Robustness of Modified Control Barrier Functions subject to External Disturbances

This paper focuses on the robustness of Control Barrier Functions (CBFs). The existing results, which combine the Control Lyapunov Functions (CLFs) and CBFs by Quadratic Programs (QP), can effectively mediate the potential conflict between control objectives and safety constraints. The system security can be guaranteed by the forward invariant safe set. However, the robustness of existing CBFs is too weak, while minor unknown disturbances can break the forward invariant property. To solve such a problem, Modified Control Barrier Functions (MCBFs) are proposed in this paper, which lead the priority of control objectives and safety constraints to be dynamically adjusted by the safety degree. The CLFs and MCBFs are combined in the QP-based controllers, to achieve the control objectives in the relative safe region, and to resist arbitrary bounded external disturbances at boundary of the safe set. The simulation results are given to demonstrate the effectiveness of the proposed control scheme.