In the field of path tracking control for wheeled mobile robots, researchers generally believe that the motion of robots meets non-holonomic constraints. However, the robot may sideslip by centrifugal force when it is steering. This kind of slip is usually uncontrollable and dangerous. In order to prevent sideslip and improve the performance of path tracking control, we propose a controller based on tire mechanics. Moreover, the new controller is based on the model predictive control, and this control method has proven to be suitable for path tracking of wheeled mobile robots. The proposed controller was verified by simulation and compared with a model predictive controller based on kinematics (non-holonomic constraints). As for the simulation results, the maximum values of displacement error, heading error, lateral velocity, and slip angle of the dynamic-based model predictive controller are 0.2086 m, 0.1609 rad, 0.1546 m/s, and 0.0576 rad, respectively. Compared with the kinematics-based model predictive controller, the maximum values of the above-mentioned parameters of the dynamic-based controller reduce by 86.55%, 72.25%, 96.30%, and 90.02%, respectively. The above-mentioned results show that the proposed controller can effectively improve the accuracy of path tracking control and avoid sideslip. INDEX TERMS Wheeled mobile robot, path tracking, path following, model predictive control, dynamic model.

Path tracking of mining vehicles plays a significant role in reducing the working time of operators in the underground environment. Because the existing path tracking control of mining vehicles, based on model predictive control, is not very effective when the longitudinal velocity of the vehicle is above 2 m/s, we have devised a new controller based on nonlinear model predictive control. Then, we compare this new controller with the existing model predictive controller. In the results of our simulation, the tracking accuracy of our controller at the longitudinal velocity of 4 m/s is close to that of the existing model predictive controller, at the longitudinal velocity of 2 m/s. When longitudinal velocity is 4 m/s, the existing model predictive controller cannot drive the mining vehicle to track the given path, but our nonlinear model predictive controller can, and the maximum displacement error and heading error are 0.1382 m and 0.0589 rad, respectively. According to these results, we believe that this nonlinear model predictive controller can be used to improve the performance of the path tracking of mining vehicles.

Recently, model predictive control (MPC) is increasingly applied to path tracking of mobile devices, such as mobile robots. The characteristics of these MPC-based controllers are not identical due to the different approaches taken during design. According to the differences in the prediction models, we believe that the existing MPC-based path tracking controllers can be divided into four categories. We named them linear model predictive control (LMPC), linear error model predictive control (LEMPC), nonlinear model predictive control (NMPC), and nonlinear error model predictive control (NEMPC). Subsequently, we built these four controllers for the same mobile robot and compared them. By comparison, we got some conclusions. The real-time performance of LMPC and LEMPC is good, but they are less robust to reference paths and positioning errors. NMPC performs well when the reference velocity is high and the radius of the reference path is small. It is also robust to positioning errors. However, the real-time performance of NMPC is slightly worse. NEMPC has many disadvantages. Like LMPC and LEMPC, it performs poorly when the reference velocity is high and the radius of the reference path is small. Its real-time performance is also not good enough.

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At present, many path tracking controllers are unable to actively adjust the longitudinal velocity according to path information, such as the radius of the curve, to further improve tracking accuracy. For this problem, we propose a new path tracking framework based on model predictive control (MPC). This is a multilayer control system that includes three path tracking controllers with fixed velocities and a velocity decision controller. This new control method is named multilayer MPC. This new control method is compared to other control methods through simulation. In this paper, the maximum values of the displacement error and the heading error of multilayer MPC are 92.92% and 77.02%, respectively, smaller than those of nonlinear MPC. The real-time performance of multilayer MPC is very good, and parallel computation can further improve the real-time performance of this control method. In simulation results, the calculation time of multilayer MPC in each control period does not exceed 0.0130 s, which is much smaller than the control period. In addition, when the error of positioning systems is at the centimeter level, the performance of multilayer MPC is still good.