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

TL;DR

This paper introduces a novel sampling-based method to synthesize controllers for unknown MIMO systems, ensuring they meet complex temporal reach-avoid-stay tasks with safety guarantees using spatiotemporal tubes.

Contribution

It proposes a new approach combining spatiotemporal tubes with scenario optimization for control synthesis in unknown systems, avoiding approximation errors.

Findings

Successfully applied to robot, manipulator, and magnetic levitation systems.

Guarantees safety and target reachability in time-dependent environments.

Provides a closed-form control strategy without approximation.

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.