  We develop a control algorithm that ensures the safety, in terms of
confinement in a set, of a system with unknown, 2nd-order nonlinear dynamics.
The algorithm establishes novel connections between data-driven and robust,
nonlinear control. It is based on data obtained online from the current
trajectory and the concept of reciprocal barriers. More specifically, it first
uses the obtained data to calculate set-valued functions that over-approximate
the unknown dynamic terms. For the second step of the algorithm, we design a
robust control scheme that uses these functions as well as reciprocal barriers
to render the system forward invariant with respect to the safe set. In
addition, we provide an extension of the algorithm that tackles issues of
controllability loss incurred by the nullspace of the control-direction matrix.
The algorithm removes a series of standard, limiting assumptions considered in
the related literature since it does not require global boundedness, growth
conditions, or a priori approximations of the unknown dynamics' terms.
