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Inspired by the success of control barrier functions (CBFs) in addressingsafety, and the rise of data-driven techniques for modeling functions, wepropose a non-parametric approach for online synthesis of CBFs using GaussianProcesses (GPs). Mathematical constructs such as CBFs have achieved safety bydesigning a candidate function a priori. However, designing such a candidatefunction can be challenging. A practical example of such a setting would be todesign a CBF in a disaster recovery scenario where safe and navigable regionsneed to be determined. The decision boundary for safety in such an example isunknown and cannot be designed a priori. In our approach, we work with safetysamples or observations to construct the CBF online by assuming a flexible GPprior on these samples, and term our formulation as a Gaussian CBF. GPs havefavorable properties, in addition to being non-parametric, such as analyticaltractability and robust uncertainty estimation. This allows realizing theposterior components with high safety guarantees by incorporating varianceestimation, while also computing associated partial derivatives in closed-formto achieve safe control. Moreover, the synthesized safety function from ourapproach allows changing the corresponding safe set arbitrarily based on thedata, thus allowing non-convex safe sets. We validate our approachexperimentally on a quadrotor by demonstrating safe control for fixed butarbitrary safe sets and collision avoidance where the safe set is constructedonline. Finally, we juxtapose Gaussian CBFs with regular CBFs in the presenceof noisy states to highlight its flexibility and robustness to noise. Theexperiment video can be seen at: https://youtu.be/HX6uokvCiGk.

Gaussian Control Barrier Functions : A Non-Parametric Paradigm to Safety