Learning Performance-oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation

Lakshmideepakreddy Manda, Shaoru Chen, Mahyar Fazlyab

Keywords: Control Barrier Functions, Safety, Hamilton-Jacobi Partial Differential Equation

TL;DR: We use Hamilton-Jacobi PDEs to learn Control Barrier Functions for complex environments

Abstract: Control Barrier Functions (CBFs) offer an elegant framework for constraining nonlinear control system dynamics to an invariant subset of a pre-specified safe set. However, finding a CBF that simultaneously promotes performance by maximizing the resulting control invariant set while accommodating complex safety constraints, especially in high relative degree systems with actuation constraints, remains a significant challenge. In this work, we propose a novel self-supervised learning framework that holistically addresses these hurdles. Given a Boolean composition of multiple state constraints defining the safe set, our approach begins by constructing a smooth function whose zero superlevel set provides an inner approximation of the safe set. This function is then used with a smooth neural network to parameterize the CBF candidate. Finally, we design a physics-informed training loss function based on a Hamilton-Jacobi Partial Differential Equation (PDE) to train the PINN-CBF and enlarge the volume of the induced control invariant set. We demonstrate the effectiveness of our approach on a 2D double integrator (DI) system and a 7D fixed-wing aircraft system (F16).

Code: https://github.com/o4lc/PINN-CBF

Student Paper: yes

Submission Number: 404