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

arXiv: https://arxiv.org/abs/2107.04094 · HTML: https://mlsanity.com/paper/2107.04094/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2021.

## Built on by (most cited first, 8 of 8)

- [Exact Verification of ReLU Neural Control Barrier Functions](https://mlsanity.com/paper/2310.09360/) (2023)
- [Sequential Neural Barriers for Scalable Dynamic Obstacle Avoidance](https://mlsanity.com/paper/2307.03015/) (2023)
- [Learning Predictive Safety Filter via Decomposition of Robust Invariant Set](https://mlsanity.com/paper/2311.06769/) (2023)
- [Neural Configuration-Space Barriers for Manipulation Planning and Control](https://mlsanity.com/paper/2503.04929/) (2025)
- [Scalable Verification of Neural Control Barrier Functions Using Linear Bound Propagation](https://mlsanity.com/paper/2511.06341/) (2025)
- [Demonstrating ViSafe: Vision-enabled Safety for High-speed Detect and Avoid](https://mlsanity.com/paper/2505.03694/) (2025)
- [Uncertainty Aware-Predictive Control Barrier Functions: Safer Human Robot Interaction through Probabilistic Motion Forecasting](https://mlsanity.com/paper/2508.20812/) (2025)
- [Safety-Guaranteed Imitation Learning from Nonlinear Model Predictive Control for Spacecraft Close Proximity Operations](https://mlsanity.com/paper/2603.18910/) (2026)

## Abstract (arXiv)

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.