  Over the decades, kinematic controllers have proven to be practically useful
for applications like set-point and trajectory tracking in robotic systems. To
this end, we formulate a novel safety-critical paradigm for kinematic control
in this paper. In particular, we extend the methodology of control barrier
functions (CBFs) to kinematic equations governing robotic systems. We
demonstrate a purely kinematic implementation of a velocity-based CBF, and
subsequently introduce a formulation that guarantees safety at the level of
dynamics. This is achieved through a new form CBFs that incorporate kinetic
energy with the classical forms, thereby minimizing model dependence and
conservativeness. The approach is then extended to underactuated systems. This
method and the purely kinematic implementation are demonstrated in simulation
on two robotic platforms: a 6-DOF robotic manipulator, and a cart-pole system.
