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.

翻译：直接从数据中学习机器人逆动力学，采用黑盒方法，对于系统知识有限的若干现实场景具有重要意义。本文提出一种基于高斯过程回归的黑盒模型，用于机器人操作臂的逆动力学辨识。该模型依赖于一种称为"拉格朗日启发多项式"核的新型多维核函数。该核函数基于两个核心思想：首先，我们不直接对逆动力学分量建模，而是将系统的动能和势能建模为高斯过程。通过应用高斯过程在线性算子下的性质，从能量先验推导出逆动力学分量的高斯过程先验。其次，在能量先验定义方面，我们证明了动能和势能的多项式结构，并推导出编码此特性的多项式核函数。因此，所提模型还能在无需这些量标签的情况下估计动能和势能。在仿真及两台真实机器人操作臂（7自由度Franka Emika Panda和6自由度MELFA RV4FL）上的实验结果表明，该模型在精度、泛化能力和数据效率方面均优于基于高斯过程和神经网络的最先进黑盒估计器。在MELFA机器人上的实验还表明，尽管所需先验信息更少，我们的方法仍能达到与精细调校的基于模型估计器相当的性能。