  Hamilton-Jacobi (HJ) reachability analysis has been developed over the past
decades into a widely-applicable tool for determining goal satisfaction and
safety verification in nonlinear systems. While HJ reachability can be
formulated very generally, computational complexity can be a serious impediment
for many systems of practical interest. Much prior work has been devoted to
computing approximate solutions to large reachability problems, yet many of
these methods may only apply to very restrictive problem classes, do not
generate controllers, and/or can be extremely conservative. In this paper, we
present a new method for approximating the optimal controller of the HJ
reachability problem for control-affine systems. While also a specific problem
class, many dynamical systems of interest are, or can be well approximated, by
control-affine models. We explicitly avoid storing a representation of the
reachability value function, and instead learn a controller as a sequence of
simple binary classifiers. We compare our approach to existing grid-based
methodologies in HJ reachability and demonstrate its utility on several
examples, including a physical quadrotor navigation task.
