  Control Barrier Functions offer safety certificates by dictating controllers
that enforce safety constraints. However, their response depends on the classK
function that is used to restrict the rate of change of the value of the
barrier function along the system trajectories. This paper introduces the
notion of a Rate-Tunable (RT) CBF, which allows for online tuning of the
response of CBF-based controllers. In contrast to existing approaches that use
a fixed classK function to ensure safety, we parameterize and adapt the classK
function parameters online. We show that this helps improve the system's
response in terms of the resulting trajectories being closer to a nominal
reference while being sufficiently far from the boundary of the safe set. We
provide point-wise sufficient conditions to be imposed on any user-given
parameter dynamics so that multiple CBF constraints continue to admit a common
control input with time. Finally, we introduce RT-CBF parameter dynamics for
decentralized noncooperative multi-agent systems, where a trust factor,
computed based on the instantaneous ease of constraint satisfaction, is used to
update parameters online for a less conservative response.
