  This paper proposes a safety controller for control-affine nonlinear systems
with unmodelled dynamics and disturbances to improve closed-loop robustness.
Uncertainty estimation-based control barrier functions (CBFs) are utilized to
ensure robust safety in the presence of model uncertainties, which may depend
on control input and states. We present a new uncertainty/disturbance estimator
with theoretical upper bounds on estimation error and estimated outputs, which
are used to ensure robust safety by formulating a convex optimization problem
using a high-order CBF. The possibly unsafe nominal feedback controller is
augmented with the proposed estimator in two frameworks (1) an uncertainty
compensator and (2) a robustifying reformulation of CBF constraint with respect
to the estimator outputs. The former scheme ensures safety with performance
improvement by adaptively rejecting the matched uncertainty. The second method
uses uncertainty estimation to robustify higher-order CBFs for safety-critical
control. The proposed methods are demonstrated in simulations of an uncertain
adaptive cruise control problem and a multirotor obstacle avoidance situation.
