Advances in the Theory of Control Barrier Functions: Addressing Practical Challenges in Safe Control Synthesis for Autonomous and Robotic Systems

TL;DR

This paper reviews recent advances in Control Barrier Functions (CBFs), addressing practical challenges in safe control for autonomous systems, including disturbances, input constraints, adversarial inputs, and implementation issues.

Contribution

The authors introduce novel CBF formulations and methods that handle complex safety constraints, disturbances, and real-world implementation challenges, enhancing safe control synthesis.

Findings

New CBFs for time and input constraints under disturbances

Methods to prevent loss of CBF validity and tune parameters online

Formulations accounting for future trajectories and non-smooth constraints

Abstract

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 CBFs and methods that handle safety constraints (i) with time and input constraints under disturbances, (ii) with high-relative degree under disturbances and input constraints, and (iii) that are affected by adversarial inputs and sampled-data effects. We then present novel CBFs and adaptation methods that prevent loss of validity of the CBF, as well as methods to tune the parameters of the CBF online to reduce conservatism in the system response. We also address the pointwise-only optimal character of CBF-induced control inputs by introducing a CBF formulation that accounts for future trajectories, as well as implementation challenges such as how to preserve safety when using output feedback control and zero-order-hold control. Finally we consider how to synthesize non-smooth CBFs when discontinuous inputs and multiple constraints are present.