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Control Barrier Functions for the Full Class of Signal Temporal Logic Tasks using Spatiotemporal Tubes

Year: 2025

Type: preprint

Abstract: This paper introduces a new framework for synthesizing time-varying control barrier functions (TV-CBFs) for general Signal Temporal Logic (STL) specifications using spatiotemporal tubes (STT). We first formulate the STT synthesis as a robust optimization problem (ROP) and solve it through a scenario optimization problem (SOP), providing formal guarantees that the resulting tubes capture the given STL specifications. These STTs are then used to construct TV-CBFs, ensuring that under any control law rendering them invariant, the system satisfies the STL tasks. We demonstrate the framework through case studies on a differential-drive mobile robot and a quadrotor, and provide a comparative analysis showing improved efficiency over existing approaches.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2510.19595

Authors: Das, Ratnangshu, Choudhury, Subhodeep, Jagtap, Pushpak

Institutions: Robert Bosch (China), Robert Bosch (Brazil)

Topic: Formal Methods in Verification

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Ministry of Education, India, Science and Engineering Research Board

OpenAlex ID: W4416247174

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