This book presents the concept of Control Barrier Function (CBF), which captures the evolution of safety requirements during the execution of a system and can be used to enforce safety. Safety is formalized using an emerging state-of-the-art approach based on CBFs, and many illustrative examples from autonomous driving, traffic control, and robot control are provided. Safety is central to autonomous systems since they are intended to operate with minimal or no human supervision, and a single failure could result in catastrophic results. The authors discuss how safety can be guaranteed via both theoretical and application perspectives. This presented method is computationally efficient and can be easily implemented in real-time systems that require high-frequency reactive control. In addition, the CBF approach can easily deal with nonlinear models and complex constraints used in a wide spectrum of applications, including autonomous driving, robotics, and traffic control. With the proliferation of autonomous systems, such as self-driving cars, mobile robots, and unmanned air vehicles, safety plays a crucial role in ensuring their widespread adoption. This book considers the integration of safety guarantees into the operation of such systems including typical safety requirements that involve collision avoidance, technological system limitations, and bounds on real-time executions. Adaptive approaches for safety are also proposed for time-varying execution bounds and noisy dynamics.
Author(s): Wei Xiao, Christos G. Cassandras, Calin Belta
Series: Synthesis Lectures on Computer Science
Publisher: Springer
Year: 2023
Language: English
Pages: 227
City: Cham
Preface
About This Book
Book Organization
Acknowledgements
Contents
About the Authors
1 Introduction to Autonomy and Safety
[DELETE]
2 Control Barrier Functions
2.1 Barrier Functions
2.1.1 Barrier Functions in Optimization
2.1.2 Barrier Functions for Safety Verification
2.2 Lyapunov-Like Barrier Functions
2.3 Control Barrier Functions
2.4 Control Lyapunov Functions
2.5 Constrained Optimal Control Problem
2.5.1 CBF-Based Approach
2.5.2 Feasibility in the CBF-Based Approach
2.5.3 Time-Driven and Event-Driven CBFs
3 High Order Control Barrier Functions
3.1 High Order Barrier Functions
3.2 High Order Control Barrier Functions (HOCBFs)
3.3 ACC Using HOCBFs
3.4 HOCBFs for Systems with Multiple Inputs
3.5 Robot Control Using iHOCBFs
4 Feasibility Guarantees for CBF-Based Optimal Control
4.1 The Penalty Method
4.2 Sufficient Conditions for Feasibility
4.2.1 Feasibility Conditions for Constraints with Relative Degree One
4.2.2 Feasibility Conditions for Safety Constraints with High Relative Degree
4.3 Feasibility Conditions for ACC
5 Feasibility for CBF-Based Optimal Control Using Machine Learning
5.1 Learning CBF Parameters for Feasibility
5.1.1 Feasibility Robustness
5.1.2 Online HOCBF and CLF-Based QP (SP1)
5.1.3 The Parameterization Method
5.1.4 Offline Feasibility-Guided Optimization (SP2)
5.1.5 Robot Control Using Feasibility-Guided Optimization
5.2 Learning Feasibility Constraints
5.2.1 Regular and Irregular Unsafe Sets
5.2.2 Feasible and Infeasible State Sets
5.2.3 Sampling and Classification
5.2.4 Feedback Training
5.2.5 Generalization
5.2.6 Robot Control by Learning Feasibility Constraints
6 Adaptive Control Barrier Functions
6.1 Adaptive Control
6.2 Parameter-Adaptive Control Barrier Functions (PACBFs)
6.2.1 Adaptivity to Changing Control Bounds and Noisy Dynamics
6.2.2 Optimal Control with PACBFs
6.2.3 Adaptive Control for ACC
6.3 Relaxation-Adaptive Control Barrier Functions
6.3.1 Optimal Control with RACBFs
6.3.2 Comparison Between PACBF and RACBF
6.3.3 Control for ACC Using RACBF
7 Safety Guarantees for Systems with Unknown Dynamics: An Event-Driven Framework
7.1 Adaptive Affine Dynamics
7.2 Event-Driven Control
7.2.1 Relative-Degree-One Constraints
7.2.2 High-Relative-Degree Constraints
7.2.3 Extension to Multi-agent Systems
7.3 ACC with Unknown Vehicle Dynamics
8 Hierarchical Optimal Control with Barrier Functions
[DELETE]
8.1 Problem Formulation and Approach
8.2 From Planning to Execution of Optimal Trajectories
8.2.1 Optimal Trajectory Planning
8.2.2 Safety-Guaranteed Optimal Control with HOCBFs
8.2.3 Constraint Violations Due to Noise
9 Applications to Autonomous Vehicles in Traffic Networks
[DELETE]
9.1 Traffic Merging
9.1.1 Traffic Merging Control as an Optimal Control Problem
9.1.2 Decentralized Online Control
9.1.3 Simulation Results for Traffic Merging Control
9.2 Roundabout Traffic Control
9.2.1 Roundabout Traffic Control as an Optimal Control Problem
9.2.2 Decentralized Online Control
9.2.3 Simulation Results for Traffic Control in Roundabouts
9.3 Multi-lane Signal-Free Intersections
9.3.1 Multi-lane Signal-Free Intersection Traffic Control as an Optimal Control Problem
9.3.2 Decentralized Online Control Framework
9.3.3 Simulation Results for Traffic Control in Intersections
10 Applications to Robotics
10.1 Ground Robot Obstacle Avoidance
10.1.1 Feasibility Robustness
10.1.2 Safe Exploration in an Unknown Environment
10.2 Rule-Based Autonomous Driving
10.2.1 Problem Formulation
10.2.2 Rules and Priority Structures
10.2.3 Rule-Based Optimal Control
10.2.4 Simulation Examples
10.3 Quadrotor Safe Navigation
References
Index
