Robust Safe Learning and Control in An Unknown Environment: An Uncertainty-Separated Control Barrier Function Approach

A main challenge restricting the application of control barrier functions (CBFs) to complex scenarios is the absence of robustness against uncertainties induced by both measurements of the environment and robot dynamics. In this paper, we propose an uncertainty-aware, learning-based approach to construct a safe controller such that safety can be guaranteed with a high probability in a complex and unknown environment. Two types of CBFs, namely nominal CBF (NCBF) and uncertainty CBF (UCBF), are constructed by means of Gaussian processes (GPs) based on real-time measurements of the environment. They are then synthesized into an uncertainty-separated control barrier function (US-CBF), which serves as hard constraints in quadratic programming (QP) based controller. To handle the dynamic uncertainties, we exploit another GP to learn the residual dynamics of the robot. The mean prediction is then feedforwarded to the controller such that the residual dynamics can be compensated. The variance function is incorporated into the QP to constrain the trajectory of the robot within a high-confidence safety tube. Moreover, we prove that the solution to the QP is locally Lipschitz continuous, which guarantees a unique solution to the system. Our proposed method demonstrates good performance in addressing safe navigation tasks in highly very complex scenarios provided by the KITTI dataset. Additionally, its reliability and safety assurance have been verified in real-world scenarios using a quadrotor under external wind disturbance.