Nonlinear Vehicle Dynamic Model Research Articles

Adaptive backstepping control for nonlinear CAVs platoon with input delays and disturbances

In recent years, the platoon control of connected autonomous vehicles (CAVs) has attracted a lot of attention in intelligent transport research. The third-order nonlinear vehicle dynamics model, due to its practicality, has been adopted in many research projects. In platoon control, controller input delays and disturbances are the significant issues that cannot be ignored. To this end, this paper investigates the cooperative control problem of third-order nonlinear CAVs platoon with controller input delays and unknown external disturbances. First, the neural network (NN) is used to approximate external disturbances with unknown bounds. Then, with the help of Pade approximation, a new variable is introduced to deal with the input delays. Subsequently, a corresponding compensation system is constructed based on the introduced variable. At last by using backstepping approach, a distributed adaptive control strategy based on vehicle-to-vehicle (V2V) communication is proposed in this paper. Additionally, Lyapunov functions and the uniformly ultimately bounded stability theorem are used to demonstrate the stability of the closed-loop systems, and the effectiveness of the control strategy is demonstrated by a simulation example.

Research on Yaw Stability Control Strategy Based on Direct Slip Rate Allocation

This paper deals with the integrated control of trajectory tracking and yaw stability for autonomous vehicles. Firstly, a nonlinear vehicle dynamics model is established. The MPC algorithm was used to determine the best front wheel angle. The PID control algorithm is used to ensure the accuracy of longitudinal speed tracking. The sliding mode control algorithm is used to generate additional yaw moment and optimize the distribution of longitudinal tire force. In order to ensure the most effective distribution of the driving torque of the four wheels of the vehicle, the PID algorithm is used to track and manage the longitudinal slip rate of each tire on the bottom layer. Simulation tools such as MATLAB/Simulink and Carsim are used to verify the effectiveness of the multi-closed-loop integrated control technology. Compared with the general control strategy (no slip rate control), the trajectory error of this control algorithm is reduced by 55.6%, which indicates that it has advantages in obtaining a high tracking accuracy and ensuring the stability of autonomous vehicles.

Reliable Estimation of Automotive States Based on Optimized Neural Networks and Moving Horizon Estimator

Accurate estimation of vehicle sideslip angle and attitude angles are essential for the safety control and lateral behaviour of driving performance. In this article, the variation of wheels cornering stiffness is considered for sideslip estimation and addressed by introducing a recursive least squares approach. Based on the nonlinear vehicle dynamic model and the investigated coupling effect between lateral and longitudinal velocity, an optimized moving horizon estimator is proposed to obtain the vehicle sideslip angle, in which an iteration decent algorithm is integrated. Furthermore, a framework, consisting of inertial navigation system measurements, a dual neural network and a square-root cubature Kalman filter, is designed, such that the influence of sensor noise and varied maneuvers are alleviated when estimating the system states. Finally, extensive simulation and field experiments are carried out on different driving scenarios to verify the effectiveness of the developed method. The obtained results clearly indicate the satisfactory estimation accuracy of the designed strategy, superior to the existing estimation methods, such as sole neural networks methods and Kalman-based filters.

Vehicle state and parameter estimation based on improved extend Kalman filter

In order to reduce the influence of historical measurement data errors in the process of vehicle state estimation and improve the accuracy of the vehicle state estimation, a limited memory random weighted extended Kalman filter (LMRWEKF) algorithm is proposed. Firstly, a 3-DOF nonlinear vehicle dynamics model is established. Secondly, the limited memory extended Kalman filter is formed by fusing the limited memory filter and the extended Kalman filter. Then, according to the random weighting theory, the weighting coefficients that obey Dirichlet distribution are introduced to further improve the filtering estimation accuracy. Finally, a virtual test based on the ADAMS/CAR is used for the experimental verification. The results show that the error in the longitudinal velocity and the yaw rate is small, especially in the mean value of estimation error of side slip angle which is different in just 0.015 degrees between the virtual test and the simulation result. And also, the results compared with traditional methods indicate that the proposed LMRWEKF algorithm can solve the problem of vehicle state estimation with the performance of noise fluctuation suppression and higher estimation accuracy. The mean absolute error (MAE) and root mean square error (RMSE) are considered to verify the estimation accuracy of the proposed algorithm. And the comparison results indicate that the estimation accuracy of the LMRWEKF algorithm is significantly higher than those of the EKF and DEKF methods.

Integrated Longitudinal and Lateral Vehicle Stability Control for Extreme Conditions With Safety Dynamic Requirements Analysis

Under extreme conditions, vehicle states change rapidly between stable and unstable, resulting in dynamic requirements for the vehicle’s overall safety stability. Simultaneously, the coupled nonlinear characteristics of vehicle dynamics cannot be ignored in controller design. To address the above problems and improve vehicle longitudinal and lateral stability integrally, an envelope-based model predictive control (MPC) strategy with dynamic objectives is proposed for four-wheel independent motor-drive electric vehicles (4WIMD EVs). First, according to the current driving behavior and the collected road information, the envelope control regions concerning vehicle side-slip angle and yaw rate are obtained online, and divided into stable, critically stable, and instable regions with different safety requirements. Then, the safety dynamic requirements are constructed in the designed MPC-based control structure. A nonlinear vehicle dynamics model with a combined-slip tire model, which integrates the longitudinal and lateral dynamics, is utilized to predict vehicle states. The switching of requirements is reflected in the variation of weighting factors and constraint values. Finally, CarSim and Matlab/Simulink co-simulation, and hardware-in-the-loop simulation test results show better satisfactory performance in improving overall vehicle stability under extreme driving conditions.

Nonlinear integrated control with friction estimation for automatic lane change on the highways

A vehicle is a highly nonlinear dynamical system with high degrees of freedom. There are also very strong couplings between the longitudinal and lateral dynamics. Therefore, the simultaneous longitudinal and lateral motion control in different road conditions is a challenging problem. This paper presents an integrated adaptive control for longitudinal and lateral vehicle guidance on the highways. The contribution of this work is the design of a robust integrated controller that can handle tyre-road friction changes with low computational cost The proposed controller can adapt to the variations of tyre and road specifications. The strength of this method is that without the use of complex models, the nonlinear tyre dynamic is considered in the design of the controller. Therefore, despite the consideration of a comprehensive nonlinear vehicle dynamic model and the ability to adapt to changes in tyre and road specifications, the computational cost of the algorithm is very small. Besides, due to the controller robustness, there are no concerns about uncertainties. To validate the proposed algorithm, a full vehicle model in CarSim software is used. In obtained results, it is assumed that the yaw rate, longitudinal and lateral acceleration signals are available and have noises. The estimation of longitudinal and lateral velocities and other vehicle states has been done using these signals. Results for different road conditions as well as various vehicle movement modes confirm that tracking of longitudinal and lateral positions has been carried out with high precision. Besides, the results show that the proposed integrated control guarantees the stability of the vehicle, it will manage the tyre-road friction changes well, and also it is resistant to unmodeled uncertainties.

A Model Predictive Control Method for Vehicle Drifting Motions with Measurable Errors

Vehicle drifting control has attracted wide attention, and the study methods are divided into expert-based and theory-based. In this paper, the vehicle drifting control was based on the vehicle drifting state characteristics. The vehicle drifting state parameters were obtained by the theory-based vehicle drifting motion mechanism analysis based on a nonlinear vehicle dynamics model, which was used to express the vehicle characteristics, together with the UniTire model, by considering the vehicle longitudinal, lateral, roll, and yaw motions. A vehicle drifting controller was designed by the model predictive control (MPC) theory and a linear dynamics model with the linearized expressions of nonlinear tire forces based on the consideration of measurable errors. The control targets were the vehicle drifting state parameters obtained by calculation, and the controller performance was proved by simulation in MATLAB/Simulink, demonstrating that the controller is good to realize vehicle drifting motions. The same target drifting motions were realized at different original states, which proved that the vehicle drifting control is possible with the designed controller.

Adaptive Cruise Control for Intelligent City Bus Based on Vehicle Mass and Road Slope Estimation

Adaptive cruise control (ACC), as a driver assistant system for vehicles, not only relieves the burden of drivers, but also improves driving safety. This paper takes the intelligent pure electric city bus as the research platform, presenting a novel ACC control strategy that could comprehensively address issues of tracking capability, driving safety, energy saving, and driving comfort during vehicle following. A hierarchical control architecture is utilized in this paper. The lower controller is based on the nonlinear vehicle dynamics model and adjusts vehicle acceleration with consideration to the changes of bus mass and road slope by extended Kalman filter (EKF). The upper controller adapts Model Predictive Control (MPC) theory to solve the multi-objective optimal problem in ACC process. Cost functions are developed to balance the tracking distance, driving safety, energy consumption, and driving comfort. The simulations and Hardware-in-the-Loop (HIL) test are implemented; results show that the proposed control strategy ensured the driving safety and tracking ability of the bus, and reduced the vehicle’s maximum impact to 5 m/s3 and the State of Charge (SoC) consumption by 10%. Vehicle comfort and energy economy are improved obviously.

On the benefit of smart tyre technology on vehicle state estimation

Among other variables, smart tyre systems are capable of determining tyre contact forces. Combining this information with the signals obtained from conventional vehicle sensors, e.g. inertial measurement units, wheel speed sensors and steering wheel angle sensors, improves the estimation accuracy of the states used by the vehicle dynamics controllers of production cars. This study assesses the performance improvement brought by the vertical and longitudinal tyre contact force signals, obtained through smart tyres, to an unscented Kalman filter (UKF) for vehicle speed and sideslip angle estimation, based on a nonlinear vehicle dynamics model. Two UKF designs, excluding and including smart tyre information, are compared by using experimental data from a purposely sensorised high-performance passenger car, along a comprehensive set of manoeuvres. The results show average ∼60% and ∼37% reductions of the root mean square values of the normalised vehicle speed and sideslip angle estimation errors for the filter design receiving the smart tyre information. In comparison with the more conventional UKF design without tyre force inputs, the smart tyre based estimator is also characterised by significantly enhanced robustness and adaptability to typical variations of vehicle and tyre parameters, such as the tyre-road friction coefficient.

A Simplified Vehicle Dynamics Model for Motion Planner Designed by Nonlinear Model Predictive Control

Motion planning by considering it as an optimal problem is an effective and widely applicable method. Its comprehensive performance greatly depends on the vehicle dynamics model, which is highly coupled and nonlinear, especially under the dynamical scenarios and causes much more consumption of computation resources for the numerical optimization. To increase the real time performance of the motion planner designed by nonlinear model predictive control (NMPC), a unified and simplified vehicle dynamics model (SDM) is presented to make a balance between the accuracy and complexity for dynamical driving scenarios. Based on the statistical analysis results of naturalistic driving conditions, a unified nonlinear vehicle dynamics model is set up, which considers the tyre cornering characteristic and is also applicable to conditions with large turning angle. After the validation of this coupled dynamics model (CDM) by comparisons with other widely used models under a variety of conditions, the coupling effect is analyzed according to the transfer functions, which are obtained by linearizing CDM at equilibrium points. Furthermore, SDM is derived by ignoring the weak part of the coupling effect. The accuracy of SDM is validated by several comparative studies with other models and it is further applied to design a motion planner by NMPC to validate its contribution on the performance improvement under dynamical driving conditions.

Vehicle State Estimation Based on Strong Tracking Central Different Kalman Filter

Vehicle active safety control was a key technology to avoid serious safety accidents, and accurate acquisition of vehicle states signals was a necessary prerequisite to achieve active vehicle safety control. Based on the purpose, a 3-DOF nonlinear vehicle dynamics model containing constant noise and a nonlinear tire model were established, and several vehicle key states were estimated by a strong tracking central different Kalman filter (CDKF). The conclusion showed that the proposed estimator had higher accuracy and less computation requirement than the CKF, CDKF, and UKF estimators. Numerical simulation and experiments indicated that the proposed vehicle state estimation method not only had higher estimation accuracy but also had higher real-time function.

Research on intelligent vehicle lane changing and obstacle avoidance control based on road adhesion coefficient

Aimed at the safety and stability problems of intelligent vehicles under extreme conditions such as low adhesion road surface and emergency lane change and obstacle avoidance, this article designs a lane change and obstacle avoidance controller based on road adhesion coefficient. Using the nonlinear vehicle dynamics model as the prediction model, using the recursive least squares method to identify the road adhesion coefficient, considering the road adhesion coefficient to plan and adjust in the obstacle avoidance path as well as limit constraint conditions of the model predictive control controller, using model predictive control method for the expectation of intelligent vehicle trajectory tracking, travels tremendously guarantee the security and stability of driving. The joint CarSim–Simulink simulations results show that under poor road conditions, the trajectory tracking accuracy after optimization is higher and the vehicle is less prone to sideslip and instability. The lane change controller designed in this article has strong adaptability to different road surface adhesion coefficient, and all parameters can be controlled within a reasonable safety range at different speeds, with good robustness.

Observer-based finite frequency [formula omitted] state-feedback control for autonomous ground vehicles

This paper studies the problem of path tracking of Autonomous Ground Vehicles (AGVs) in the presence of sideslip angles. An observer is designed to estimate both the sideslip angle and the vehicle yaw rate, based on which an observer-based controller is established such that the closed-loop system is stable and the vehicle follows a desired path accurately. In particular, the nonlinear vehicle dynamics model is reformulated as a Linear Parameter Varying (LPV) system, and a finite frequency H∞ criteria is satisfied such that the disturbances are attenuated effectively, the parameter-dependent gain matrices are calculated simultaneously by solving a convex optimization problem. Simulation results show the effectiveness of the method proposed.

Design of Vehicle Stability Controller Based on Fuzzy Radial Basis Neural Network Sliding Mode Theory with Sideslip Angle Estimation

This study is targeted at the key state parameters of vehicle stability controllers, the controlled vehicle model, and the nonlinearity and uncertainty of external disturbance. An adaptive double-layer unscented Kalman filter (ADUKF) is used to compute the sideslip angle, and a vehicle stability control algorithm adaptive fuzzy radial basis function neural network sliding mode control (AFRBF-SMC) is proposed. Since the sideslip angle cannot be directly determined, a 7-degrees-of-freedom (DOF) nonlinear vehicle dynamic model is established and combined with ADUKF to estimate the sideslip angle. After that, a vehicle stability sliding mode controller is designed and used to trace the ideal values of the vehicle stability parameters. To handle the severe system vibration due to the large robustness coefficient in the sliding mode controller, we use a fuzzy radial basis function neural network (FRBFNN) algorithm to approximate the uncertain disturbance of the system. Then the adaptive rate of the system is solved using the Lyapunov algorithm, and the systemic stability and convergence of this algorithm are validated. Finally, the controlling algorithm is verified through joint simulation on MATLAB/Simulink-Carsim. ADUKF can estimate the sideslip angle with high precision. The AFRBF-SMC vehicle stability controller performs well with high precision and low vibration and can ensure the driving stability of vehicles.

Vehicle State Estimation Based on Unscented Kalman Filtering and a Genetic-particle Swarm Algorithm

Vehicle state and parameter estimation has gradually become an important way to soft-sense some variables that are difficult to measure directly using general sensors. In the traditional Kalman filtering algorithm, the selection of the process noise covariance matrix and the measurement noise covariance matrix will directly affect the filtering accuracy of the algorithm. In order to improve the filtering accuracy of the filter algorithm to obtain the optimal solution, based on a 7-DOF nonlinear vehicle dynamics model and the Magic formula tire model, a hybrid algorithm containing an unscented Kalman filter (UKF) and a genetic-particle swarm algorithm (genetic-particle swarm UKF) is used to estimate several vehicle key states. Compared with traditional estimator based on UKF and the unscented particle filter (UPF), the simulation and real vehicle test results show that the proposed estimator based on the genetic-particle swarm UKF algorithm has higher accuracy and less computation requirements than the UKF estimator. And also, the proposed hybrid algorithm has superiority on the convergence speed of the optimization than the UPF algorithm. The results of a real-vehicle experiment demonstrate that the proposed hybrid algorithm can be used effectively for solving the vehicle-state estimation problem.

On co-estimation and validation of vehicle driving states by a UKF-based approach

Abstract. It is necessary to acquire the accurate information of vehicle driving states for the implementation of automobile active safety control. To this end, this paper proposes an effective co-estimation method based on an unscented Kalman filter (UKF) algorithm to accurately predict the sideslip angle, yaw rate, and longitudinal speed of a ground vehicle. First, a 3 degrees-of-freedom (DOFs) nonlinear vehicle dynamics model is established as the nominal control plant. Then, based on CarSim software, the simulation results of the front steer angle and longitudinal and lateral acceleration are obtained under a variety of working conditions, which are regarded as the pseudo-measured values. Finally, the joint simulation of vehicle state estimation is realized in the MATLAB/Simulink environment by using the pseudo-measured values and UKF algorithm concurrently. The results show that the proposed UKF-based vehicle driving state estimation method is effective and more accurate in different working scenarios compared with the EKF-based estimation method.

Motion Control of a 4WS4WD Path-Following Vehicle: Dynamics-Based Steering and Driving Models

This paper deals with a four-wheel-steering four-wheel-driving (4WS4WD) vehicle under the path-following control. Focuses are placed on the motion control of the vehicle, and the drive forces and steering angles for achieving accurate path-following by the vehicle are determined. In this research, a nonlinear vehicle model of three degrees of freedom (DOFs) is used. The vehicle path-following dynamics are modeled using the classical mass-damper-spring vibration theory, which is described by three ordinary differential equations of second order with lateral, heading and velocity deviations, and control parameters. Combined with the vehicle path-following dynamic model, the nonlinear vehicle dynamic model is decoupled in generalized coordinate space. The required drive forces and steering angles for the vehicle path-following controllers are thus calculated and control models are obtained. Theoretical analysis for steering and driving control models is also carried out. It discloses that control models can maintain good performance against uncertainties. The vehicle path-following control is exhibited by dynamic simulation in CarSim with consideration of a complex vehicle model and a variable-curvature planned path. Numerical results obtained are analyzed and show control models have capable of dealing with a complex path-following problem. This paper provides a new insight into understanding path-following control of a 4WS4WD vehicle at the generalized vibration level.

Adaptive non‐linear coordinated optimal dynamic platoon control of connected autonomous distributed electric vehicles on curved roads

A novel adaptive coordinated platoon control of connected autonomous distributed electric vehicles (CADEVs) on curved roads is proposed to increase traffic security. The nonlinear vehicle dynamic model that can precisely reflect the driving behaviours of CADEVs on curved roads is deduced by the Newton–Euler method. Owing to the fact that CADEVs have the strong coupled, uncertain non-linear and over-actuated features, a novel disturbance observer-based adaptive coordinated optimal dynamic platoon control strategy is presented to supervise the lateral and longitudinal coupled motions of CADEVs on curved roads, in which the switching gains of backstepping sliding mode control term are precisely adjusted by the neural-network technique, and the uniform ultimate boundedness of closed-loop high-level control system is guaranteed through the Lyapunov stability theory. Then, a sequential quadratic programming (SQP) tire distributor is the basic component of the low-level control law, which can realise the dynamic control distribution of over-actuated tire actuators of CADEVs. Finally, the results manifest the effectiveness of the proposed adaptive coordinated platoon control strategy.

Model predictive control of steering torque in shared driving of autonomous vehicles.

The current path tracking control method is usually based on the steering wheel angle loop, which often makes the driver lose control of the automatic driving control loop. In order to involve the driver in the automatic driving control loop, and to solve the vehicle path tracking control problem with system robustness and model uncertainty, this paper puts forward a steering torque control method based on model predictive control algorithm. Based on the vehicle model, this method introduces the steering system model and the steering resistance torque model, and calculates the optimal control torque of the vehicle through the real-time vehicle status, so as to make up for the model mismatch, interference and other uncertainties, and ensure the real-time participation of the driver in the automatic driving control loop. To combine the nonlinear vehicle dynamics model with the steering column model, and to take the vehicle state parameters as the feedback variables of the model predictive controller model, then input the solution of the steering superposition control rate into the vehicle model, the design of the steering controller is realized. Finally, to carry out the simulation of lane keeping based on CarSim software and Simulink control model, and the hardware in-the-loop test on the hardware in-the-loop experimental platform of CarSim/LabVIEW-RT. The simulation and test results indicate that the designed torque loop path tracking control method based on model predictive control can help the driver track the target path better.

The validation of a semi-recursive vehicle dynamics model for a real-time simulation

Semi-recursive formulations and their various versions have made it possible to describe complex nonlinear systems such as vehicles precisely while still solving the relevant equations of motion in real time. An optimal combination of an efficient multibody formulation and a fast numerical time integration scheme are needed to accurately simulate complex systems in real time. This paper introduces a double-step semi-recursive multibody formulation and analyzes its performance with high-order numerical time-integration algorithms for real-time simulation. The Runge-Kutta, Gill, Runge-Kutta-Fehlberg, Adams-Bashforth-Moulton, and adaptive time step Runge-Kutta numerical methods are explained and compared. Results are verified against a commercial multibody software solution. A 15-degree-of-freedom sedan vehicle model serves as a benchmark to verify the theoretical results. The results highlight the differences between the numerical algorithms and suggest appropriate approaches for a nonlinear vehicle dynamics model, particularly for cases where simulation times are long.