Learning a Better Control Barrier Function

TL;DR

This paper introduces a neural network-based method to improve control barrier functions (CBFs), making them less conservative and more efficient for safety-critical control, validated on two dynamic systems.

Contribution

The authors develop a novel approach starting from a conservative CBF to learn a less conservative, more accurate CBF using trajectory data and neural networks, ensuring safety during training with MPC.

Findings

Learned CBF recovers a larger portion of the safe set

Method reduces conservativeness of CBFs

Validated on second-order integrator and ball-on-beam systems

Abstract

Control barrier functions (CBFs) are widely used in safety-critical controllers. However, constructing a valid CBF is challenging, especially under nonlinear or non-convex constraints and for high relative degree systems. Meanwhile, finding a conservative CBF that only recovers a portion of the true safe set is usually possible. In this work, starting from a "conservative" handcrafted CBF (HCBF), we develop a method to find a CBF that recovers a reasonably larger portion of the safe set. Since the learned CBF controller is not guaranteed to be safe during training iterations, we use a model predictive controller (MPC) to ensure safety during training. Using the collected trajectory data containing safe and unsafe interactions, we train a neural network to estimate the difference between the HCBF and a CBF that recovers a closer solution to the true safe set. With our proposed approach, we can generate safe controllers that are less conservative and computationally more efficient. We validate our approach on two systems: a second-order integrator and a ball-on-beam.