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

Robust Control Barrier Functions under High Relative Degree and Input Constraints for Satellite Trajectories