Embedded Control Barrier Functions: Concept and Application to Safety-Critical Control Design of High-Relative-Degree Systems

This article proposes a novel safety-critical control (SCC) framework based on embedded control barrier functions (EMB-CBF-SCC) for high-order strict-feedback nonlinear affine control systems. It is aimed at reconciling the potential conflict between predesigned desired trajectory and multiple safety constraints that could have different high relative degrees. Compared with existing CBF-based SCCs, our method can significantly reduce differential order and computational burden. Specifically, we first propose a novel concept of embedded control barrier function (EMB-CBF), which can reduce an arbitrary high-relative-degree safety constraint to relative degree one, and ensure safety of high-relative-degree systems. Further, EMB-CBF-SCC divides the original system into a top-level and a bottom-level subsystem. Then, it embeds between the two subsystems a quadratic program based on EMB-CBF, and introduces command filters to smooth virtual control inputs and obtain differential signals. Coordination performance of safety and stability is analyzed, considering the impact of filter errors. Finally, we present two real safety-critical robotic application scenarios with different safety constraint settings, namely, multiple state constraints for a single-link manipulator numerical model and dynamic obstacle avoidance constraints for a self-developed micro mobile robot experimental platform, respectively. The effectiveness of the proposed framework is demonstrated in both scenarios.