Safe Control of Robotic Systems Under Nonparametric Uncertainty Using Gaussian Process Regression
Jiayi Zhang, Yueyue Liu, Xiaoyu Wu, Qigao Fan · 2024
This paper addresses the safety control problem for robotic systems under nonparametric uncertainty conditions by proposing a control scheme based on Gaussian Process Regression (GPR). Initially, leveraging historical data collected online, the GPR is employed to learn nonparametric uncertainty and time-varying disturbances. Subsequently, by employing a feedback linearization based on Lyapunov theory, we can obtain the system Global Uniform Ultimate Boundedness (GUUB). Furthermore, considering safety constraints, an additional layer is introduced to the feedback controller using Control Barrier Functions (CBF). The control input is minimally adjusted based on Quadratic Programming (QP) to satisfy optimization requirements while maintaining safety. The paper establishes, in a high probability sense, the boundedness of the closed-loop system and the forward invariance of the state safety domain. The efficacy of the proposed control approach is validated through simulation on trajectory tracking and obstacle avoidance under nonparametric uncertainty. The results confirm the validity of the control approach in handling safety and performance concerns simultaneously.