amid time-varying unsafe regions. We propose a novel, approximation-free closed-loop control framework based on sampled spatiotemporal tubes (STTs), which transforms the infinite-dimensional robust optimization into a tractable scenario optimization problem—without requiring an explicit system model or dynamic approximation. The method integrates STT-based modeling, scenario optimization, and model-free controller synthesis. It is validated on an omnidirectional robot, a SCARA manipulator, and a magnetic levitation system. Results demonstrate strict satisfaction of three key safety objectives: time-bounded reachability to the target set, avoidance of time-varying obstacles, and safe dwell within the target region. The approach significantly enhances control reliability and practicality under complex spatiotemporal constraints.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: Multi-Robot Systems
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Novel mobile and WoT systems, and system-of-systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements

Abstract

The paper considers the controller synthesis problem for general MIMO systems with unknown dynamics, aiming to fulfill the temporal reach-avoid-stay task, where the unsafe regions are time-dependent, and the target must be reached within a specified time frame. The primary aim of the paper is to construct the spatiotemporal tube (STT) using a sampling-based approach and thereby devise a closed-form approximation-free control strategy to ensure that system trajectory reaches the target set while avoiding time-dependent unsafe sets. The proposed scheme utilizes a novel method involving STTs to provide controllers that guarantee both system safety and reachability. In our sampling-based framework, we translate the requirements of STTs into a Robust optimization program (ROP). To address the infeasibility of ROP caused by infinite constraints, we utilize the sampling-based Scenario optimization program (SOP). Subsequently, we solve the SOP to generate the tube and closed-form controller for an unknown system, ensuring the temporal reach-avoid-stay specification. Finally, the effectiveness of the proposed approach is demonstrated through three case studies: an omnidirectional robot, a SCARA manipulator, and a magnetic levitation system.

Problem

• Controller synthesis for unknown MIMO systems with time-dependent unsafe regions
• Construct spatiotemporal tubes using sampling for reach-avoid-stay tasks
• Develop approximation-free control ensuring safety and reachability in unknown dynamics

Innovation

• Constructs spatiotemporal tubes using sampling-based approach
• Develops approximation-free control strategy for unknown systems
• Uses scenario optimization to handle infinite constraints