  This paper addresses the challenge of integrating explicit hard constraints
into the control barrier function (CBF) framework for ensuring safety in
autonomous systems, including robots. We propose a novel data-driven method to
derive CBFs from these hard constraints in practical scenarios. Our approach
assumes that the forward invariant safe set is either a subset or equal to the
constrained set. The process consists of two main steps. First, we randomly
sample states within the constraint boundaries and identify inputs meeting the
time derivative criteria of the hard constraint; this iterative process
converges using the Jaccard index. Next, we formulate CBFs that enclose the
safe set using the sampled boundaries. This enables the creation of a
control-invariant safe set, approaching the maximum attainable level of control
invariance. This approach, therefore, addresses the complexities posed by
complex autonomous systems with constrained control input spaces, culminating
in a control-invariant safe set that closely approximates the maximal control
invariant set.
