## 2 Overview of the Hybrid-Driven Dynamic Position Prediction Approach  
The overall structure of the proposed HDPP approach is shown in Figure 2. The input is the reference trajectory generated by motion planning of the robot controller. And the output is the predicted position of the robot EE at time t. HDPP consists of two modules, namely, a primary predictor based on a PDM and machine learning-based RECs. Therefore, the predicted value can be obtained by  
\[p_{t}^{*}=\text{Kinematic}(q_{ct}^{\prime}+e_{t}) \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Full Title** & **Acronym** & **Full Title** & **Acronym** \\ \hline Industrial Robot & IR & Recurrent Neural & RNN \\  & & Network & RNN \\ \hline Hybrid-Driven & & & \\ Dynamic Position & HDPP & End-to-End & ETE \\ Prediction & & & \\ \hline Parametric Dynamic & & Continuous Action & \\ Model & & Reinforcement & CARLA \\  & & Learning Automata & \\ \hline Residual Error & & & \\ Compensator & & & \\ \hline Reinforcement & & & \\ Learning & & & \\ \hline Temporal & & & \\ Convolutional & & & \\ Network & & & \\ \hline Long Short-Term & & & \\ Memory & LSTM & Recurrent Entity & REC \\ \hline Dynamics-Integrated & DI & & \\  & & Error & \\ \hline End-Effector & EE & Mean Absolute Error & MAE \\ \hline Data-Driven Model & & & \\ \hline Proportional–Integral– & & & \\ Derivative & PID & Degree-of-Freedom & DoF \\ \hline Inverse Dynamic & & & \\ Identification Model & & & \\ \hline Least Squares & LS & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: List of nomenclature.  
where \(q_{et}^{\prime}\) is the predicted joint position by the primary predictor, \(e_{t}\) obtained by RECs is the gap between \(q_{et}^{\prime}\) and the actual value \(q_{et}\), and Kinematic\((\cdot)\) means the kinematic model of robot. Since an IR typically consists of multiple joints with different dynamic features, multiple RECs are deployed, each specifically tailored to address the residual error of individual joints, thereby enhancing prediction accuracy while simultaneously reducing model complexity.  
The PDM of robots involves multi-domain issues and can be divided into a servo system model and dynamic model of the mechanical system. A servo system model converts the reference joint position to motor torque. The mechanical system is then driven by motor torque, which can be described by the dynamic model. Theoretically, PDM represents the physical knowledge of robots and can basically estimate the response to reference input. Therefore, PDM is used as the primary predictor of HDPP. However, the existing parameter identification methods for the minimum parameter set cannot obtain independent parameters and limits the application of PDM. In pursuit of this goal, the current study introduces a novel method for parameter identification utilizing RL. The methodology and its detailed procedures are thoroughly elaborated in Section 3 of this document.  
Compared with the physics-based PDM, RECs require higher ability in nonlinear fitting. The data-driven model is therefore employed. To achieve an accurate and stable learning model, two key issues require attention. Firstly, an appropriate time-series model is necessary to extract the long-term nonlinear features considering the robot's complex multi-axis coupling properties. Secondly, a comprehensive dataset encompassing a diverse range of dynamic attributes of the target system is imperative for achieving high precision in predictive modeling and ensuring robust adaptability to fluctuating motion trajectories. Hence, an REC based on a TCN-LSTM neural network and the corresponding dataset construction scheme are developed, which are given in Section 4.