Path Tracking Control of Autonomous Vehicle Based on Nonlinear Tire Model

Advanced vehicle dynamics control systems, such as integrated chassis control systems, are generally designed in a two layers structure: a tire force determination layer, and a tire force generation layer. The tire force generation layer works as a servo function that follows the force commands from the force determination layer. Therefore, the tire force generation layer should not require a lot of computing resources. This paper presents an inverse tire model that calculates required slip ratios and slip angles when tire forces are commanded. The inverse tire model is based on a nonlinear tire model that is sufficiently complex and, thus, can capture the nonlinear characteristics of tires. Because mathematical inversion of the nonlinear tire model is challenging, recursive methods can be considered for an inverse model. However, recursive methods, such as Newton Raphson method, do not guarantee the fixed time span required for finishing the computation. This paper presents a method for inverse tire model that does not require recursive computations.

Recent research suggests the various applications of Model Predictive Control on vehicle systems. In numerous cases, nonlinear tire models such as the Magic Formula, which are highly complex and are more detailed than necessary, are used. This paper presents a nonlinear tire model that excludes the region of negative slope but expresses the nonlinear properties of tire well enough for tracking the lane of a racing course. The proposed inverse tire model can also be used to calculate the slip angle from the tire force. Thus, the model can be utilized to design the Model Predictive Controller.

This paper presents a motion control method of 6WD/6WS (6-wheel-drive and 6-wheel-steering) vehicle using optimum tire force distribution method. When we make used of independent driving and steering system, the motion control performance of the 6WD/6WS vehicle can be improved. For example, vehicle's maneuverability is more improved at low speed and vehicle's stability is also improved at high speed. Therefore, it needs to find a control strategy using optimum tire forces. A control strategy must satisfy the driver's command and minimize the energy consumption. When the driver commands vehicle (input steering angle and acceleration/brake pedal stroke), we can obtain the desired yaw moment, the desired lateral force and the desired longitudinal force. Those values are used in the optimum tire force distribution method. The optimum tire force distribution method can find the longitudinal tire force and lateral tire force. That force minimizes the cost function. The cost function is the sum of normalized tire force. The longitudinal tire forces and lateral tire force of each wheel are converted to the reference torque inputs and steering wheel angle inputs. The method was tested on the simulation and effectiveness was verified.

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 this paper, by making use of the important merit that electric vehicle's motor torque can be measured and controlled accurately, a body slip angle (beta angle) observer based on nonlinear tire model and a novel control method of body slip angle are introduced. Experimental results by UOT March II are shown to verify the effectiveness of the proposed observer. Simulations and tests are conducted to test the control method. The torque difference can be generated directly with in-wheel motors to control body slip angle at its desired value to keep vehicle's stability.

Longitudinal and lateral forces acting on tyres are known to be closely related to tractive ability, braking characteristics, handling stability and manoeuvrability of ground vehicles. However, it is not feasible in the operating vehicles to measure the tyre forces directly because of the high cost of sensors, the limitations in sensor technology, interference with tyre rotation and the harsh environment. Another approach is the indirect monitoring technique that can estimate the tyre forces based on remote sensor outputs and vehicle dynamics models. In this paper, in order to develop tyre force-monitoring systems, a monitoring model is proposed utilizing not only the yawing motion but also the roll motion. Based on the monitoring model, a monitoring system is designed to estimate the lateral tyre force acting on each tyre. The monitoring system is constructed on the basis of a new scaled Kalman filter with model error compensator (SKFMEC) technique that is developed in this study to improve the robustness performance of Kalman filter methods. The SKFMEC technique adopts both the well-conditioned observer and the model error compensator concepts. Tyre force estimation performance of the monitoring system is evaluated in the MATLAB simulations where true tyre force data are generated from a 14-degree-of-freedom vehicle model with the combined-slip ‘magic formula’ tyre model.

This paper proposes a new LTVMPC method for AFS vehicles to enhance the vehicle stability and improve the control performance of traditional LTVMPC when tire force is near saturation. A prediction of tire force is performed in the prediction horizon on the basis of the nonlinear tire model. The control problem is solved by the quadratic programming. Finally, the proposed method is verified based on the CarSim and Matlab simulation environment. Simulation results show that the control performance of the proposed method is obviously improved compared with the traditional method.

Under extreme conditions, a vehicle's handling performance and yaw stability can significantly deteriorate. This paper proposes a handling and stability decoupled control strategy for four-wheel independent drive (4WID) and four-wheel independent steering (4WIS) vehicles based on tire force vector control (TFVC). To address the conflicting objectives of handling and stability, the turning curvature is employed as the lateral reference, while the sideslip angle serves as the stability indicator, thereby decoupling handling and stability control. Additionally, a driver intention remapping method is introduced to maximise the preview turning curvature, effectively balancing longitudinal and lateral objectives. A yaw controller is developed using non-singular terminal sliding mode control (NTSMC) to maintain vehicle stability. Pentagon constraints are formulated to integrate all tire force constraints. Deviations from the driver's expectations are incorporated into the objective function to ensure the solvability of tire force allocation. The TFVC is implemented by integrating a UniTire-based inverse tire model and a saturated tire model to accurately regulate tire forces under both combined and saturated conditions. Finally, hardware-in-the-loop (HIL) and real vehicle test results confirm that the proposed handling and stability decoupled control strategy not only ensures vehicle stability but also enhances handling performance under extreme conditions.

Reeds–Shepp (RS) curves are widely employed for path smoothing in path planning algorithms such as Hybrid A* and Rapidly-Exploring Random Trees (RRT). To ensure the stability of autonomous vehicles when traversing RS-curve paths, this paper proposes a velocity prediction and planning algorithm based on vehicle lateral dynamics. Specifically, given the path curvature and initial velocity, the yaw rate and side-slip angle of the vehicle during steady-state steering are derived using the lateral dynamics model. Considering load transfer effects, the lateral tire force is calculated from the rate of change of vertical loads, and the safe driving velocity is predicted through gradient descent with the tire force saturation coefficient as the optimization objective. Subsequently, a velocity planning method that integrates the Gaussian pseudospectral method (GPM) with sequential quadratic programming (SQP) is developed. The problem is formulated as a nonlinear programming model, in which the predicted safe velocity serves as the upper velocity constraint. Joint simulations in MATLAB/Simulink and CarSim are then conducted to evaluate the proposed framework. The results show that the prediction accuracy of the lateral tire force exceeds 94% under different road friction coefficients, confirming the reliability of the proposed prediction model. Furthermore, comparative experiments demonstrate that the velocity planning method can effectively reduce vehicle velocity from unsafe to safe levels, thereby ensuring driving stability and safety when negotiating curves.

SUMMARYA four wheel steering (4WS) control strategy is derived and evaluated using a nonlinear vehicle model along with a nonlinear tire model. The vehicle model used is a.three degree-of-freedom model. Yaw rate, lateral velocity and longitudinal velocity are considered with the roll effects included in the calculation of the normal loads for each of the four wheels. These normal forces are used in the tire model to calculate the tire forces and moments for each wheel. The results of simulation indicate the potential benefits gained by using 4WS. These benefits include stability and performance at high speeds and maneuverability at low speeds.

In this study, a collision avoidance method with model predictive control is proposed for a nonlinear model of a four-wheeled vehicle. The C/GMRES algorithm is used for solving the nonlinear model predictive control (NMPC) problem within a short sampling period. A nonlinear tire model is employed to represent the realistic behavior of a vehicle. Here, to consider whether it is possible to avoid an obstacle physically, an unavoidable region (UR) is constructed as the region in which the vehicle cannot avoid the obstacle owing to physical limitations. Even if the distance between the vehicle and the obstacle is short, the vehicle is controlled by NMPC not only to avoid the UR but also to stay on the road. A performance index for satisfying the above constraints is proposed, and control responses are investigated through numerical simulations.

This paper presents a method to design a path tracking controller with four-wheel independent braking (4WIB), drive (4WID) and steering (4WIS) systems equipped in in-wheel motor-driven electric vehicles (IWM-EVs). Generally, it is difficult to calculate the steering angles of 4WIS and the braking/traction torques of 4WIB/4WID for path tracking control. Moreover, there have been limitations of an error dynamics-based path tracking controller, which requires assumptions on a target path. To cope with these problems, the path tracking problem on a target path is converted into the yaw rate tracking one with a reference yaw rate in this paper. Two methods are adopted for the purpose of calculating a reference yaw rate. The first is to use a pure pursuit method, which generates a steering angle for path tracking. From the steering angle, a reference yaw rate is calculated. The second is to derive a reference yaw rate from a target path and a current vehicle position. For yaw rate tracking, direct yaw moment control is adopted to generate a control yaw moment. A control allocation method is adopted to distribute a control yaw moment into tire forces, generated by 4WIS, 4WID and 4WIB. Several actuator combinations are represented by various sets of virtual weights in the control allocation method. A simulation with a vehicle simulation program, CarSim^®, shows that the proposed path tracking controller is effective in enhancing the path tracking performance with 4WIS, 4WID and 4WIB. From the simulation, effects of actuator combinations on path tracking performance are analyzed.

This study investigates an integrated wheel slip, yaw rate, and sideslip angle control via torque vectoring to improve both the longitudinal and lateral stability of electric vehicles (EVs) with four in‐wheel motors. The algorithm is developed based on model predictive control (MPC) and thus can optimally reach a balance among different objectives while considering actuation and state constraints. Firstly, to deal with tyre non‐linearity and variations in the lateral tyre forces due to changes in tyre slip ratios, the mechanism of using torque vectoring to improve vehicle stability is analysed. Then, a non‐linear tyre model is introduced into the predictive model to characterise the tyre force coupling relationship. Here, a linear‐parameter‐varying (LPV) model is employed, which is derived by linearising the nonlinear vehicle model online. Moreover, the stability control of EVs with in‐wheel motors is transformed into a constrained online optimisation problem and solved using the proposed LPV‐MPC method. Finally, the proposed LPV‐MPC is compared with some existing well‐established techniques from literature in different test scenarios. The obtained results demonstrate that the LPV‐MPC approach could reduce the computational burden and shows a precise longitudinal control and obviously improves the lateral stability.

In this study, to improve the accuracy of path tracking in intelligent vehicles, we propose an intelligent vehicle path-tracking control method based on improved model predictive control (MPC) combined with hybrid proportional-integral-derivative (PID) control theory. In the lateral control, a constraint on the side deflection of the front wheel is added based on traditional MPC and a relaxation factor is introduced to improve the stability of vehicle control for the driving stability. In longitudinal control, a hybrid PID controller is designed for different road conditions to improve the accuracy of control of vehicle speed. We present the results of a co-simulation using Carim and MATLAB/Simulink and a test with a sample vehicle, which show that the proposed path tracking controller can greatly improve the path tracking accuracy and stability of an intelligent vehicle. The model-based prediction, rolling optimization solution, feedback control, and the addition of a constraint on the side deflection of the front wheel as well as a relaxation factor can ensure the lateral driving stability of an intelligent vehicle. The proposed approach achieved a lateral error of less than 1%, and the yaw angle was controlled within 4°. The longitudinal speed control based on hybrid PID controller can improve the response speed of the system and meet the real-time requirements of vehicle driving.

Trajectory tracking capability is important for automatic vehicle guidance. One difficulty for realizing accurate trajectory tracking is the requirement of knowing the tire cornering stiffness under linear tire force range or the nonlinear tire force function when tire force becomes large. In this study, the vehicle trajectory tracking problem is firstly formulated in the vehicle's local frame. Then an adaptive control methodology is adopted here to tune the discretized nonlinear cornering stiffness function. The method also has the advantage of avoiding the direct usage of vehicle's lateral velocity in generating the steering control signal. In the simulation result part, the performance of the method considering the nonlinear tire force effect is compared with a linear one. Simulation results in CarSim® illustrate that the proposed method considering the nonlinear tire force effect can show improved performance over the method only considers the linear tire force model.