ProBF: Learning Probabilistic Safety Certificates with Barrier Functions
This work addresses safety-critical applications in robotics and control by providing a probabilistic method to guarantee safety with high confidence, representing an incremental improvement over existing deterministic learning methods.
The paper tackles the problem of ensuring safety in control systems with inaccurate dynamics by learning residual dynamics with a probabilistic Gaussian process model, resulting in a significant reduction in safety violations compared to deterministic neural network approaches in Segway and quadrotor simulations.
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.