Safe Backstepping with Control Barrier Functions

TL;DR

This paper introduces a novel control design method called Control Barrier Function Backstepping, which simplifies safety-critical controller synthesis for higher-order nonlinear systems by integrating CBFs with Lyapunov backstepping.

Contribution

It presents a constructive framework for designing safety-critical controllers for higher-order systems by combining CBFs with Lyapunov backstepping techniques.

Findings

Effective safety guarantees demonstrated in simulation.

Framework simplifies controller synthesis for complex systems.

Joint stability and safety achieved through integrated design.

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 safety-critical 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 higher-order 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.