State-Action Control Barrier Functions

Abstract

Learning-based control with safety guarantees usually requires real-time safety certification and modifications of possibly unsafe learning-based policies. The control barrier function (CBF) method uses a safety filter (SF) containing a constrained optimization problem to produce safe policies. However, finding a valid CBF for a general nonlinear system requires a complex function parameterization, which in general makes the policy optimization problem difficult to solve in real time. For nonlinear systems with nonlinear state constraints, this paper proposes the novel concept of state-action CBFs (SACBFs), which do not only characterize the safety at each state but also evaluate the control inputs taken at each state. SACBFs, in contrast to CBFs, enable a flexible parameterization, resulting in a SF that involves a convex quadratic optimization problem, which significantly alleviates the online computational burden. We propose a learning-based approach to synthesize SACBFs. The effect of learning errors on the effectiveness of SACBFs is addressed by constraint tightening and introducing a new concept called contractive-set CBFs. This ensures formal safety guarantees for the learned CBFs and control policies. Simulation results on an inverted pendulum with elastic walls validate the proposed CBFs in terms of constraint satisfaction and CPU time.