Disturbance Rejection Control Barrier Functions

Most existing robust control barrier functions (CBFs) can only handle matched disturbances, restricting their applications in real-world scenarios. While some recent advances extend robust CBFs to unmatched disturbances, they heavily rely on differentiability property of disturbances, and fail to accommodate non-differentiable case for safety constraints with high relative degree.To address these limitations, this paper proposes a class of disturbance rejection CBFs (DRCBFs), including knowledge-based DRCBFs (kDRCBFs) and reciprocal-compensated DRCBFs (rDRCBFs).These two DRCBFs can strictly guarantee safety under general bounded disturbances, which includes both matched or unmatched, differentiable or non-differentiable disturbances as special cases. Moreover, no information of disturbance is needed in rDRCBFs. Simulation results illustrate that the proposed DRCBFs outperform existing robust CBFs.