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In this paper, we propose a black-box model based on Gaussian processregression for the identification of the inverse dynamics of roboticmanipulators. 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 directlymodeling the inverse dynamics components, we model as GPs the kinetic andpotential energy of the system. The GP prior on the inverse dynamics componentsis derived from those on the energies by applying the properties of GPs underlinear operators. Second, as regards the energy prior definition, we prove apolynomial structure of the kinetic and potential energy, and we derive apolynomial kernel that encodes this property. As a consequence, the proposedmodel allows also to estimate the kinetic and potential energy withoutrequiring any label on these quantities. Results on simulation and on two realrobotic manipulators, namely a 7 DOF Franka Emika Panda and a 6 DOF MELFARV4FL, show that the proposed model outperforms state-of-the-art black-boxestimators based both on Gaussian Processes and Neural Networks in terms ofaccuracy, generality and data efficiency. The experiments on the MELFA robotalso demonstrate that our approach achieves performance comparable tofine-tuned model-based estimators, despite requiring less prior information.

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