Safe Online Dynamics Learning with Initially Unknown Models and Infeasible Safety Certificates

TL;DR

This paper introduces a novel learning-based safety control method that guarantees safety even when initial safety certificates are infeasible, by actively exploring system dynamics to recover feasibility without prior models.

Contribution

It presents the first algorithm that ensures safety with initially infeasible safety certificates by exploring dynamics and recovering feasibility without prior models or backup controllers.

Findings

Guarantees safety despite infeasible initial certificates

Recovers feasibility through system exploration and Bayesian optimization

No need for prior models or backup controllers

Abstract

Safety-critical control tasks with high levels of uncertainty are becoming increasingly common. Typically, techniques that guarantee safety during learning and control utilize constraint-based safety certificates, which can be leveraged to compute safe control inputs. However, excessive model uncertainty can render robust safety certification methods or infeasible, meaning no control input satisfies the constraints imposed by the safety certificate. This paper considers a learning-based setting with a robust safety certificate based on a control barrier function (CBF) second-order cone program. If the control barrier function certificate is feasible, our approach leverages it to guarantee safety. Otherwise, our method explores the system dynamics to collect data and recover the feasibility of the control barrier function constraint. To this end, we employ a method inspired by well-established tools from Bayesian optimization. We show that if the sampling frequency is high enough, we recover the feasibility of the robust CBF certificate, guaranteeing safety. Our approach requires no prior model and corresponds, to the best of our knowledge, to the first algorithm that guarantees safety in settings with occasionally infeasible safety certificates without requiring a backup non-learning-based controller.