Adaptive Safety-Critical Control for High-Order Systems: A Real-Time Gaussian Process Approach

This paper proposes a novel adaptive fast variational sparse Gaussian process (AFVSGP) framework to ensure real-time safety for high-order systems under model uncertainties and dynamic obstacle environments. The framework effectively addresses the challenge of maintaining real-time safety guarantees during unknown trajectory transitions in nonstationary environments. To achieve this, the proposed framework incorporates three key innovations. First, a specialized kernel function is embedded within the VSGP algorithm to decouple control inputs from uncertainties while preserving the convexity of posterior-based safety constraints. Second, an adaptive online incremental learning mechanism is introduced, integrating forgetting capabilities with dynamic reconstruction rules for training datasets and inducing sets, thereby accelerating inference convergence and enabling compact uncertainty prediction with reduced computational complexity. Third, a high-order control barrier function (HOCBF)-based safety filter is developed to synthesize safe control inputs by leveraging the proposed learning model, thereby establishing rigorous probabilistic bounds on the satisfaction of safety specifications. The effectiveness of the proposed framework is validated through both simulation and real-world obstacle avoidance experiments on a 7-DOF Franka robot. The video is available at: https://www.youtube.com/watch?v=2tCKYM_79S8.