  This paper extends the gap-based navigation technique in Potential Gap by
guaranteeing safety for nonholonomic robots for all tiers of the local planner
hierarchy, so called Safer Gap. The first tier generates a Bezier-based
collision-free path through gaps. A subset of navigable free-space from the
robot through a gap, called the keyhole, is defined to be the union of the
largest collision-free disc centered on the robot and a trapezoidal region
directed through the gap. It is encoded by a shallow neural network zeroing
barrier function (ZBF). Nonlinear model predictive control (NMPC), with Keyhole
ZBF constraints and output tracking of the Bezier path, synthesizes a safe
kinematically-feasible trajectory. Low-level use of the Keyhole ZBF within a
point-wise optimization-based safe control synthesis module serves as a final
safety layer. Simulation and experimental validation of Safer Gap confirm its
collision-free navigation properties.
