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

2024-09-22

arXiv.org

AI Summary

Ensuring safety for input-constrained nonlinear systems remains challenging due to the difficulty of constructing feasible, non-conservative control barrier functions (CBFs). Method: This paper proposes a learning-based online adaptive integrated CBF (ICCBF) framework. It introduces a probabilistic ensemble neural network prediction model that jointly captures epistemic and aleatoric uncertainties, and designs a two-step verification mechanism leveraging Jensen–Rényi divergence and distributionally robust conditional value-at-risk (CVaR) to dynamically select state-dependent safety parameters. Under discrete-time nonlinear system modeling, the ICCBF’s class-K function parameters are optimized in real time. Contribution/Results: In multi-robot navigation experiments, the approach achieves zero safety violations, improves trajectory smoothness by 23%, and accelerates convergence by 18%, significantly outperforming both fixed-parameter and existing adaptive CBF methods.

Technology Category

• Intelligent Robots: State Estimation
• Natural Language Processing: Safety and Robustness
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Ensuring safety in nonlinear systems with input constraints
• Overcoming conservative behavior or safety violations in CBF-based controllers
• Dynamic refinement of ICCBF parameters for optimized performance and safety

Innovation

• Online adaptation of ICCBF parameters using neural networks
• Two-step verification with Jensen-Renyi Divergence and CVaR
• Dynamic refinement of parameters for safety and performance