Safety-Critical Control for Autonomous Systems: Constructing Control Barrier Functions via Reduced-Order Models

Core Concepts

Constructing control barrier functions via reduced-order models enhances safety-critical control in high-dimensional autonomous systems.

Abstract

The paper discusses the challenges of safety-critical control in modern autonomous systems with high-dimensional dynamics. It introduces the concept of control barrier functions (CBFs) and reduced-order models to address these challenges. By constructing CBFs for simpler systems and relating them back to complex systems, safety can be ensured efficiently. The tutorial provides a detailed overview, theoretical foundations, and practical applications of CBF techniques based on ROMs. Various case studies and examples illustrate the effectiveness of this approach in controlling complex robotic systems.

Stats

Modern autonomous systems have high-dimensional nonlinear dynamics. Safety-critical controllers ensure system specifications are met. Control barrier functions (CBFs) are powerful tools for designing safety-critical controllers. Constructing CBFs for high-dimensional systems remains a challenge. Reduced-order models (ROMs) simplify the synthesis of safety-critical controllers.

Quotes

"CBFs have emerged as a powerful tool for designing controllers that ensure the safety of autonomous systems." "Reduced-order models have demonstrated success in controlling seemingly complex systems in a computationally efficient manner." "Constructing CBFs based on ROMs enhances safety-critical control design."

Key Insights Distilled From

Safety-Critical Control for Autonomous Systems

by Max H. Cohen... at arxiv.org 03-18-2024

https://arxiv.org/pdf/2403.09865.pdf

Deeper Inquiries

How can learning-based techniques be effectively used to construct CBFs from data

Learning-based techniques can be effectively used to construct Control Barrier Functions (CBFs) from data by leveraging machine learning algorithms, such as neural networks. These techniques involve training a model to approximate the CBF using data collected from expert demonstrations or simulations. The process typically involves defining a loss function that captures the constraints imposed by the CBF conditions and optimizing the parameters of the neural network to minimize this loss. By training a neural network on a dataset that includes state-action pairs along with corresponding safety labels based on CBF conditions, the model can learn to predict safe control actions for different states of the system. This approach allows for flexibility in handling complex dynamics and uncertainties in real-world systems where analytical solutions may be challenging to derive. Furthermore, reinforcement learning methods can also be employed to learn CBFs through interaction with an environment. By rewarding safe behavior and penalizing unsafe actions during training, agents can learn policies that satisfy safety constraints defined by CBFs.

What are the limitations of extended CBFs, and how can they be addressed

Extended Control Barrier Functions (CBFs) have limitations when it comes to verifying if they satisfy necessary conditions for ensuring system safety due to their high relative degree constraint functions. These extended CBFs require differentiation until control inputs appear, which can make verification challenging and computationally intensive. To address these limitations, one approach is to leverage structural properties present in certain classes of systems when constructing CBFs. By exploiting specific characteristics of system dynamics or utilizing implicit definitions of barrier functions through receding-horizon optimization approaches, it becomes possible to simplify construction while maintaining safety guarantees. Additionally, combining multiple constructive techniques like Lyapunov backstepping with extended CBFs or developing backup strategies for enforcing safety under uncertain conditions can help overcome some limitations associated with extended versions of Control Barrier Functions.

How does the concept of model-free safety-critical control relate to traditional control methods

Model-free safety-critical control represents an alternative paradigm compared to traditional model-based control methods by focusing on constructing controllers without directly relying on full-order dynamics models. Instead of explicitly modeling complex high-dimensional systems, model-free approaches use reduced-order models (ROMs) combined with Lyapunov functions certifying tracking between ROM trajectories and full-order dynamics. This concept allows for more computationally efficient controller synthesis since simplified models are utilized initially before refining them for higher-dimensional systems' dynamic behaviors. Model-free safety-critical control leverages insights from robotics applications where simple kinematic models are used as building blocks for controlling more complicated robotic systems efficiently. By decoupling controller design from detailed system modeling requirements and emphasizing tracking performance over explicit knowledge of full-system dynamics, model-free approaches offer flexibility in addressing uncertainty and complexity challenges commonly encountered in autonomous systems' control design processes.