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This tutorial paper presents recent work of the authors that extends the theory of Control Barrier Functions (CBFs) to address practical challenges in the synthesis of safe controllers for autonomous systems and robots. We present novel…

This paper introduces the notion of an Input Constrained Control Barrier Function (ICCBF), as a method to synthesize safety-critical controllers for non-linear control affine systems with input constraints. The method identifies a subset of…

Safety filters based on Control Barrier Functions (CBFs) provide formal guarantees of forward invariance, but are often difficult to implement in networked dynamical systems. This is due to global coupling and communication requirements.…

This paper presents a safe controller synthesis of discrete-time stochastic systems using Control Barrier Functions (CBFs). The proposed condition allows the design of a safe controller synthesis that ensures system safety while avoiding…

This paper presents a framework for designing provably safe feedback controllers for sampled-data control affine systems with measurement and actuation uncertainties. Based on the interval Taylor model of nonlinear functions, a sampled-data…

Control Barrier Functions (CBFs) have been demonstrated to be a powerful tool for safety-critical controller design for nonlinear systems. Existing design paradigms do not address the gap between theory (controller design with continuous…

Control Barrier Functions (CBFs) enforce safety by rendering a prescribed safe set forward invariant. However, standard CBFs are limited to safety constraints with relative degree one, while High-Order CBF (HOCBF) methods address higher…

A common tool in system theory for formulating control laws that achieve local asymptotic stability are Control Lyapunov functions (CLFs), while Control Barrier functions (CBFs) are typically employed to enforce safety constraints.…

We consider the problem of designing controllers to guarantee safety in a class of nonlinear systems under uncertainties in the system dynamics and/or the environment. We define a class of uncertain control barrier functions (CBFs), and…

Safety is a fundamental requirement of control systems. Control Barrier Functions (CBFs) are proposed to ensure the safety of the control system by constructing safety filters or synthesizing control inputs. However, the safety guarantee…

This paper presents a new approach for guaranteed safety subject to input constraints (e.g., actuator limits) using a composition of multiple control barrier functions (CBFs). First, we present a method for constructing a single CBF from…

Control Barrier Functions (CBFs) are a practical approach for designing safety-critical controllers, but constructing them for arbitrary nonlinear dynamical systems remains a challenge. Recent efforts have explored learning-based methods,…

Industrial control applications require high performance under strict constraints. Control barrier functions (CBFs) provide principled safety mechanisms, but constructing CBF-based safety filters for large-scale systems is challenging. We…

Control barrier functions guarantee safety but typically require accurate system models. Parametric uncertainty invalidates these guarantees. Existing robust methods maintain safety via worst-case bounds, limiting performance, while modular…

This paper addresses the challenge of ensuring safety and feasibility in control systems using Control Barrier Functions (CBFs). Existing CBF-based Quadratic Programs (CBF-QPs) often encounter feasibility issues due to mixed relative degree…

Using control barrier functions (CBFs) as safety filters provides a computationally inexpensive yet effective method for constructing controllers in safety-critical applications. However, using CBFs requires the construction of a valid CBF,…

Control barrier functions (CBFs) have recently been introduced as a systematic tool to ensure safety by establishing set invariance. When combined with a control Lyapunov function (CLF), they form a safety-critical control mechanism.…

This paper addresses the challenge of ensuring safety in stochastic control systems with high-relative-degree constraints, while maintaining feasibility and mitigating conservatism in risk evaluation. Control Barrier Functions (CBFs)…

Control Barrier Functions (CBFs) have emerged as a powerful paradigm in control theory, providing a principled approach to enforcing safety-critical constraints in dynamic systems. This survey paper comprehensively explores the foundational…

Safety has been a critical issue for the deployment of learning-based approaches in real-world applications. To address this issue, control barrier function (CBF) and its variants have attracted extensive attention for safety-critical…