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

TL;DR

This paper presents a novel framework that synthesizes control barrier functions for complex temporal logic tasks using spatiotemporal tubes, with formal guarantees and improved efficiency demonstrated on robotic systems.

Contribution

It introduces a new method to generate time-varying control barrier functions for STL tasks via spatiotemporal tubes, formulated as a robust optimization problem with scenario-based solutions.

Findings

Formal guarantees for STL specification satisfaction

Improved efficiency over existing methods

Successful case studies on mobile robot and quadrotor

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.