The vehicle trajectory tracking algorithm is one of the key and difficult issues of intelligent driving technologies. In current control algorithms for the vehicle trajectory tracking, there are three main assumptions: the standard working condition for the driving path, the same control model used for the entire control process, and a fixed value for the longitudinal vehicle speed. However, the above determinations in current control algorithms are inconsistent with the actual vehicle driving conditions. To overcome those problems, a vehicle trajectory tracking method with a time-varying model is proposed. The time-varying model is developed by using a two-dimensional vehicle kinematics model. This method considers the influences of the longitudinal speed and road curvature on the vehicle trajectory tracking stability under the low-speed complex driving condition. Thus, the proposed method can improve the trajectory tracking accuracy when the unmanned vehicle is located at the road with a sharp curvature under the low-speed complex driving condition. Moreover, the proposed model can achieve the real time calculation. Meanwhile, the prediction accuracy of the vehicle kinematics model is ensured. The proposed approach with the above characteristics can complete the trajectory tracking for the route composed of arbitrary curves. The results show that the proposed method can effectively improve the trajectory tracking stability of the unmanned vehicle on the roads with different curvatures under complex driving conditions.

The motion planning and control method of automated vehicles, as the key technology of automated vehicles, directly affects the safety, comfort, and other technical indicators of vehicles. The planning module is responsible for generating a vehicle driving path. The control module is responsible for driving the vehicle. In this study, we review the main methods and achievements in motion planning and motion control for automated vehicles. The advantages and disadvantages of various planning and control methods are comparatively analyzed. Finally, some predictions and summaries based on the existing research results and trends are proposed. Through this analysis, it is believed that various types of algorithms will be further integrated in the future to complement each other’s strengths and weaknesses. The next area of research will be to establish more accurate vehicle models to describe vehicle motion, improve the generalization-solving ability of algorithms, and enhance the planning and control of integrated ‘human-vehicle-road’ traffic systems.

Fault diagnosis and vibration control are the tracking of any aspect of an industry mechanical components’ performance using reliably measured data and analytical simulations in conjunction with the heuristic experience, so that the current and expected future performance of the machine for at least the most critical limit events can be described in a proactive manner

The trajectory planning is addressed for a redundant spacemanipulator.

Uncertainty is inevitable in real-world systems. If uncertainty is not effectively addressed, it may degrade the performance of model predictive control (MPC). This paper proposes a stochastic dual model predictive control (SDMPC) method for linear systems with parameter uncertainty and measurement noise. The method not only actively explores uncertainty while optimizing control but also introduces probabilistic output constraints to expand the set of feasible solutions. Specifically, Kalman filtering is employed to construct a real-time parameter estimator. The future output errors are incorporated into the nominal cost function as exploration signals to balance exploration and exploitation. Simulation results in the field of solar collectors show that SDMPC can effectively track the temperature by varying the inlet flow under changing environmental and opportunity constraints. The cumulative performance index of SDMPC is 125.3, compared to 316.4 obtained by conventional MPC, validating its effectiveness.

Autonomous vehicle trajectory tracking control is one of the hot topics in the autonomous driving field. One of the most widely used control methods is MPC (Model Predictive Control). As the control system generally becomes more nonlinear and complex, more nonlinear system factors are added to the MPC method. However, tracking accuracy and the amount of calculation needed are both dependent on a lot of contradictions for NMPC (Nonlinear Model Predictive Control). This research proposes a control algorithm for MPC-fused PID (Proportional-Integral-Derivative) control that ensures tracking accuracy under different high-speed driving conditions on wet and slippery road surfaces. The objective of the algorithm is twofold: first, to enhance trajectory tracking accuracy, and second, to ensure real-time control and optimize the vehicle’s comfort, economy, and safety indexes. The results of the joint simulation in Carsim/MATLAB Simulink show that trajectory tracking accuracy is improved by at least 22.2% under high-speed driving conditions of a vehicle on a wet and slippery road. At the same time, the comfort, economy, and safety of the vehicle are improved by at least 9.4%, 19.8%, and 5.3%, respectively.