# Research on Trajectory Planning and Tracking Methods for Coal Mine Mobile Robots
## 5 Conclusions  
This paper researches the trajectory planning and tracking technology of CMRR and puts forward the planning algorithm based on MINCO trajectory in a safety corridor with a tracking algorithm based on MPC. A large number of field experiments were carried out in the simulated lineway based on a crawler-type CMRR platform, which verifies that the  
Figure 38: Linear tracking test results on bumpy road: (**a**) MPC algorithm tracking results, (**b**) PID algorithm tracking results. The red curve is the actual trajectory of the robot and the green curve is the desired trajectory.  
Figure 39: Comparison of MPC and PID motion trajectories on bumpy roads.  
methods of this paper are also applicable to the field environment, and it has a certain value of practical application. The main research work and results of this paper are as follows:  
(1) The MINCO trajectory class and its spatio-temporal deformation are derived in detail, and the MINCO trajectory is used to generate the optimal control trajectory under the constraints of a downhole environment. The planning effects of the MINCO trajectory method and the Fast-Planner algorithm are compared through several field experiments. The results show that the trajectories of the MINCO trajectory method are smoother and shorter, accomplishing the same planning task at a smaller cost; planning tasks were completed in fewer than 10 planning sessions for each scenario, which proves that the proposed algorithm is better adapted to the complex environment of underground coal mines.  
(2) The kinematic model of the experimental platform of a tracked coal mine robot is established. The MPC trajectory tracking method is further designed. The field tests prove that the tracking error is always less than 0.05 m, which is more adaptable to the tracking of different paths compared with the PID algorithm.  
(3) A highly reliable trajectory planning and tracking system that meets the performance requirements is provided for CMRRs, which can be used for autonomous navigation and remote control assisted driving. The effectiveness of the planning and tracking system is verified through a large number of field tests, which provide key technical support for the application of CMRRs.  
Conceptualization, M.L. and G.Z.; methodology, M.L. and W.H.; software, K.H.; validation, K.H., E.H. and C.T.; formal analysis, M.L.; investigation, M.L. and G.Z.; resources, G.Z. and E.H.; data curation, W.H.; writing--original draft preparation, K.H. and W.H.; writing--review and editing, M.L.; visualization, W.H.; supervision, M.L. and G.Z.; project administration, G.Z., funding acquisition, M.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant number: 52304183, 52274159), the Joint Open Fund of State Key Laboratory of Robotics (grant number: 2022-KF-22-05), and the Natural Science Foundation of Jiangsu Province for Youths (grant number: BK20210497).  
Not applicable.  
The data are unavailable.  
The authors declare no conflict of interest.