# Trajectory Tracking Algorithm Study of Coal Mine Water Detector Drilling Bar Installation
## 7 Conclusions  
In order to improve the connection accuracy of drilling bars in the automatic drilling process of intelligent water detectors, the trajectory tracking control of the drilling device was studied. First, the MDH method described the positional attitude of the supplied material device and was then used to construct the dynamic model based on the Lagrange equation. The sliding mold controller was designed on the basis of the dynamics model. The controller used the exponential approximation law and replaced the symbol function with the saturated function to weaken the inevitable vibration in the sliding mold control. Finally, using PSO to optimize the parameters of the controller, compared to the manually determined controller parameters, the combination of parameters obtained by PSO leads to sliding mold controller having a better effect on joints3 and -4 of the supplied material device, which can be summarized by the following points:  
1. The time of the expected trajectory of joint3's tracking decreased by approximately 36.6%. The time of the expected trajectory of joint4's tracking decreased by approximately 19.4%. The above-detailed description of an optimized sliding mold controller increases the speed of the expected position on the tracking of the joints.
2. The expected speed of joint3's tracking decreased by approximately 16.4%. The expected speed of joint4's tracking decreased by approximately 30.2%. The above-detailed description of an optimized sliding mold controller decreases the expected speed of the tracking of the joints.
3. The sliding mold controller, before optimizing, used 2.8126 s to converge the overall tracking error of the supplied material device to 0.0012. Compared to the above effects, it took 2.0321 s to converge the overall tracking error of the supplied material device to 0.0010. The above data show that the sliding mold controller improves the convergence rate of the control error after optimizing the parameters using PSO.  
Conceptualization and Supervision, Z.C.; Methodology and Writing--original draft, S.L.; Project administration, H.G.; Writing--Review and Editing, J.Q.; Software and Validation, Y.Z. and S.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by New Drilling Bars Used in Coal Mine Install Automatic and Fast, Grant Number: 2045150001000048, a Joint Fund Project of the Natural Science Fund of the Autonomous Region of Inner Mongolia, Grant Number: 2023 LHMS05029, and Shandong Province's key research and development project. Grant Number: 2021 JMRH0302.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy concerns.  
We wish to acknowledge [PERSON] and [PERSON] for acquiring funding, calculating data, and contributing during the article revision process. We wish to acknowledge [PERSON] for providing funding for this project. We wish to acknowledge [PERSON] and [PERSON] for providing data support for this project. We wish to acknowledge [PERSON] for analyzing the data.  
The authors declare no conflicts of interest.