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.

在这篇论文中，我们提出了一种基于高斯过程回归的黑盒模型，用于识别机器人操纵器的反向动力学。我们的模型基于一种新颖的多维核函数，称为拉格朗日启发的多项式核。该模型能够估计动能和势能，而无需这些量的标签，并且在准确性、广泛性和数据效率方面优于基于高斯过程和神经网络的最先进的黑盒估计器。在模拟和两个真实的机器人操纵器上的实验结果表明，我们的方法实现了与精细调整的基于模型的估计器相当的性能，尽管需要更少的先验信息。