Coupled Lateral And Longitudinal Control For Vehicles Based On Differential Flatness Approach

Vehicle motion control technology is of great significance and practical application value to improve the comprehensive performance of vehicle driving.The vehicle system considering the lateral and longitudinal coupling can more comprehensively describe the dynamic characteristics of vehicle driving and reveal the interaction and influence between the lateral and longitudinal motion.However,with the increase of degree of freedom and strong nonlinear and coupling characteristics of vehicle system,the design and analysis of control methods are difficult and challenging.This dissertation focuses on the vehicle motion control method considering lateral and longitudinal coupling.By looking for suitable flat output to transform the system,the coupling nonlinear problem in vehicle motion control is solved.A series of control strategies are designed to improve the stability and trajectory tracking performance of the vehicle system.The control quality of the system can be guaranteed under the influence of parameters uncertainty,unmodeled dynamics and external disturbances.The main research contents are summarized as follows:Considering the nonlinear,strong coupling and under-actuated vehicle coupling dynamics model,the control strategy is designed based on differential flatness method to improve the handling stability of the vehicle system.In order to solve the problem that the vehicle sideslip angle is difficult to be directly measured by the sensors,a reduced order state observer is designed based on the robust fixed-time sliding mode control method to estimate the unknown vehicle sideslip angle.By selecting a group of suitable flat outputs,the control of the sideslip angle and yaw rate of the vehicle can be adjusted automatically with the change of the velocity,so as to solve the problem that the sideslip angle and yaw rate of the vehicle cannot converge to the reference signal at the same time.A calculation method of the flat output reference signal is given according to the steady-state steering relationship of the vehicle.Based on the selected flat output,the under-actuated coupled vehicle dynamics model is transformed into Brunovsky canonical form,and considering the non-negligible mismatched disturbance in the flat system due to the influence of longitudinal motion on the dynamics of sideslip angle,a robust fixed-time sliding mode controller is designed to deal with both matched and mismatched disturbances in the system.At the same time,the fixed time convergence of the system is guaranteed while taking into account the control performance of vehicle sideslip angle and yaw rate.Simulation results show that the proposed control strategy can effectively improve vehicle handling stability and has strong adaptability to different driving speeds.Considering the uncertainty of the parameters and the unmodeled dynamics of the system,an adaptive robust integral of the sign of the error control strategy based on the inverse model is designed to improve the robustness of the vehicle’s lateral and longitudinal coupling dynamics system based on four-wheel independent drive/brake.Since the driving/braking torque of the same side of the vehicle chassis has the same effect on the lateral motion of the vehicle,the three-degree-of-freedom coupling dynamic model of the vehicle is obtained by using the direct proportional distribution method,and the differential flatness property and reversibility of the model are verified.Considering that the key parameters of the vehicle system may change with the road environment,which leads to the increase of the uncertainty of the system,an adaptive robust integral of the sign of the error controller based on the inverse model of the system and nominal parameters is designed.For the problem of unknown upper bound of system uncertainty,an adaptive method is designed to adjust the threshold of the robustness term of the auxiliary system,and the introduction of auxiliary variables avoids the use of filter tracking error signals which are difficult to measure in the controller.The proposed method ensures the vehicle’s handling stability and adaptability to parameter changes.The Lyapunov method is used to prove that all signals of the system are bounded and tracking errors converge asymptotically.The simulation results show that the proposed control method has strong robustness to the vehicle parameter change and unknown disturbances.Aiming at the path tracking control problem of a vehicle system considering lateral and longitudinal coupling,a path tracking controller based on flat output preview is designed to ensure the vehicle’s path tracking accuracy and transient performance of the system.Considering the impact of longitudinal motion on lateral path tracking performance,a path tracking model for under-actuated vehicles is established based on the Serret-Frenet coordinate system.In order to take into account the control of lateral displacement error and heading angle error during path tracking,a preview tracking error model is established using the flat output of the under-actuated vehicle system as the preview point.The advantage is to decouple the vehicle’s rear axle tire lateral force from the dynamic equation of the preview tracking error,effectively suppressing the uncertainty impact caused by the rear axle tire lateral force while simplifying the model.Considering the modeling errors,nonlinearity,and strong coupling characteristics in the system,a fixed-time second-order sliding mode controller based on the super-twisting algorithm is designed to effectively handle the impact of system uncertainty on tracking performance while ensuring fast and stable convergence of tracking errors.The simulation results show that the proposed control strategy can ensure good path tracking accuracy and transient performance under different speeds and path curvature.The trajectory tracking control problem of four-wheel independent drive/brake vehicle is studied.Based on differential flatness theory and backstepping method,nonlinear control strategies are designed to improve the stability and tracking performance of vehicle system.Considering the vehicle kinodynamic model composed of the vehicle kinematics equation in the global coordinate system and the vehicle dynamics equation of four-wheel independent drive/brake,the differential flatness property of the whole system is proved by finding a group of suitable flat outputs,and the complex vehicle kinodynamic model is transformed into three fully-actuated subsystems with the same structure.The design process of controller is greatly simplified.Considering the impact of system uncertainty,a backstepping controller based on disturbance observer is designed to ensure the input-state stability of the closed-loop system.The simulation results show that the proposed control scheme can effectively improve the vehicle trajectory tracking accuracy.Furthermore,considering the impact of the constraints of the sideslip angle and yaw rate on the transient performance and tracking accuracy,the constant constraint on the sideslip angle and the time-varying constraint on the yaw rate are converted into partial state constraints of each flat subsystem.A time-invariance constraint tracking controller and a time-varying constraint tracking controller based on barrier Lyapunov function method are designed respectively,which can ensure the transient performance and tracking accuracy of trajectory tracking while taking into account the lateral stability.Simulation results under different driving conditions verify the effectiveness of the proposed method.