ProBF: Learning Probabilistic Safety Certificates with Barrier Functions

Athindran Ramesh Kumar, Sulin Liu, Jaime Fernández Fisac, Ryan P Adams, Peter Ramadge

Abstract:

Safety-critical applications require controllers/policies that can guarantee safety
with high confidence. The control barrier function is a useful tool to guarantee
safety if we have access to the ground-truth system dynamics. In practice, we
have inaccurate knowledge of the system dynamics, which can lead to unsafe
behaviors due to unmodeled residual dynamics. Learning the residual dynamics
with deterministic machine learning models can prevent the unsafe behavior but can
fail when the predictions are imperfect. In this situation, a probabilistic learning
method that reasons about the uncertainty of its predictions can help provide
robust safety margins. In this work, we use a Gaussian process to model the
projection of the residual dynamics onto a control barrier function. We propose a
novel optimization procedure to generate safe controls that can guarantee safety
with high probability. The safety filter is provided with the ability to reason
about the uncertainty of the predictions from the GP. We show the efficacy of this
method through experiments on Segway and Quadrotor simulations. Our proposed
probabilistic approach is able to reduce the number of safety violations significantly
as compared to the deterministic approach with a neural network.