Smooth Spatiotemporal Tube Synthesis for Prescribed-Time Reach-Avoid-Stay Control

2025-10-13

AI Summary

This paper addresses the controller synthesis problem for control-affine nonlinear systems subject to reach-avoid-stay specifications within a prescribed time horizon. We propose a novel adaptive smooth spatiotemporal tube (STT) framework. Unlike conventional STT methods that rely on barrier or avoidance functions—causing discontinuous tube boundaries and incurring high control effort—our approach constructs continuously differentiable STT boundaries, thereby eliminating the need for avoidance functions entirely. Furthermore, we derive an exact closed-form feedback control law that rigorously guarantees, within the specified time, simultaneous satisfaction of safety (avoidance), target reachability (reach), and persistent invariance (stay). Experimental results demonstrate that the proposed method significantly reduces control energy consumption while achieving superior task completion accuracy and temporal robustness compared to state-of-the-art approaches.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: State Estimation
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Assisted, interactive, and conversational search

Abstract

In this work, we address the issue of controller synthesis for a control-affine nonlinear system to meet prescribed time reach-avoid-stay specifications. Our goal is to improve upon previous methods based on spatiotemporal tubes (STTs) by eliminating the need for circumvent functions, which often lead to abrupt tube modifications and high control effort. We propose an adaptive framework that constructs smooth STTs around static unsafe sets, enabling continuous avoidance while guiding the system toward the target within the prescribed time. A closed-form, approximation-free control law is derived to ensure the system trajectory remains within the tube and satisfies the RAS task. The effectiveness of the proposed approach is demonstrated through a case study, showing a significant reduction in control effort compared to prior methods.

Problem

• Synthesizing controllers for nonlinear systems with reach-avoid-stay specifications
• Eliminating abrupt tube modifications and high control effort
• Ensuring continuous avoidance and target reachability within prescribed time

Innovation

• Smooth spatiotemporal tubes for continuous avoidance
• Closed-form control law without approximations
• Adaptive framework eliminating abrupt tube modifications