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.

翻译：本文提出了一种基于高斯过程回归的黑箱模型，用于机器人机械臂逆动力学的辨识。该模型依赖于一种名为拉格朗日启发式多项式（\kernelInitials{}）核的全新多维核函数。\kernelInitials{}核基于两个核心思想：首先，我们不再直接建模逆动力学分量，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，从能量高斯过程先验推导出逆动力学分量的高斯过程先验。其次，针对能量先验的定义，我们证明了动能和势能的多项式结构，并据此推导出编码该性质的多项式核。因此，该模型还无需依赖能量标签即可估计动能和势能。在仿真实验及两台真实机器人（7自由度Franka Emika Panda与6自由度MELFA RV4FL）上的结果表明，本模型在精度、泛化能力和数据效率上均优于基于高斯过程和神经网络的最新黑箱估计器。在MELFA机器人上的实验还证明，尽管所需先验信息更少，但本方法的性能可与精调后的基于模型的估计器相媲美。