This paper presents an adaptive online learning framework for systems with
uncertain parameters to ensure safety-critical control in non-stationary
environments. Our approach consists of two phases. The initial phase is
centered on a novel sparse Gaussian process (GP) framework. We first integrate
a forgetting factor to refine a variational sparse GP algorithm, thus enhancing
its adaptability. Subsequently, the hyperparameters of the Gaussian model are
trained with a specially compound kernel, and the Gaussian model's online
inferential capability and computational efficiency are strengthened by
updating a solitary inducing point derived from new samples, in conjunction
with the learned hyperparameters. In the second phase, we propose a safety
filter based on high-order control barrier functions (HOCBFs), synergized with
the previously trained learning model. By leveraging the compound kernel from
the first phase, we effectively address the inherent limitations of GPs in
handling high-dimensional problems for real-time applications. The derived
controller ensures a rigorous lower bound on the probability of satisfying the
safety specification. Finally, the efficacy of our proposed algorithm is
demonstrated through real-time obstacle avoidance experiments executed using
both a simulation platform and a real-world 7-DOF robot.

本文提出了一种适应不确定参数系统的自适应在线学习框架，以确保非平稳环境下的安全临界控制；该方法包括两个阶段，第一阶段基于稀疏高斯过程算法改进，第二阶段提出了基于高阶控制屏障函数的安全过滤器与学习模型相结合，并通过实时障碍物避免实验证明了算法的有效性。