  Control barrier functions are widely used to enforce safety properties in
robot motion planning and control. However, the problem of constructing barrier
functions online and synthesizing safe controllers that can deal with the
associated uncertainty has received little attention. This paper investigates
safe navigation in unknown environments, using onboard range sensing to
construct control barrier functions online. To represent different objects in
the environment, we use the distance measurements to train neural network
approximations of the signed distance functions incrementally with replay
memory. This allows us to formulate a novel robust control barrier safety
constraint which takes into account the error in the estimated distance fields
and its gradient. Our formulation leads to a second-order cone program,
enabling safe and stable control synthesis in a priori unknown environments.
