Gaussian Control Barrier Functions: Non-Parametric Paradigm to Safety

Inspired by the success of control barrier functions (CBFs) in addressing safety, and rise data-driven techniques for modeling functions, we propose a non-parametric approach online synthesis CBFs using Gaussian Processes (GPs). A dynamical system is defined to be safe if subset its states remains within prescribed set, also called safe set . achieve safety designing candidate function priori. However, such can challenging. Consider CBF disaster recovery scenario where navigable regions need determined. The decision boundary here unknown cannot designed Moreover, employ parametric design handle arbitrary changes set practice. In our approach, work with xmlns:xlink="http://www.w3.org/1999/xlink">safety samples construct assuming flexible GP prior on these samples, term formulation as xmlns:xlink="http://www.w3.org/1999/xlink">Gaussian CBF. GPs have favorable properties analytical tractability robust uncertainty estimation. This allows realizing posterior high guarantees while computing associated partial derivatives analytically control. change arbitrarily based sampled data, thus allowing non-convex sets. We validated experimentally quadrotor demonstrating 1) sets, 2) collision avoidance synthesis, 3) juxtaposed presence noisy states. experiment video link is: https://youtu.be/HX6uokvCiGk.