Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation

Control barrier functions (CBFs) are a powerful tool to enforce safety constraints for nonlinear control systems (Ames et al., 2019), with many successful applications in autonomous driving (Xiao et al., 2021), UAV navigation (Xu and Sreenath, 2018), robot locomotion (Grandia et al., 2021), and safe reinforcement learning (Marvi and Kiumarsi, 2021). For control-affine nonlinear systems, CBFs can be used to construct a convex quadratic programming (QP)-based safety filter that can be deployed online to safeguard against potentially unsafe control commands. The induced safety filter, which we denote as CBF-QP, guarantees that the closed-loop system remains in a safe control invariant set by correcting a reference controller online. While CBFs provide an efficient method to ensure safety, in general, it is difficult to find such functions. As the complexity of both the environment and the dynamics increases, we are faced with the following challenges: (C1) Complex safety specifications: CBFs inherently handle single constraint functions, but complex environments often involve multiple constraints. In this work, we consider specifications that are described by the composition of multiple constraints through Boolean logical operations such as AND, OR, and negation, which can capture complex constraints. Shaoru Chen is with Microsoft Research, 300 Lafayette Street, New York, NY, 10012, USA.