## 6 Conclusions  
This study develops a hybrid-driven dynamic position prediction approach consisting of a PDM and machine learning-based RECs. The PDM including the flexible dynamic model of the mechanical system and servo system model is established as the primary predictor in HDPP. A novel parameter identification technique leveraging RL is introduced to determine autonomous dynamic parameters, with its efficacy confirmed through experimental validation. Due to the inherent simplifications in modeling the actual system with the PDM, a novel TCN-LSTM network is built to compensate the residual error of PDM prediction. Concurrently, a DI dataset extraction strategy has been introduced with the aim of enhancing the precision of the predictions. The comparative experiments conducted on the heart and random paths show that the proposed DI dataset can improve the performance of the REC effectively. Meanwhile, the comprehensive experimental analysis comparing various forecasting techniques, such as the PDM, LSTM, and the hybrid PDM + LSTM approach, demonstrates that the HDPP model achieves superior accuracy and stability in predictions. HDPP can be utilized as a tool for engineers in production optimization such as processing optimization, trajectory planning, and quality prediction. Subsequent studies will concentrate on the continuous enhancement of HDPP throughout the robot's service period. And the transfer learning methods will be implemented to extend HDPP to various IRs. Current HDPP methods mainly rely on off-line prediction models, which to some extent limits their adaptability in real-time dynamic environments. In practical applications, industrial robots are often faced with complex and variable working conditions and external environment interference, which may introduce noise, thus affecting the accuracy and robustness of the prediction model. Therefore, how to enhance the model's ability to \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Prediction Error Metrics**} & \multicolumn{4}{c}{**Heart**} & \multicolumn{4}{c}{**Random Path**} \\ \cline{2-9}  & \multirow{2}{*}{**PDM**} & \multirow{2}{*}{**LSTM**} & \multicolumn{2}{c}{**PDM +**} & \multirow{2}{*}{**HDPP**} & \multirow{2}{*}{**PDM**} & \multirow{2}{*}{**LSTM**} & \multicolumn{2}{c}{**PDM +**} & \multirow{2}{*}{**HDPP**} \\  & & & **LSTM** & & & & & **LSTM** & \\ \hline MAE of joint 1 & 29.22 & 1282.30 & 7.06 & **3.90** & 28.05 & 1110.31 & 5.95 & **4.70** \\ MAE of joint 2 & 21.02 & 1045.72 & 3.88 & **2.35** & 21.85 & 1359.77 & 3.99 & **3.06** \\ MAE of contour error & 103.64 & 4043.99 & 25.20 & **12.98** & 91.11 & 4015.10 & 15.77 & **11.77** \\ RMSE of joint 1 & 35.60 & 2038.11 & 8.43 & **4.79** & 34.20 & 1313.29 & 7.31 & **5.87** \\ RMSE of joint 2 & 24.61 & 1223.63 & 4.61 & **2.89** & 24.86 & 1679.76 & 4.87 & **3.94** \\ RMSE of contour error & 126.28 & 5188.93 & 31.59 & **17.30** & 105.01 & 5026.16 & 20.45 & **15.43** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Prediction accuracy comparison of different methods. Figure 17: Prediction results of the test random path with different methods. (**a**) Prediction error of joint 1. (**b**) Prediction error of joint 2. (**c**) Prediction contour error. process real-time data and how to maintain stable prediction performance in the presence of noise interference is an important direction of future work. Conceptualization, H.N. and C.X. ; methodology, H.N., C.X., Y.Y. and S.J. ; software, B.C. ; validation, S.L. ; writing--original draft preparation, H.N. and C.X. ; writing--review and editing, Y.Y. and S.J. All authors have read and agreed to the published version of the manuscript. This work is supported by the Key R&D Program of Shandong Province (Grant No. 2022 CXGC010101) and the Natural Science Foundation of Shandong Province (Grant No. ZR2021 QE128). Not applicable. The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.