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Domain Adaptive Safety Filters via Deep Operator Learning

Lakshmideepakreddy Manda, Shaoru Chen, Mahyar Fazlyab

TL;DR

This work proposes a self-supervised deep operator learning framework that learns the mapping from environmental parameters to the corresponding CBF, rather than learning the CBF directly, using the residual of a parametric Partial Differential Equation (PDE).

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.

Domain Adaptive Safety Filters via Deep Operator Learning

TL;DR

This work proposes a self-supervised deep operator learning framework that learns the mapping from environmental parameters to the corresponding CBF, rather than learning the CBF directly, using the residual of a parametric Partial Differential Equation (PDE).

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.

Paper Structure

This paper contains 18 sections, 33 equations, 2 figures.

Table of Contents

  1. introduction
  2. Literature Review
  3. CBF synthesis
  4. Adaptive CBF
  5. Notation
  6. Background
  7. Control Barrier Functions (CBFs)
  8. Neural Network-based CBF
  9. Performance-Oriented CBF via HJ PDE
  10. Main Idea: Domain Adaptation via Operator Learning
  11. Training Loss Function
  12. CBF Parameterization
  13. Complex Enviroments
  14. Pipeline
  15. Experiments
  16. ...and 3 more sections

Figures (2)

  • Figure 1: start state, target state, zero contour of the CBF instance $h_{\theta}(\cdot,e)$, horizontal-axis (position) and vertical-axis (velocity). The circular obstacles are marked black. For each environment, the CBF value $h_\theta(\cdot, e)$ is denoted by the color, with red denoting high values and blue denoting low values.
  • Figure 2: : start state. : target state. The horizontal and vertical axes denote the position of the unicycle, and the arrow denotes its orientation. Top row: An obstacle moves from left to right trying to block the agent. Bottom row: the smaller obstacle chases the agent while the bigger obstacle moves slowly and grows over time. During motion, the CBF operator value changes in response to the moving obstacles. The heatmap on the arrows indicates the CBF values along the trajectory, with warmer colors denoting higher values.

Theorems & Definitions (1)

  • Example 1