English

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

Systems and Control 2025-10-23 v1 Systems and Control

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.

Keywords

Cite

@article{arxiv.2510.19595,
  title  = {Control Barrier Functions for the Full Class of Signal Temporal Logic Tasks using Spatiotemporal Tubes},
  author = {Ratnangshu Das and Subhodeep Choudhury and Pushpak Jagtap},
  journal= {arXiv preprint arXiv:2510.19595},
  year   = {2025}
}