Safe Neural Control for Non-Affine Control Systems with Differentiable Control Barrier Functions

TL;DR

This paper introduces a neural network-based approach using differentiable High Order Control Barrier Functions to ensure safety in non-affine control systems, overcoming limitations of traditional CBF methods.

Contribution

It integrates higher-order CBFs into neural ODE models as trainable, differentiable functions, enabling safety guarantees and learning complex control policies for non-affine systems.

Findings

Effective safety guarantees in autonomous driving scenarios

Outperforms existing CBF-based methods in safety and control quality

Learned control policies are complex and near-optimal

Abstract

This paper addresses the problem of safety-critical control for non-affine control systems. It has been shown that optimizing quadratic costs subject to state and control constraints can be sub-optimally reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs). Our recently proposed High Order CBFs (HOCBFs) can accommodate constraints of arbitrary relative degree. The main challenges in this approach are that it requires affine control dynamics and the solution of the CBF-based QP is sub-optimal since it is solved point-wise. To address these challenges, we incorporate higher-order CBFs into neural ordinary differential equation-based learning models as differentiable CBFs to guarantee safety for non-affine control systems. The differentiable CBFs are trainable in terms of their parameters, and thus, they can address the conservativeness of CBFs such that the system state will not stay unnecessarily far away from safe set boundaries. Moreover, the imitation learning model is capable of learning complex and optimal control policies that are usually intractable online. We illustrate the effectiveness of the proposed framework on LiDAR-based autonomous driving and compare it with existing methods.