  This paper presents methodologies for constructing Control Barrier Functions
(CBFs) for nonlinear, control-affine systems, in the presence of input
constraints and bounded disturbances. More specifically, given a constraint
function with high-relative-degree with respect to the system dynamics, the
paper considers three methodologies, two for relative-degree 2 and one for
higher relative-degrees, for creating CBFs whose zero sublevel sets are subsets
of the constraint function's zero sublevel set. Three special forms of Robust
CBFs (RCBFs) are developed as functions of the input constraints, system
dynamics, and disturbance bounds, such that the resultant RCBF condition on the
control input is always feasible for states in the RCBF zero sublevel set. The
RCBF condition is then enforced in a switched fashion, which allows the system
to operate safely without enforcing the RCBF condition when far from the safe
set boundary and allows tuning of how closely trajectories approach the safe
set boundary. The proposed methods are verified in simulations demonstrating
the developed RCBFs in an asteroid flyby scenario for a satellite with
low-thrust actuators, and in asteroid proximity operations for a satellite with
high-thrust actuators.
