  This paper introduces the notion of an Input Constrained Control Barrier
Function (ICCBF), as a method to synthesize safety-critical controllers for
non-linear control affine systems with input constraints. The method identifies
a subset of the safe set of states, and constructs a controller to render the
subset forward invariant. The feedback controller is represented as the
solution to a quadratic program, which can be solved efficiently for real-time
implementation. Furthermore, we show that ICCBFs are a generalization of Higher
Order Control Barrier Functions, and thus are applicable to systems of
non-uniform relative degree. Simulation results are presented for the adaptive
cruise control problem, and a spacecraft rendezvous problem.
