  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.
