Data Driven Control Barrier Functions

Abstract

This research presents a novel method to define the Barrier Function (BF) used for the synthesis of a Control Barrier Function (CBF). The proposed method uses multivariate B-spline estimators as the BF which allows for the creation of a more data-driven CBF. Additionally usage of B-splines offer a local basis, linearity in parameters and allow for additional constraints to be added to the regression problem. New theory is derived in order to utilize the power of multivariate B-splines for the creation of CBFs. The proposed methodology is implemented on Dubin's car. In the experiments two distinct multivariate B-splines are used as BFs. The first of these is created based on data sampled from a more conventional continuous reference function. The second one is based on data sampled from a reference function which is based on a combination of step functions. Numerical simulations using the created multivariate B-splines as BFs show that the the proposed methodology can be used to create a functional CBF. This is under the condition that the used multivariate B-spline has a degree of continuity equal to the relative degree of the system state which is to be controlled. In addition, the spline BFs estimated from discontinuous data show that the proposed methodology offers significant flexibility with regards to the types of safe sets which can be turned into functional CBFs using the proposed method.