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Learning to Refine Input Constrained Control Barrier Functions via Uncertainty-Aware Online Parameter Adaptation

Taekyung Kim, Robin Inho Kee, Dimitra Panagou

TL;DR

This work addresses safety-critical control for discrete-time nonlinear systems under input constraints by learning to adapt the class $\mathcal{K}$ functions of ICCBFs online. It introduces a Probabilistic Ensemble Neural Network (PENN) to predict safety and performance metrics for candidate parameterizations, and uses Jensen-Renyi Divergence and distributionally robust CVaR to filter valid parameters. An online MPC-ICCBF framework updates the parameters in real time to balance safety guarantees with performance in navigation tasks. Experiments show the proposed method outperforms fixed-parameter and other adaptive approaches in collision avoidance and goal achievement.

Abstract

Control Barrier Functions (CBFs) have become powerful tools for ensuring safety in nonlinear systems. However, finding valid CBFs that guarantee persistent safety and feasibility remains an open challenge, especially in systems with input constraints. Traditional approaches often rely on manually tuning the parameters of the class K functions of the CBF conditions a priori. The performance of CBF-based controllers is highly sensitive to these fixed parameters, potentially leading to overly conservative behavior or safety violations. To overcome these issues, this paper introduces a learning-based optimal control framework for online adaptation of Input Constrained CBF (ICCBF) parameters in discrete-time nonlinear systems. Our method employs a probabilistic ensemble neural network to predict the performance and risk metrics, as defined in this work, for candidate parameters, accounting for both epistemic and aleatoric uncertainties. We propose a two-step verification process using Jensen-Renyi Divergence and distributionally-robust Conditional Value at Risk to identify valid parameters. This enables dynamic refinement of ICCBF parameters based on current state and nearby environments, optimizing performance while ensuring safety within the verified parameter set. Experimental results demonstrate that our method outperforms both fixed-parameter and existing adaptive methods in robot navigation scenarios across safety and performance metrics.

Learning to Refine Input Constrained Control Barrier Functions via Uncertainty-Aware Online Parameter Adaptation

TL;DR

This work addresses safety-critical control for discrete-time nonlinear systems under input constraints by learning to adapt the class functions of ICCBFs online. It introduces a Probabilistic Ensemble Neural Network (PENN) to predict safety and performance metrics for candidate parameterizations, and uses Jensen-Renyi Divergence and distributionally robust CVaR to filter valid parameters. An online MPC-ICCBF framework updates the parameters in real time to balance safety guarantees with performance in navigation tasks. Experiments show the proposed method outperforms fixed-parameter and other adaptive approaches in collision avoidance and goal achievement.

Abstract

Control Barrier Functions (CBFs) have become powerful tools for ensuring safety in nonlinear systems. However, finding valid CBFs that guarantee persistent safety and feasibility remains an open challenge, especially in systems with input constraints. Traditional approaches often rely on manually tuning the parameters of the class K functions of the CBF conditions a priori. The performance of CBF-based controllers is highly sensitive to these fixed parameters, potentially leading to overly conservative behavior or safety violations. To overcome these issues, this paper introduces a learning-based optimal control framework for online adaptation of Input Constrained CBF (ICCBF) parameters in discrete-time nonlinear systems. Our method employs a probabilistic ensemble neural network to predict the performance and risk metrics, as defined in this work, for candidate parameters, accounting for both epistemic and aleatoric uncertainties. We propose a two-step verification process using Jensen-Renyi Divergence and distributionally-robust Conditional Value at Risk to identify valid parameters. This enables dynamic refinement of ICCBF parameters based on current state and nearby environments, optimizing performance while ensuring safety within the verified parameter set. Experimental results demonstrate that our method outperforms both fixed-parameter and existing adaptive methods in robot navigation scenarios across safety and performance metrics.
Paper Structure (17 sections, 2 theorems, 27 equations, 2 figures, 1 table, 1 algorithm)

This paper contains 17 sections, 2 theorems, 27 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. PROBLEM FORMULATION
  4. Input Constrained Control Barrier Functions
  5. Problem Setup
  6. METHODOLOGY
  7. Safety Loss Density Function
  8. Training Data Generation - Offline Sampling
  9. Probabilistic Ensemble Neural Network Model
  10. Uncertainty-Aware Class $\mathcal{K}$ Functions Verification
  11. Epistemic Uncertainty Quantification
  12. Distributionally Robust Risk Assessment
  13. Online Parameter Adaptation
  14. RESULTS
  15. Experimental Setup
  16. ...and 2 more sections

Key Result

Lemma 1

Given a discrete-time CBF $h$ satisfying condition eq:cbf with the associated set $\mathcal{S}$, any control input ${\boldsymbol u}_t \in K_\textup{cbf}({\boldsymbol x}_t)$, with $K_\textup{cbf}({\boldsymbol x}_t) \coloneqq \{{\boldsymbol u}_t \in \mathcal{U} : \Delta h({\boldsymbol x}_t, {\boldsymb

Figures (2)

  • Figure 1: Visualization of robot trajectories generated by five different approaches and class $\mathcal{K}$ function parameters refined over time by our online adaptive MPC-ICCBF method. The blue and yellow squares represent the start and goal location. The black circles represent the obstacles.
  • Figure 2: Visualization of robot trajectories in a more complex environment.

Theorems & Definitions (11)

  • Definition 1: Discrete-Time CBF agrawal_discrete_2017
  • Lemma 1
  • Remark 1
  • Definition 2: Inner Safe Set
  • Definition 3: Discrete-Time ICCBF
  • Remark 2
  • Lemma 2
  • Remark 3
  • Definition 4: Locally Valid Class $\mathcal{K}$ Functions
  • Example 1
  • ...and 1 more