Safe robust adaptive control under both parametric and nonparametric uncertainty

This article presents a method for guaranteeing the safety of a system with both parametric and nonparametric uncertainties, while at the same time decreasing the conservatism compared to existing approaches. This is obtained by combining robust adaptive control barrier functions (RaCBF) and Gaussian process control barrier functions (GPCBF). We provide a condition under which the considered system is safe with a given probability, and show that the proposed method is less conservative than GPCBF. We evaluate the method through a simulation study, where we consider a force controlled robot manipulator in contact with a partially unknown environment. The results show that our proposed GPRaCBF can guarantee bounds on the contact forces despite parametric and nonparametric uncertainties in the contact dynamics and outperforms GPCBF in terms of the conservatism.