Comparative Analysis of Control Barrier Functions and Artificial Potential Fields for Obstacle Avoidance

TL;DR

This paper compares control barrier functions and artificial potential fields for obstacle avoidance, proving theoretical connections and demonstrating that CBFs outperform APFs in simulations and hardware tests.

Contribution

It establishes that APFs are a special case of CBFs, introduces benefits of CBFs for nonlinear systems, and empirically compares their performance.

Findings

CBFs outperform APFs in obstacle avoidance tasks

APFs are a subset of CBFs with specific properties

CBFs are effective for nonlinear system safety guarantees

Abstract

Artificial potential fields (APFs) and their variants have been a staple for collision avoidance of mobile robots and manipulators for almost 40 years. Its model-independent nature, ease of implementation, and real-time performance have played a large role in its continued success over the years. Control barrier functions (CBFs), on the other hand, are a more recent development, commonly used to guarantee safety for nonlinear systems in real-time in the form of a filter on a nominal controller. In this paper, we address the connections between APFs and CBFs. At a theoretic level, we prove that APFs are a special case of CBFs: given a APF one obtains a CBFs, while the converse is not true. Additionally, we prove that CBFs obtained from APFs have additional beneficial properties and can be applied to nonlinear systems. Practically, we compare the performance of APFs and CBFs in the context of obstacle avoidance on simple illustrative examples and for a quadrotor, both in simulation and on hardware using onboard sensing. These comparisons demonstrate that CBFs outperform APFs.