## 4 Conclusions  
Path tracking of articulated vehicles is one of the key technologies for mining system automation, which can reduce operators' working time in the underground environment. For path tracking control methods, the researches of [PERSON] et al. prove that MPC is very useful. In order to improve the ability of mining vehicles to track complex given paths at 2 m/s or faster, we propose an NMPC-based path tracking control method for mining vehicles. By comparing the NMPC controller and the switching-MPC controller, we obtained the following conclusions.  
Firstly, the NMPC controller allows mining vehicles to track the given path with less error at longitudinal velocities that are no more than 4 m/s. In the simulation presented in this paper, displacement error is not more than 0.1382 m, and heading error is not more than 0.0461 rad. Secondly, in the simulation presented in this paper, when the mining vehicle is traveling at the same longitudinal velocity, the displacement error of the NMPC controller is at least 70.70% smaller than that of the switching-MPC. Tracking accuracy of the NMPC controller is higher than that of the switching-MPC controller. Thirdly, tracking the accuracy of NMPC at the longitudinal velocity of 4 m/s is similar to that of switching-MPC at the longitudinal velocity of 2 m/s. On the basis of ensuring the same tracking accuracy, NMPC can improve the operating efficiency of mining vehicles better than switching-MPC. Besides, although NMPC is inferior to switching-MPC in real-time performance, the maximum computation time of NMPC is still less than the sampling interval. Therefore, the real-time performance of the NMPC controller can meet the requirements of path tracking.  
From the perspective of science, we make the following contributions. On one hand, although NMPC has been proposed very early, its application in path tracking, especially path tracking of articulated vehicles, is not mature. The application of NMPC has not been found before in path  
Figure 21: Heading error of the third group simulation.  
Figure 22: The computation time of the third group simulation.  
tracking of articulated vehicles. Thus, our work is the application of NMPC in a new field. On the other hand, articulated vehicles have different motion characteristics relative to other vehicles, so the control strategies of other vehicles are difficult to use for articulated vehicles directly. In this respect, our work provides a new solution for the automation of articulated vehicles. Furthermore, though it is known that NMPC outperforms linearized MPC in some areas, what are its advantages in path tracking, especially in the path tracking of articulated vehicles? Our work is a satisfactory answer to this question.  
In the future, we will focus on the longitudinal velocity control of the articulated vehicle in path tracking. The switching-MPC controller and our NMPC controller can only work at different longitudinal velocities, and they do not automatically adjust the longitudinal velocity within a large range. We also hope to add a dynamic model of the articulated vehicle in future work.  
Conceptualization, G.B., Q.G., and Y.M.; methodology, G.B. and Q.G.; software, G.B.; validation, G.B., and B.M.; investigation, G.B.; writing--original draft preparation, G.B.; writing--review and editing, Y.M., L.L., W.L., and Q.G.; supervision, L.L. and W.L.; project administration, L.L. and W.L.; funding acquisition, L.L., W.L., Y.M., and Q.G.  
This research was funded by the National Key Research and Development Program of China, grant number 2018 YC0604043 and 2016 YC0802905, the National High Technology Research and Development Program of China (863 program), grant number 2011 AA060408 and the Fundamental Research Funds for the Central Universities, grant number FRF-TP-17-010A2.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.