This paper addresses learning safe control laws from expert demonstrations.
We assume that appropriate models of the system dynamics and the output
measurement map are available, along with corresponding error bounds. We first
propose robust output control barrier functions (ROCBFs) as a means to
guarantee safety, as defined through controlled forward invariance of a safe
set. We then present an optimization problem to learn ROCBFs from expert
demonstrations that exhibit safe system behavior, e.g., data collected from a
human operator. Along with the optimization problem, we provide verifiable
conditions that guarantee validity of the obtained ROCBF. These conditions are
stated in terms of the density of the data and on Lipschitz and boundedness
constants of the learned function and the models of the system dynamics and the
output measurement map. When the parametrization of the ROCBF is linear, then,
under mild assumptions, the optimization problem is convex. We validate our
findings in the autonomous driving simulator CARLA and show how to learn safe
control laws from RGB camera images.

本文就如何通过 ROCBF 来学习安全控制法则进行探讨。同时，提出了从专家演示中学习 ROCBFs 的优化问题，并提供确保 ROCBF 有效性的可验证条件。最后，在 CARLA 自动驾驶模拟器中验证了该发现，并展示了如何通过 RGB 相机图像学习安全控制法则。