Safe Backstepping with Control Barrier Functions

Abstract

Complex control systems are often described in a layered fashion, represented as higher-order systems where the inputs appear after a chain of integrators. While Control Barrier Functions (CBFs) have proven to be powerful tools for safetycritical controller design of nonlinear systems, their application to higher-order systems adds complexity to the controller synthesis process-it necessitates dynamically extending the CBF to include higher order terms, which consequently modifies the safe set in complex ways. We propose an alternative approach for addressing safety of higher-order systems through Control Barrier Function Backstepping. Drawing inspiration from the method of Lyapunov backstepping, we provide a constructive framework for synthesizing safety-critical controllers and CBFs for higherorder systems from a top-level dynamics safety specification and controller design. Furthermore, we integrate the proposed method with Lyapunov backstepping, allowing the tasks of stability and safety to be expressed individually but achieved jointly. We demonstrate the efficacy of this approach in simulation.

Robust Control for Underactuated Fixed-Wing Unmanned Aerial Vehicles

“…To date, backstepping control (BSC) is a well-known powerful tool for high-order systems with essential nonlinearity [1,2]. The key idea behind BSC is decomposing the complex high-order system into subsystems whose order is lower than that of the origin system.…”