A Black-Box Physics-Informed Estimator based on Gaussian Process Regression for Robot Inverse Dynamics Identification

Learning the inverse dynamics of robots directly from data, adopting a black-box approach, is interesting for several real-world scenarios where limited knowledge about the system is available. In this paper, we propose a black-box model based on Gaussian Process (GP) Regression for the identification of the inverse dynamics of robotic manipulators. The proposed model relies on a novel multidimensional kernel, called \textit{Lagrangian Inspired Polynomial} (\kernelInitials{}) kernel. The \kernelInitials{} kernel is based on two main ideas. First, instead of directly modeling the inverse dynamics components, we model as GPs the kinetic and potential energy of the system. The GP prior on the inverse dynamics components is derived from those on the energies by applying the properties of GPs under linear operators. Second, as regards the energy prior definition, we prove a polynomial structure of the kinetic and potential energy, and we derive a polynomial kernel that encodes this property. As a consequence, the proposed model allows also to estimate the kinetic and potential energy without requiring any label on these quantities. Results on simulation and on two real robotic manipulators, namely a 7 DOF Franka Emika Panda, and a 6 DOF MELFA RV4FL, show that the proposed model outperforms state-of-the-art black-box estimators based both on Gaussian Processes and Neural Networks in terms of accuracy, generality and data efficiency. The experiments on the MELFA robot also demonstrate that our approach achieves performance comparable to fine-tuned model-based estimators, despite requiring less prior information.