Physics-inspired neural networks are proven to be an effective modeling method by giving more physically plausible results with less data dependency. However, their application in robotics is limited due to the non-conservative nature of robot dynamics and the difficulty in friction modeling. Moreover, these physics-inspired neural networks do not account for complex input matrices, such as those found in underactuated soft robots. This paper solves these problems by extending Lagrangian and Hamiltonian neural networks by including dissipation and a simplified input matrix. Additionally, the loss function is processed using the Runge-Kutta algorithm, circumventing the inaccuracies and environmental susceptibility inherent in direct acceleration measurements. First, the effectiveness of the proposed method is validated via simulations of soft and rigid robots. Then, the proposed approach is validated experimentally in a tendon-driven soft robot and a Panda robot. The simulations and experimental results show that the modified neural networks can model different robots while the learned model enables decent anticipatory control.

翻译：物理启发式神经网络已被证明是一种有效的建模方法，能以较少的数据依赖获得更符合物理规律的结果。然而，由于机器人动力学的非保守特性以及摩擦建模的困难，这类方法在机器人领域的应用受到限制。此外，这类物理启发式神经网络无法处理复杂的输入矩阵，例如欠驱动软体机器人中出现的矩阵。本文通过扩展拉格朗日神经网络和哈密顿神经网络，引入耗散项和简化输入矩阵，解决了上述问题。同时，利用龙格-库塔算法处理损失函数，避免了直接加速度测量固有的不准确性和环境敏感性。首先，通过软体机器人和刚性机器人的仿真验证了所提方法的有效性。然后，在腱驱动软体机器人和Panda机器人上进行了实验验证。仿真与实验结果表明，改进后的神经网络能够对不同机器人进行建模，且学习到的模型可实现良好的预测控制。