  In this paper, we propose a black-box model based on Gaussian process
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.
