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arXiv · 2510.19595

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

Ratnangshu Das·Subhodeep Choudhury·Pushpak Jagtap
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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.

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Ratnangshu Das, Subhodeep Choudhury, Pushpak Jagtap. 2025-10-22. Control Barrier Functions for the Full Class of Signal Temporal Logic Tasks using Spatiotemporal Tubes. https://arxiv.org/abs/2510.19595

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