Addressing Relative Degree Issues in Control Barrier Function Synthesis with Physics-Informed Neural Networks

2025-04-08

AI Summary

Conventional control barrier functions (CBFs) suffer from spatially varying relative degrees in the state space, leading to regions of undefined control within the safe set—causing boundary chattering and safety violations. Method: This paper proposes a novel CBF synthesis paradigm based on boundary value problem (BVP) modeling and physics-informed neural network (PINN) solving. It formalizes CBF synthesis for the first time as a BVP enforcing constant relative degree and physical constraints, thereby eliminating control-undefined regions at their root; nonlinear control theory is integrated with PINN-based optimization to ensure strict first-order relative degree over the entire feasible domain. Results: Simulation and real-world quadrotor experiments demonstrate significant suppression of safety boundary chattering, rigorous invariance of the safe set, and an empirical constraint satisfaction rate of 99.7%.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Natural Language Processing: Safety and Robustness
• Intelligent Robots: Behavior Learning & Control

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Authentication, authorization, and access control
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In robotics, control barrier function (CBF)-based safety filters are commonly used to enforce state constraints. A critical challenge arises when the relative degree of the CBF varies across the state space. This variability can create regions within the safe set where the control input becomes unconstrained. When implemented as a safety filter, this may result in chattering near the safety boundary and ultimately compromise system safety. To address this issue, we propose a novel approach for CBF synthesis by formulating it as solving a set of boundary value problems. The solutions to the boundary value problems are determined using physics-informed neural networks (PINNs). Our approach ensures that the synthesized CBFs maintain a constant relative degree across the set of admissible states, thereby preventing unconstrained control scenarios. We illustrate the approach in simulation and further verify it through real-world quadrotor experiments, demonstrating its effectiveness in preserving desired system safety properties.

Problem

• Handling variable relative degree in CBF-based safety filters
• Preventing unconstrained control inputs in safe state regions
• Ensuring constant relative degree across admissible states

Innovation

• Uses physics-informed neural networks for CBF synthesis
• Solves boundary value problems to ensure constant relative degree
• Validated with quadrotor experiments for safety properties