# Research on Trajectory Planning and Tracking Methods for Coal Mine Mobile Robots
[12] analyzed that the minimum order of a Bessel curve that can satisfy the condition that the curvature value of the start point and the end point are both zero is the fifth order, and a feasible trajectory planning algorithm for intelligent cars is proposed based on the fifth order Bessel curve. [PERSON] et al. [13] established a step-by-step planning model based on B spline curves and verified through simulation that the method can better solve the intelligent vehicle trajectory planning problem under simple obstacle scenarios. [PERSON] et al. [14] generated executable paths with continuous curvature based on cubic B spline curves for unmanned vehicles in mineral operations. [PERSON] et al. [15] present a trajectory optimization method by parameterized curvature control to reach the goal state with the vehicle model and its dynamic constraints considered to deal with the highly dynamic environments for on-road automotive driving. Trajectory tracking is the basis for robots to be able to accomplish various tasks such as autonomous navigation and movement in unknown and complex environments. However, mobile robots are inherently characterized by noncomplete constraints and strong nonlinearities [16], which make it difficult to control them well. The task of trajectory tracking is to output appropriate control quantities according to the real-time position and model constraints of the robot, so that the actual position of the robot is consistent with the position on the target trajectory, and its commonly used methods include PID control, sliding mode control (SMC), and MPC control. [PERSON] et al. [17] used a fuzzy adaptive PID control algorithm to track and control the trajectory of AGV to improve the trajectory tracking accuracy in response to the problems of low running accuracy and long PID control adjustment time when the Automated Guided Vehicle (AGV) is performing circular motion. [PERSON] et al. [18] based a trajectory tracking controller on visual neuron PID, so that the robot can meet the robustness of the tracking controller even when it makes a rapid response. [PERSON] et al. [19] proposed an algorithm combining the backstepping technique and sliding mode control for trajectory tracking of four-wheeled omni-directional mobile robots,so that the robots can track any type of trajectory. [PERSON] et al. [20] designed an adaptive trajectory tracking controller based on sliding film feedback for tracked mobile robots to improve the trajectory tracking accuracy of tracked mobile robots. [PERSON] et al. [21] designed a nonlinear MPC control algorithm for controlling the robot to track the feasible paths generated directly by nonlinear dynamics equations. [PERSON] et al. [22] established a three-degree-of-freedom dynamics model of a vehicle and designed an MPC controller based on it to improve the trajectory tracking accuracy of an intelligently driven vehicle under extreme operating conditions. [PERSON] et al. [23] designed a trajectory tracking controller for intelligent vehicles based on MPC and fuzzy control, and verified in simulation that this method has a good tracking effect under high-speed working conditions. [PERSON] et al. [24] present a method of bicurve polynomial transition curve application for making agricultural aggregate movement paths during headland turn drives as well as within the field. In summary, among the current trajectory planning methods, the polynomial spline, the Bezier curve, or B-spline methods have a more flexible trajectory characterization than other traditional methods, but the continuity, parameter dimensions, and the degree of difficulty of implementation still can be improved. Compared to PID and SMC, MPC can handle nonlinear systems and high-order systems, which is more suitable for CMRRs in complex environments.