Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments

TL;DR

This paper introduces a differentiable control barrier function framework embedded in deep learning to enhance safety and generalization of control systems in novel environments, especially for high relative-degree systems.

Contribution

It proposes a novel differentiable safety-critical control method using ECBF-QP as a layer in neural networks, enabling better generalization and safety guarantees.

Findings

Successfully applied to 2D double integrator systems

Validated in various environments with high relative-degree systems

Achieved forward invariance guarantees in control design

Abstract

Control barrier functions (CBFs) have become a popular tool to enforce safety of a control system. CBFs are commonly utilized in a quadratic program formulation (CBF-QP) as safety-critical constraints. A class $\mathcal{K}$ function in CBFs usually needs to be tuned manually in order to balance the trade-off between performance and safety for each environment. However, this process is often heuristic and can become intractable for high relative-degree systems. Moreover, it prevents the CBF-QP from generalizing to different environments in the real world. By embedding the optimization procedure of the exponential control barrier function based quadratic program (ECBF-QP) as a differentiable layer within a deep learning architecture, we propose a differentiable safety-critical control framework that enables generalization to new environments for high relative-degree systems with forward invariance guarantees. Finally, we validate the proposed control design with 2D double and quadruple integrator systems in various environments.