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arXiv · 2411.13834

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

Ratnangshu Das·Ahan Basu·Pushpak Jagtap
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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.

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BibTeXRIS

Ratnangshu Das, Ahan Basu, Pushpak Jagtap. 2024-11-21. Spatiotemporal Tubes for Temporal Reach-Avoid-Stay Tasks in Unknown Systems. https://doi.org/10.1109/tac.2025.3592723

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