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

TL;DR

This paper develops robust control barrier functions for nonlinear systems with high-relative-degree constraints and input limits, enabling safe satellite trajectory control near asteroids with verified simulation results.

Contribution

It introduces new methodologies for constructing robust control barrier functions for high-relative-degree constraints under input constraints and disturbances.

Findings

Successfully verified RCBFs in asteroid flyby simulations

Demonstrated safe satellite operations with low and high-thrust actuators

Enforced RCBF conditions in a switched manner for safety and flexibility

Abstract

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.