I. Introduction
In the field of robotics, the trajectory tracking of manipulators has been widely studied in practical application scenarios such as surgical operation, industrial production, and human-machine interaction. In the above practical applications, dynamic modeling of manipulators is often considered the premise of various control operations, and machine learning methods are increasingly applied to robot modeling with prior knowledge of the dynamics. Lutter et al. [1] constructed deep Lagrangian networks (DeLaNs) based on Lagrangian dynamics to quickly and effectively learn the system dynamics equations with a deep network and ensure its physical rationality. Gupta et al. [2] further constructed a general framework for structured learning of mechanical systems by combining Lagrangian dynamics with the neural network method to accurately balance the deviation and variance of the model. Chen et al. [3] used multilayer neural networks to approximate dynamic nonlinear parameters, which enabled the controlled system to quickly adapt to the dynamic changes of the system to achieve efficient and stable control of the joints. However, the above works used randomly generated data in the simulation environment to train model parameters, which may cause the data to be inconsistent with the actual situation of the controlled manipulator. In addition, they can only solve specific problems while ignoring physical interference in the process of manipulator movement operation.