Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Learning Local Control Barrier Functions for Hybrid Systems

Shuo Yang, Yu Chen, Xiang Yin, George J. Pappas, Rahul Mangharam

TL;DR

This work tackles safety in hybrid dynamical systems by learning a local Control Barrier Function (CBF) refinement that scales to high dimensions. Building on local CBFs, it introduces a Control Barrier-Value Function (CBVF) learned via neural PDE solvers to approximate the Hamilton–Jacobi–Isaacs VI without grid-based methods, enabling safe switching in complex multi-mode systems. The approach yields a neural switch-aware safety controller that closely matches MPC performance while dramatically reducing online computation, demonstrated in high-dimensional autonomous racing and ACC with multi-friction roads. It also shows that standard backward-unsafe set computations can be avoided, simplifying safety synthesis. The results indicate substantial practical impact for real-time safety in large-scale robotic systems, with public code and extensive experimental validation.

Abstract

Hybrid dynamical systems are ubiquitous as practical robotic applications often involve both continuous states and discrete switchings. Safety is a primary concern for hybrid robotic systems. Existing safety-critical control approaches for hybrid systems are either computationally inefficient, detrimental to system performance, or limited to small-scale systems. To amend these drawbacks, in this paper, we propose a learning-enabled approach to construct local Control Barrier Functions (CBFs) to guarantee the safety of a wide class of nonlinear hybrid dynamical systems. The end result is a safe neural CBF-based switching controller. Our approach is computationally efficient, minimally invasive to any reference controller, and applicable to large-scale systems. We empirically evaluate our framework and demonstrate its efficacy and flexibility through two robotic examples including a high-dimensional autonomous racing case, against other CBF-based approaches and model predictive control.

Learning Local Control Barrier Functions for Hybrid Systems

TL;DR

This work tackles safety in hybrid dynamical systems by learning a local Control Barrier Function (CBF) refinement that scales to high dimensions. Building on local CBFs, it introduces a Control Barrier-Value Function (CBVF) learned via neural PDE solvers to approximate the Hamilton–Jacobi–Isaacs VI without grid-based methods, enabling safe switching in complex multi-mode systems. The approach yields a neural switch-aware safety controller that closely matches MPC performance while dramatically reducing online computation, demonstrated in high-dimensional autonomous racing and ACC with multi-friction roads. It also shows that standard backward-unsafe set computations can be avoided, simplifying safety synthesis. The results indicate substantial practical impact for real-time safety in large-scale robotic systems, with public code and extensive experimental validation.

Abstract

Hybrid dynamical systems are ubiquitous as practical robotic applications often involve both continuous states and discrete switchings. Safety is a primary concern for hybrid robotic systems. Existing safety-critical control approaches for hybrid systems are either computationally inefficient, detrimental to system performance, or limited to small-scale systems. To amend these drawbacks, in this paper, we propose a learning-enabled approach to construct local Control Barrier Functions (CBFs) to guarantee the safety of a wide class of nonlinear hybrid dynamical systems. The end result is a safe neural CBF-based switching controller. Our approach is computationally efficient, minimally invasive to any reference controller, and applicable to large-scale systems. We empirically evaluate our framework and demonstrate its efficacy and flexibility through two robotic examples including a high-dimensional autonomous racing case, against other CBF-based approaches and model predictive control.
Paper Structure (18 sections, 5 theorems, 9 equations, 5 figures, 2 tables, 1 algorithm)

This paper contains 18 sections, 5 theorems, 9 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminary and Problem Formulation
  4. Control Barrier Functions
  5. Hybrid Systems
  6. Problem Formulation
  7. Methodology: Learning Local CBFs
  8. Local CBFs for Safety Control
  9. Learn to Refine Local CBFs
  10. Application in Multi-Modes Systems
  11. Numerical Experiments
  12. Adaptive Cruise Control
  13. 2D Autonomous Racing
  14. Conclusion and Discussion
  15. Appendix
  16. ...and 3 more sections

Key Result

Theorem 1

ames2016control Assume $h(x)$ is a CBF on $D \supset \mathcal{C}$. Then any Lipschitz continuous controller $u(x)$ such that $u(x) \in K_{cbf}(x)$ for all $x \in \mathcal{C}$ will render the set $\mathcal{C}$ forward invariant.

Figures (5)

  • Figure 1: (a)Hybrid System 1: no transition cycle. (b) Hybrid System 2: with a transition cycle. (c) An unfolded system from System 1. (d) Hybrid adaptive cruise control system. The switching conditions are when the position $p\ge 50$ and $p\ge 100$.
  • Figure 2: (a)Average mean square error of training outcome. (b) Safe and unsafe volume errors. (c) Multi-friction racing track. The trajectory from our approach is also presented.
  • Figure 3: Comparisons of different methods. The performance metrics of ACC and racing are trajectory cost and lap time (s) respectively.
  • Figure 4: Training results of adaptive cruise control. Left figure: DNN value for $p=95$; middle figure: ground truth for $p=95$; right figure: training loss curve.
  • Figure : Learning to Refine CBF

Theorems & Definitions (12)

  • Theorem 1
  • Definition 1: Hybrid Systems
  • Definition 2: Hybrid System Solution
  • Definition 3: Transition Safety
  • Definition 4: Global Safety
  • Definition 5
  • Theorem 2
  • Proposition 1
  • Theorem 3
  • proof
  • ...and 2 more