Domain Adaptive Safety Filters via Deep Operator Learning

TL;DR

This paper introduces a self-supervised deep operator learning framework that adaptively constructs Control Barrier Functions for safety-critical control, enabling better generalization to unseen environments and complex safety constraints.

Contribution

It proposes a novel approach that learns the mapping from environmental parameters to CBFs using PDE residuals, improving adaptability over traditional methods.

Findings

Effective in navigation tasks with dynamic obstacles

Handles complex safety constraints and actuation limits

Demonstrates improved adaptability to unseen environments

Abstract

Learning-based approaches for constructing Control Barrier Functions (CBFs) are increasingly being explored for safety-critical control systems. However, these methods typically require complete retraining when applied to unseen environments, limiting their adaptability. To address this, we propose a self-supervised deep operator learning framework that learns the mapping from environmental parameters to the corresponding CBF, rather than learning the CBF directly. Our approach leverages the residual of a parametric Partial Differential Equation (PDE), where the solution defines a parametric CBF approximating the maximal control invariant set. This framework accommodates complex safety constraints, higher relative degrees, and actuation limits. We demonstrate the effectiveness of the method through numerical experiments on navigation tasks involving dynamic obstacles.