GPBF: A Gaussian Process-Driven Adaptive Barrier Functions for Safety-Critical Control of Quadrotors

This paper addresses the critical challenge of safe control for quadrotor UAVs operating in environments with unknown disturbances. Existing robust control barrier function methods typically rely on fixed safety boundaries, which are often overly conservative under low uncertainty and insufficiently protective under high uncertainty. To overcome these limitations, we propose a new class of certificates, Gaussian Process-based Parameterized Barrier Function (GPBF), which combines learningbased disturbance estimation with adaptive safety constraint design. Specifically, a Gaussian Process regression model is employed in a reduced-order model (RoM) to identify and predict disturbances online. The predicted disturbances are used to construct an adaptive parameterized barrier function that dynamically adjusts the safety boundary according to the uncertainty level. In addition, a predictive robust term is derived from iterative full-order model (FoM) computations and incorporated into the RoM-based GPBF condition to address model discrepancies. The proposed GPBF framework enables real-time adaptation to varying uncertainty levels and dynamic adjustment of safety constraints. Extensive simulations and experimental studies with both single and multiple quadrotors validate the effectiveness of the approach in improving safety guarantees.