  Control barrier functions (CBF) have become popular as a safety filter to
guarantee the safety of nonlinear dynamical systems for arbitrary inputs.
However, it is difficult to construct functions that satisfy the CBF
constraints for high relative degree systems with input constraints. To address
these challenges, recent work has explored learning CBFs using neural networks
via neural CBF (NCBF). However, such methods face difficulties when scaling to
higher dimensional systems under input constraints. In this work, we first
identify challenges that NCBFs face during training. Next, to address these
challenges, we propose policy neural CBF (PNCBF), a method of constructing CBFs
by learning the value function of a nominal policy, and show that the value
function of the maximum-over-time cost is a CBF. We demonstrate the
effectiveness of our method in simulation on a variety of systems ranging from
toy linear systems to an F-16 jet with a 16-dimensional state space. Finally,
we validate our approach on a two-agent quadcopter system on hardware under
tight input constraints.
