Optimal Safety Control using High-Order Control Barrier Functions
Robotics
Summary
The authors study how to keep nonlinear systems safe while controlling them effectively. They introduce new mathematical tools called high-order control barrier functions (HOCBFs) to design safety controls more directly than before. Additionally, they develop a new type of control Lyapunov function to ensure the system remains stable. They show how these methods work together to achieve both safety and stability at the same time, and demonstrate their approach using a drone navigation example.
Authors
Neng Li, Zuodong Pan, Jiaxing Wang, Weiguo Xia, Wei Ren
Abstract
This paper investigates the optimal safety control problem of nonlinear control systems by proposing novel high-order control barrier functions (HOCBFs). Different from zeroing HOCBFs, two novel HOCBFs are derived and the safety controllers are designed in an explicit way. Next, we implement vector Lyapunov function approach to propose a novel high-order control Lyapunov function (HOCLF) for the stabilization control problem. The relations between the proposed and existing HOCBFs are discussed. Afterwards, the compatibility of the proposed HOCLF and HOCBF is addressed to guarantee the stabilization and safety control objectives simultaneously, and thus the optimal controller is established. Finally, a numerical example from the navigation problem of quadrotors is presented to illustrate the efficacy of the derived results.