# A Method for Precise Tracking Control of Pneumatic Artificial-Muscle-Driven Exoskeletal Robot
## 5 Conclusions  
The hysteresis of the output force of the pneumatic muscle affects the tracking control accuracy of the Upper Limb Exoskeletal Robot driven by it. In this paper, based on the traditional pneumatic muscle output force, the influence of elastic force and friction force on PAM's output force and the empirical coefficient are added to PAM's pressure, and PAM's expansion and load, to establish a new output force model, and an inverse model of output force is established using the BP neural network. Finally, the particle swarm optimization algorithm is used to determine the optimal parameters in the model. With the change in posture in the process of handling, the variable load problem in the process of handling is handled according to the principle of torque equivalence. The control system is built based on the inverse model of the exoskeleton robot's inverse dynamics combined with the output force of the pneumatic muscle, and elbow angle tracking control in the process of Upper Limb Exoskeleton handling is realized. The results of the mean absolute error and root mean square error show that the control method can achieve high accuracy in elbow angle tracking control of the Upper Limb Exoskeleton system during the handling process. This research result is not only of great help to PAM in the field of assistance and rehabilitation, but also of reference significance regarding the control of flexible actuator exoskeleton robots. However, the accuracy of the proposed control method is largely dependent on the precision of the inverse model of the pneumatic muscle output force, and the calculation of the load depends on the elbow angle and the variation in the angle, which requires a more accurate sensor. In this paper, a BP neural network is used to calculate the inverse output force model, which has no generalization. Therefore, future work will also focus on these limitations.  
Conceptualization, G.M. and H.J.; methodology, G.M.; software, G.M.; validation, G.M., H.J. and J.X.; formal analysis, G.M.; investigation, G.M.; resources, G.M.; data curation, G.M.; writing--original draft preparation, G.M.; writing--review and editing, G.M.; visualization, H.J.; supervision, L.H.; project administration, L.H.; funding acquisition, L.H. All authors have read and agreed to the published version of the manuscript.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **MAX** & **MAE** & **RMSE** & **ITAE** \\ \hline Angle & 0.0175 & 0.0038 & 0.0048 & 4.6426 \\ Angular velocity & 0.0031 & 0.0012 & 0.0013 & 1.4645 \\ Angular acceleration & 0.0049 & 0.0018 & 0.0021 & 2.2687 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Error value of tracking control.  
**Funding:** This work was supported by the National Natural Science Foundation of China under grant number 62073063.  
**Institutional Review Board Statement:** Not application.  
**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.  
**Data Availability Statement:** Data are contained within the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.