  In this paper, we have demonstrated that the controllers designed by a
classical motion planning tool, namely artificial potential fields (APFs), can
be derived from a recently prevalent approach: control barrier function
quadratic program (CBF-QP) safety filters. By integrating APF information into
the CBF-QP framework, we establish a bridge between these two methodologies.
Specifically, this is achieved by employing the attractive potential field as a
control Lyapunov function (CLF) to guide the design of the nominal controller,
and then the repulsive potential field serves as a reciprocal CBF (RCBF) to
define a CBF-QP safety filter. Building on this integration, we extend the
design of the CBF-QP safety filter to accommodate a more general class of
dynamical models featuring a control-affine structure. This extension yields a
special CBF-QP safety filter and a general APF solution suitable for
control-affine dynamical models. Through a reach-avoid navigation example, we
showcase the efficacy of the developed approaches.
