Learning‐Based Model Predictive Control for Autonomous Vehicles Path Tracking Based on Gaussian Processes and Snake Optimizer

To improve the accuracy of tracking unmanned vehicles on known trajectories, two optimised model predictive control (MPC) trajectory tracking control systems are designed based on the adaptive compensation and robust control of a radial basis function (RBF) neural network. Based on the traditional MPC trajectory tracking controller and the local approximation characteristics of the RBF neural network, the proposed RBF compensation–MPC control system is designed to compensate for the inaccuracy in the MPC prediction model arising from modelling errors. The results show that this method can achieve a root mean square error of less than 0.3703 m for the lateral position. Subsequently, to suppress the error generated by the RBF neural network and reduce the degree of vehicle sideslip, the error is considered to be external interference, and the anti-interference characteristic of the RBF robust control is incorporated into the RBF robust-MPC control system. Following the re-optimisation of the RBF robust control, the root mean square error of the lateral position is set within 0.2352 m. The results of a MATLAB/Carsim joint simulation show that using the RBF robust control can improve the tracking accuracy of the traditional MPC controller compared with RBF compensation control, while simultaneously improving the driving stability of the vehicle.

Robots and automated systems are increasingly being introduced to unknown and dynamic environments where they are required to handle disturbances, unmodeled dynamics, and parametric uncertainties. Robust and adaptive control strategies are required to achieve high performance in these dynamic environments. In this paper, we propose a novel adaptive model predictive controller that combines model predictive control (MPC) with an underlying $\mathcal{L}_{1}$ adaptive controller to improve trajectory tracking of a system subject to unknown and changing disturbances. The $\mathcal{L}_{1}$ adaptive controller forces the system to behave in a predefined way, as specified by a reference model. A higher-level model predictive controller then uses this reference model to calculate the optimal reference input based on a cost function, while taking into account input and state constraints. We focus on the experimental validation of the proposed approach and demonstrate its effectiveness in experiments on a quadrotor. We show that the proposed approach has a lower trajectory tracking error compared to non-predictive, adaptive approaches and a predictive, nonadaptive approach, even when external wind disturbances are applied.

<div>Intelligent vehicles can utilize a variety of sensors, computing, and control technologies to autonomously perceive the environment and make decisions to achieve safe, efficient, and automated driving. If the speed planning of intelligent vehicles ignores the vehicle dynamics state, it leads to unreasonable planning speed and is not conducive to improving the accuracy of trajectory tracking control. Meanwhile, trajectory tracking usually does not consider the road and speed information beyond the prediction horizon, resulting in poor tracking precision that is not conducive to improving driving comfort. To solve these problems, this study proposes a new longitudinal speed planning method based on variable universe fuzzy rules and designs the piecewise preview model predictive control (PPMPC) to realize the vehicle trajectory tracking. First, the three-degrees-of-freedom vehicle dynamics model and trajectory tracking model are established and verified. Then, the variable universe fuzzy rules are introduced to design the longitudinal speed planning method, in which the road friction coefficient and road curvature are defined as the input of the speed planning method, and the vehicle lateral deviation is defined as the scaling factor input of the speed variable universe. Based on the dynamics model and trajectory tracking model, the PPMPC method is proposed to improve the accuracy and stability of trajectory tracking. During the PPMPC method design, the reference value of state quantity in the prediction horizon can be updated by using further road information and planning longitudinal speed information. Finally, the results show that the proposed planning algorithm can provide a reasonable longitudinal speed to reduce the tracking lateral error in the tracking control, and the proposed PPMPC can significantly improve the vehicle speed-tracking accuracy and control stability compared with the traditional model predictive control (MPC) method.</div>

Since the traditional Model Predictive Control(MPC), which is widely used for trajectory tracking of autonomous vehicle, cannot analyze and determine specific parameters of the controller by mathematical methods. In this paper, a trajectory tracking control method based on model prediction is proposed to solve the problem of unmanned vehicle trajectory tracking, and the controller is optimized in a performance objective driven way. Specifically, the cost function of the model predictive controller is parameterized. And the global optimal performance in a specific scenario as the goal to build the global performance cost function. Then, the global performance cost is expressed as a Gaussian process, and new parameters of the next optimization are inferred by Bayesian optimization. The controller parameters of global performance optimization are found with a small learning cost through multiple iterations to improve tracking performance. To verify the effectiveness of this data-driven optimization algorithm, lane-changing experiments with Carsim and Matlab/Simulink are carried out. According to the test data, it is proved that the performance of trajectory tracking under this data-driven MPC algorithm is optimized.

Accurate trajectory tracking control of mobile robots is a complex task due to inherent system nonlinearities, modeling uncertainties, and external disturbances. To tackle these challenges, this paper proposes a neural network-based residual learning approach (NNRes) for high-fidelity and efficient system modeling. Unlike full model learning, the NNRes framework focuses on learning only the residual error between a nominal physical model and the actual system dynamics, thus preserving prior knowledge while enhancing adaptability. This hybrid model, combining the physical model and learned residual, is embedded into a Nonlinear Model Predictive Control (NMPC) scheme to improve control accuracy and robustness. The proposed method is systematically compared with state-of-the-art methods: full model learning using NNs (NNFull) and residual learning using Gaussian Processes (GPRes). Comparative simulation results demonstrate that NNRes achieves superior trajectory tracking control performance, enhanced robustness, and lower computational cost. These findings validate the effectiveness of NNRes within NMPC frameworks and offer valuable insights for the intelligent control of complex robotic systems.

Intelligent vehicle trajectory tracking exhibits problems such as low adaptability, low tracking accuracy, and poor robustness in complex driving environments with uncertain road conditions. Therefore, an improved method of adaptive model predictive control (AMPC) for trajectory tracking was designed in this study to increase the corresponding tracking accuracy and driving stability of intelligent vehicles under uncertain and complex working conditions. First, based on the unscented Kalman filter, longitudinal speed, yaw speed, and lateral acceleration were considered as the observed variables of the measurement equation to estimate the lateral force of the front and rear tires accurately in real time. Subsequently, an adaptive correction estimation strategy for tire cornering stiffness was designed, an AMPC method was established, and a dynamic prediction time-domain adaptive model was constructed for optimization according to vehicle speed and road adhesion conditions. The improved AMPC method for trajectory tracking was then realized. Finally, the control effectiveness and trajectory tracking accuracy of the proposed AMPC technique were verified via co-simulation using CarSim and MATLAB/Simulink. From the results, a low lateral position error and heading angle error in trajectory tracking were obtained under different vehicle driving conditions and road adhesion conditions, producing high trajectory-tracking control accuracy. Thus, this work provides an important reference for improving the adaptability, robustness, and optimization of intelligent vehicle tracking control systems.

Differential-algebraic equation-based model predictive control for trajectory tracking of spacecraft-mounted continuum manipulators

Japan’s rapidly aging population and shrinking workforce are creating serious challenges, especially in jobs that require long hours outdoors. To solve this, Japan urgently needs innovative solutions, including automation technologies for outdoor work such as farming, construction, and maintenance. One promising approach is the application of model predictive control (MPC) to outdoor mobile robots. Although MPC has been widely studied in the context of mobile robotics, there remains a paucity of practical research specifically targeting cleaning robots operating in outdoor environments. Alternative approaches, such as geometric path-following methods like pure pursuit, are frequently employed in simpler applications, but often encounter limitations in achieving high-precision trajectory tracking. This study proposes a model predictive contouring control (MPCC) framework for trajectory tracking in outdoor cleaning robots. The proposed method offers the capability to balance the trade-off between execution time and trajectory accuracy. Both simulation and experimental results validate the effectiveness of the proposed MPCC approach.

A novel model predictive control- (MPC-) based trajectory tracking controller for mobile robot is proposed using the event-triggering mechanism, and the aim is to solve the problem that the MPC optimization problem requires a large amount of online computation and communication resources. This method includes two different event-triggering strategies, namely, the event-triggering based on threshold curve and the event-triggering based on threshold band. The selection of the triggering threshold is achieved by applying the statistical method to the historical data of the trajectory tracking of the mobile robot under the classic MPC method. Simulation and experimental tests illustrate that the proposed approach is able to significantly reduce the computation and communication burdens without affecting the control performance. Furthermore, the experimental results show that compared with the classic MPC-based tracking method, the proposed two event-triggering strategies can reduce 28.1% and 75.7% of the computation load and 0.886 s and 2.385 s communication time.

In this paper, a simplified dynamic vehicle model is established to accurately describe the dynamics of Unmanned Ground Vehicle (UGV) in trajectory tracking, while meeting the real-time computing requirement. And a modified model predictive control (MPC) algorithm with soft constraint for UGV trajectory tracking is proposed to improve the tracking stability and rapidity. The optimal control problem at each sampling time is converted into a quadratic program (QP), which has mature solutions. To verify the trajectory tracking capabilities, the proposed MPC controller is compared with a PD controller under different longitudinal velocities. The simulation results demonstrate that the MPC controller can effectively reduce the tracking error and ensure the vehicle's traveling smoothness.

Unmanned logistics vehicle (ULV) realize the automation and intelligence of cargo transportation, which improves the efficiency, cost-effectiveness and safety of logistics and distribution, while the trajectory tracking control of ULV is the key technology to ensure their safe and efficient delivery of goods. In order to solve the trajectory tracking problem of ULV in the process of delivering goods, this paper proposes a model predictive control (MPC) method based on event-triggered and fuzzy adaptive optimization parameters. Firstly, the dynamics model of the ULV is established. Secondly, an event-triggered mechanism is introduced to establish ET-MPC, while a disturbance observer is designed considering the external disturbance and the controller calculation discarding the nonlinear term. Thirdly, the advantages of fuzzy control and MPC algorithms are integrated, and the four important parameters in the MPC controller are adaptively optimized by fuzzy control, and the improved MPC control strategy is designed. Finally, the CarSim-Matlab/Simulink co-simulation platform and the experimental vehicle platform are constructed to verify the effectiveness of the improved MPC trajectory tracking controller proposed in this paper. The results show that the improved MPC control strategy can reduce the computation time of the controller, and the total number of triggering times of the controller is reduced by 46.44% compared with the classical MPC, which reduces the computational complexity of the controller and improves the accuracy and smoothness of the trajectory tracking of the ULV.

This paper proposes an improved constrained networked model predictive tracking control design for the chamber pressure of a coke furnace under uncertainty and packet losses. Unlike conventional constrained model predictive control (MPC) strategies that have a limitation in the consideration of both set-point tracking and the dynamic process responses, the system state variables and output tracking errors are combined and thus can be regulated simultaneously in the new MPC scheme. Based on such advantages, there are more degrees of freedom for the subsequent controller design and improved system performance can then be obtained. Case studies on the regulation of chamber pressure of a coke furnace under process uncertainties and packet losses are investigated to verify the proposed approach in comparison with typical traditional constrained MPC schemes.

For continuously changing road conditions and vehicle operating states, the exactitude of vehicle path tracking has not been secured by model predictive control based on linear lateral stiffness. An amended square root cubature Kalman filter method based on the minimization of a new covariance of interest is proposed to calculate the tire lateral deflection force in real time. The ratio of the estimated tire force to the linear tire force was used as a ratio to adjust the lateral deflection stiffness, and an adaptive model predictive controller was built based on the vehicle path-tracking error model to correct the tire lateral deflection stiffness. Finally, an analysis based on the joint CarSim and Simulink simulation platform shows that compared to a conventional model predictive control (MPC) controller, a trajectory-following controller built based on this method can effectively reduce the lateral distance error and heading error of an autonomous vehicle. Especially under low adhesion conditions, the conventional MPC controllers will demonstrate large instability during trajectory tracking due to the deviation of the linear tire force calculation results, whereas the adaptive model predictive control (AMPC) controllers can correct the side deflection stiffness by estimating the tire force and still achieve stable and effective tracking of the target trajectory. This suggests that the proposed algorithm can improve the effectiveness of trajectory tracking control for autonomous vehicles, which is an important reference value for the optimization of autonomous vehicle control systems.

In order to fully explore the potential of distributed drive electric vehicle, an integrated coordination control method consists of model predictive control (MPC) and speed tracking control for trajectory tracking is proposed in this paper. Firstly, the vehicle dynamics model including the slip ratio of each wheel is established. Then, a multi-objective function of the MPC controller is established based on the principle of minimum tracking error, control vector, and control increment. And the optimal control sequences are obtained by optimizing the solution and correcting the feedback of the MPC, which satisfy both the actual kinematic constraints and the actuator performance constraints. The steering angle signal is sent to the steering motor directly, and the torque signal of each wheel which is obtained by superimposing the torque value output by the MPC controller and speed tracking controller is sent to the driving motor simultaneously. Finally, the proposed method is validated by using MATLAB/Simulink-Carsim co-simulation on different roads with conventional and severe pavement conditions. The simulation results show that the designed integrated coordination controller has obvious advantages in terms of tracking accuracy and body attitude stability during the course of lane change.

In this paper, a nonlinear model predictive control (NMPC) scheme for path tracking of autonomous vehicles using discrete previewed points in the inertial coordinate is presented. The control objective is to improve the tracking accuracy under small lateral acceleration in the scenario of low speed and narrow space. The path tracking problem is formulated as a nonlinear model predictive control model, in which the vertical distance between the vehicle position and the tangent of previewed point is adopted to evaluate the tracking error. The discrete previewed points are generated from the path points independently, which does not rely on the approximate path functions. The iterative initial values of the optimization model are appropriately selected by combining with the Stanley method to accelerate optimization computations. A simulation comparison between the proposed NMPC controller and a linear model predictive control (LMPC) controller is conducted through Carsim-Matlab/Simulink co-simulations. Simulation results show that the proposed controller exhibits better tracking accuracy than the LMPC controller under small lateral acceleration, especially when the path curvature is large and continuously changing.