Online Synthesis of Control Barrier Functions with Local Occupancy Grid Maps for Safe Navigation in Unknown Environments

TL;DR

This paper introduces a real-time method for synthesizing Control Barrier Functions directly from local occupancy grid maps, enabling safe navigation in unknown environments with formal safety guarantees.

Contribution

It presents a novel approach that uses steady-state thermal field analogy and Laplace's equation to efficiently generate CBFs from perception data in real time.

Findings

CBFs synthesized in milliseconds on 200x200 maps

Effective safety filtering demonstrated in simulations and real-world tests

Approach enables safe navigation in unknown environments

Abstract

Control Barrier Functions (CBFs) have emerged as an effective and non-invasive safety filter for ensuring the safety of autonomous systems in dynamic environments with formal guarantees. However, most existing works on CBF synthesis focus on fully known settings. Synthesizing CBFs online based on perception data in unknown environments poses particular challenges. Specifically, this requires the construction of CBFs from high-dimensional data efficiently in real time. This paper proposes a new approach for online synthesis of CBFs directly from local Occupancy Grid Maps (OGMs). Inspired by steady-state thermal fields, we show that the smoothness requirement of CBFs corresponds to the solution of the steady-state heat conduction equation with suitably chosen boundary conditions. By leveraging the sparsity of the coefficient matrix in Laplace's equation, our approach allows for efficient computation of safety values for each grid cell in the map. Simulation and real-world experiments demonstrate the effectiveness of our approach. Specifically, the results show that our CBFs can be synthesized in an average of milliseconds on a 200 * 200 grid map, highlighting its real-time applicability.