Steering Angle Input Research Articles

An algorithm for solving the equilibrium points of high-dimensional nonlinear vehicle dynamic system based on a combination of genetic algorithm, sequential quadratic programming method, and continuation method

The paper proposes an algorithm that combines Genetic Algorithm, Sequential Quadratic Programming, and Continuation Method to solve the equilibrium points of a multi-degree-of-freedom vehicle nonlinear system. The algorithm’s effectiveness is demonstrated by applying it to search for equilibrium points of a 5-degree-of-freedom (5DOF) nonlinear vehicle model, which considers both longitudinal and lateral motion. The dynamic equilibrium points of front-wheel-drive, rear-wheel-drive, and all-wheel-drive vehicles with different front-wheel steering angle inputs are calculated. Taking the front-wheel-drive system as an example, the system equilibrium points are further analyzed using phase space analysis and eigenvalue analysis for verification. In addition, the impact of the driving effect on the equilibrium points bifurcation is investigated. The results show that compared with the Genetic Algorithm alone and the combination method of Genetic Algorithm and Sequential Quadratic Programming, the proposed algorithm can effectively and accurately solve the equilibrium points of the 5DOF vehicle model. The study also reveals that the driving effect significantly influences the vehicle equilibrium point bifurcation.

Dynamic Modeling and Analysis of a Driving Passenger Vehicle

This study presents a dynamic model of a passenger vehicle and analyzes its dynamic characteristics and responses. A dynamic vehicle model with seven degrees of freedom was established to analyze the behavior of a driving vehicle. The vehicle model had three degrees of freedom for the sprung mass’s motion and four degrees for the unsprung masses. For this model, the equations of motion were derived using Lagrange’s equation. To verify the model, the suspension deformations computed using the model were compared with those measured through three actual vehicle driving tests: the slalom, double lane change, and step steer tests. Furthermore, we investigated the effects of suspension stiffness, suspension damping, and anti-roll bar torsional stiffness on the dynamic characteristics and responses of the vehicle model. This study presented a new full-car model that can analyze a turning vehicle’s behavior in response to changes in the steering angle input. The developed dynamic vehicle model may help vehicle designers predict the dynamic responses of a vehicle through simulation without performing a driving test.

An Integrated Approach for Yaw Stability of Linear Time Varying Bicycle Model Utilizing Adaptive Model Predictive Control

Accidents during critical maneuvering on roads while overtaking or changing lanes are mainly due to the insufficient generation of the stability matrices of vehicles, including yaw rate. The parameters responsible for stable operation of the vehicle during these driving scenarios may vary, causing improper steering angle input actuation to the vehicle, due to which the desired yaw rate is not generated. To overcome this problem, corrective yaw moments are applied to the yaw dynamics to generate the desired yaw rate and operate the vehicle within the defined stability limit. Therefore - in this paper - to improve the yaw stability of the vehicle, a novel yaw rate gradient-based control approach is proposed for a linear time-varying (LTV) bicycle model. A 2 degrees of freedom bicycle model with the linear approximation for low slip angles in the magic formula tire model is utilized to develop the LTV model. The longitudinal velocity and friction coefficient are chosen as the parameters of interest to be varied during model simulation. Two different critical driving scenarios, including a sine maneuver and a double lane change, are chosen as input actuation with and without corrective yaw moments. The obtained simulation results unveil that, by the application of steering angle with a corrective yaw moment, the yaw stability has effectively been improved by obtaining a feasible adaptive model predictive control solution. Additionally, the root mean square error (RMSE) is calculated to evaluate the performance of the proposed methodology. A RMSE of 0.0768 and 0.0395 for steering without corrective yaw moment (CYM) is decreased to 0.0234 and 0.0214 for sine and double lane change steering input with CYM, respectively. Moreover, the proposed methodology is compared with previous methods and found to have better yaw stability.

A Shared Control Design for Steering Assistance System Considering Driver Behaviors

With the rapid development of advanced driver assistance systems, driver-automation cooperative control becomes more challenging due to the uncertainty of driver behaviors. To this end, this paper proposes a shared control approach to assist drivers in path-tracking and collision avoidance. A high-fidelity CarSim vehicle model embedded driver simulator is built to collect the driver data, based on which the normalized steering angle input and the time to collision are defined to quantify the driving performance. Then, these performance indices are employed to develop the fuzzy controller and determine the control authority for the steering assistance system (SAS). A multi-constraints model predictive control is designed to follow the desired path, and simultaneously ensure the vehicle stability. Different from the traditional constraints handling method, the state constraint is transformed into the input constraint considering the nonlinearity. The effectiveness of the proposed method is verified with two less experienced drivers. The test results show that the path-tracking performance and vehicle stability can be guaranteed with less control effort.

Nonlinear Tire Model Approximation Using Machine Learning for Efficient Model Predictive Control

Model Predictive Controller (MPC) is widely used as a technique for path tracking control since it allows for dealing with system constraints and future forecasts. However, the performance of MPC is directly affected by the adopted model. A complex dynamic model can guarantee accuracy in path tracking but may not be suitable in computational terms. On the other hand, a simplified model may not capture essential nonlinear aspects. Thus, to cope with these problems, this paper deals with data-driven tire modeling to improve autonomous ground vehicle path tracking control. The main contribution of the present work is to show that neural tires can capture the nonlinearities present in the interaction between lateral and longitudinal vehicle dynamics, with a reduced computational cost for predictive controllers. Simulated and experimental tire data are approximate to design data-driven tire models using radial basis function and multilayer perceptron neural networks. Then, based on ground vehicles with neural tires, model predictive controllers are designed to regulate wheel torque and steering angle inputs. Comparative tests were conducted to compare the proposed data-driven MPC approach with the classical nonlinear MPC controller. The results show that the neural tires approximate nonlinear tire models and experimental data with arbitrary precision in terms of accuracy and error-based metrics. The proposed methodology was successfully applied to perform trajectory and velocity tracking of ground vehicles. In addition, MPC with a neural tire model as prediction inference reduces the computational effort compared to traditional approaches.

Robust steering control for trajectory following in road traffic environments

The process of modelling vehicle motion in a road traffic environment requires the integration of trajectory generation with vehicle control. The steps involved here are generating a feasible trajectory based on the existing traffic and tracking the trajectory to control it with a steering angle input. Since the parameters of a physical system vary with changes in operating conditions, it is important to consider robustness when designing controllers. This article aims at developing a trajectory-following model with robust steering control strategies to accurately follow a generated trajectory. In this study, performance-based proportional, robust proportional and sliding mode control strategies are designed for trajectory following. The robustness of the proportional controller is established using Kharitonov’s theorem, which is compared with a proportional controller tuned for performance. Sliding mode control is designed for robustness and chattering elimination using two kinds of reaching laws – a constant reaching law and a novel power rate exponential reaching law. The controllers are designed using a dynamic bicycle model considering the error with respect to the trajectory. The controllers are then evaluated in IPG CarMaker®. The resulting trajectories and control inputs are compared for the considered control methodologies using the ISO double lane change and the Slalom tests. Sliding mode control with power rate exponential reaching law is concluded to be more robust as compared to the other controllers, with lower response times, up to 84% lower heading angle deviations from the trajectory and an overshoot of only 3.2% in lane changing.

Development of mathematical model for real time estimation and comparison of individual lateral tire force generation

All the forces and torque generated by the powertrain are transmitted through the tires to the ground. Hence intensive study on the generation of longitudinal and lateral forces and its characteristic behavior in real time conditions is paramount. Proper understanding of the change of tire parameters such as slip ratio and slip angle in real time condition will lead to a smart onboard vehicle control system. After extensive study on control systems used in vehicles such as ESC, it is seen that the system relies on driver intended path by monitoring steering angle input and makes decision on basis of difference in intended path and actual path. But this system does not give any idea to the ECU about the rate of change of slip angle which is very important for proper mathematical understanding of behavior of vehicle while cornering since it is the slip angle because of which tire develops lateral force. This project emphasizes on lateral dynamics and aims to determine slip angle and henceforth lateral force of each tire by using two track model in Simulink. The real time data obtained is compared to the existing raw tire data at particular vertical load condition and conclusion is made on the percentage variation of lateral force. Various steady state analysis and response including path curvature and yawing velocity also shows the handling characteristics of the vehicle such as understeering or oversteering while cornering. This way of determination leads to a better approximation and understanding of the behavior of tires in real time. The system along with sophisticated higher degree of freedom models can also be used as a closed loop system along with stability control system to predict the behavior of vehicle and enhance vehicle performance both in straight lines and corners.

Actuator fault-based integrated control for vehicle chassis system

An integrated fault tolerant controller is proposed for vehicle chassis system. Based on the coupled characteristics of vertical and lateral system, the fault tolerant controller mainly concentrates on the cooperative control of controllable suspension and lateral system with external disturbances and actuator faults. A nine-DOF coupled model is developed for fault reconstruction and accurate control. Firstly, a fault reconstruction mechanism based on sliding mode is introduced; when the sliding mode achieves, actuator fault signals can be observed exactly through selecting appropriate gain matrix and equivalent output injection term. Secondly, an active suspension controller, a roll moment controller and a stability controller is developed respectively; the integrated control strategy is applied to the system under different driving conditions: when the car is traveling straightly, the main purpose of the integrated strategy is to improve the vertical performance; the lateral controller including roll moment control and stability control will be triggered when there is a steering angle input. Simulations experiments verify the performance enhancement and stability of the proposed controller under three different driving conditions.

Vehicle Lateral Stability Control Based on Shiftable Stability Regions and Dynamic Margins

Vehicle lateral stability control is one of the most critical aspects of vehicle safety control. In this paper, aiming at keeping the vehicle states (lateral velocity and yaw rate) always in the vehicle stability regions, a novel lateral stability control method, which consists of shiftable region-based stability analyses and a corresponding stability controller, is proposed. In the stability analyses, two features of the stability regions are introduced. First, a shifting vector is formulated to explicitly describe the shifting feature of lateral stability regions, so that the shiftable regions are not necessarily re-estimated with respect to a varying steering angle input. Second, dynamic margins of the stability regions are formulated and applied to avoid the penetration of vehicle state trajectory with respect to the stability region boundaries. With these two features, the shiftable stability regions are feasible for an accurate stability analysis, where a projection method is adopted to determine the relative location/distance between the vehicle state point and the closest boundary of the stability region. Based on the analyses, a dynamic sliding mode controller, where the sliding surfaces are selected as the stability region boundaries with the proposed dynamic margins, is designed to keep the vehicle states always in the shiftable stability region. To validate the effectiveness of the proposed control design and analyses, two maneuvers through the co-simulation between Matlab/Simulink and CarSim, namely a high-speed constant cornering and a double lane change maneuvers, are presented and discussed.

Vehicle Path Tracking Maneuver Based on Model Predictive Control Theory

Vehicle path tracking problem has been a hot research topic in the field of automotive safety. Therefore, combined with a 3-DOF vehicle model is established. The basic idea behind the work was to identify the optimal steering angle input during a vehicle travels along a prescribed path. Based on Model Predictive Control (MPC), the steering angle input was determined as the control variable, tracking the desired path was determined as control object. By using the Model Predictive Control, the optimal control problem was converted into a secondary plan problem which was then solved by the active set method. The results show that the minimum error of lateral position for the generated path-tracking trajectory can be good indicators of successful solving of the path-tracking problem in vehicle handling inverse dynamics for MPC. The study can help drivers identify safe lane-keeping trajectories and area easily as well as evaluating performance of emergency collision-avoidance for a vehicle.

Yaw Angle Control of Heavy Commercial Road Vehicle with Faulty Brake

Faults in an air brake system affect the performance of Heavy Commercial Road Vehicles (HCRVs). One of the major faults in the air brake system is the “out-of-adjustment”of pushrod due to excessive brake wear, which may cause a significant yaw angle deviation from the current path and an increase in stopping distance. Hence, this paper aims to design a controller that would maintain the vehicle’s directional stability under brake fault scenario. In order to design such a controller, knowledge of vehicle side slip angle is essential, but this is not a measurable quantity. Hence, an Artificial Neural Network (ANN) based estimation scheme for side slip angle prediction is also proposed. As an output regulator problem, Sliding Mode Control (SMC) was used for correction of yaw angle under brake fault scenario through appropriate steering angle input. This controller provided a percentage correction of yaw angle of 93.4 % and 99.8 % respectively for fully laden and fully unladen vehicle on a high friction tire road interface surface, and the same corresponding to a low friction tire road interface was 99.8 % and 98.9 % respectively.

Vehicle Dynamics Modeling and Electronic Stability Program/ Active Front Steering Sliding Mode Integrated Control

AbstractChassis integrated control can significantly improve vehicle handling stability and comfort. Because of the complexity of the problem, it has attracted significant research attention. We built a vehicle nonlinear dynamic model with multi‐degree freedom, including body movement, wheel movement, and electronically controlled hydraulic power steering system. We compared the magic formula tire model, Dugoff tire model, brush tire model, and LuGre dynamic friction tire model and steady model. The precision of the model was verified by a comparison between simulation results and the real vehicle test results. Then, based on the vehicle dynamics model, an AFS (active front steering) controller was designed based on sliding mode variable structure control, and an AFS and ESP (electronic stability program) integrated coordination controller was proposed. Finally, based on the nonlinear tire model and multi‐DOF (degree of freedom) vehicle model, sinusoidal and step steering angle input simulation analysis was proposed on different road friction coefficients. The results show that the vehicle has better response characteristics with coordinated control strategy when compared with AFS and ESP only control. The evidence suggests that the proposed integrated control system in this paper can improve vehicle stability and safety.

Minimum Time Approach to Emergency Collision Avoidance by Vehicle Handling Inverse Dynamics

Vehicle driving safety is the urgent key problem to be solved of automobile independent development while encountering emergency collision avoidance with high speed. And it is also the premise and one of the necessary conditions of vehicle active safety. A new technique of vehicle handling inverse dynamics which can evaluate the emergency collision avoidance performance is proposed. Based on optimal control theory, the steering angle input and the traction/brake force imposed by driver are the control variables; the minimum time required to complete the fitting biker line change is the control object. By using the improved direct multiple shooting method, the optimal control problem is converted into a nonlinear programming problem that is then solved by means of the sequential quadratic programming. The simulation results show that the proposed method can solve the vehicle minimum time maneuver problem, and can compare the maneuverability of two different vehicles that complete fitting biker line change with the minimum time and the correctness of the model is verified through real vehicle test.

Simulation Research on Nonlinear Vehicle Handling Inverse Dynamics

Based on a brief review of the developing history of vehicle handling inverse dynamics. Using radial basis function neural networks, completely considered the cornering force of tyres, the nonlinear mapping relation between lateral angular velocity and steering angle input is found. The identification results of step steering angle input show the feasibility of the approach and its advantage in accuracy, convergence and stability.

Simulation Research on Vehicle Handling Inverse Dynamics Based on Radial Basis Function Neural Networks

Based on a brief review of the developing history of vehicle steering inverse dynamics, and using radial basis function neural network, the nonlinear mapping relation between lateral angular velocity and steering angle input is found. The identification results of step and sine steering angle input show that the proposed identification method is not only practical, but also with high accuracy.

A Physical Interpretation of Lead Time Constant of Yaw Angular Velocity in Planar Motion of Automobile

This paper discusses lead time constant of yaw angular velocity based on equations of motion of automobiles in planar motion. However, the equations of motion are too complex to be interpreted because the steering angle input generates two variables, lateral and yaw angular accelerations simultaneously. Under reasonable assumption, I derive an equivalent transformation models that generates only one acceleration value from the equations of motion. To generate only one variable against steering input, rigid body of an automobile is replaced by two particles located at the front and rear axles. The equations of motion of the equivalent transformation models imply a mechanism of automobiles transient behavior as follows. Steering angle input causes a yaw angular acceleration around the rear axle. This acceleration changes into a yaw angular velocity by time integration. The yaw angular velocity causes an attitude angular velocity of the rear axle. The velocity changes into an attitude angle at the rear axle by time integration. This attitude angle generates a yaw angular acceleration as restoring yaw moment. In this equivalent transformation models, lead time constant of the yaw angular velocity implies time difference between the yaw angular velocity and attitude angle at the rear axle. Therefore the lead time constant is suitable for criteria of behavior of the automobile at the rear axle. Furthermore the equations of motion will introduce a control law to improve automobile dynamic behaviors.

A Study on Effect of Phase Delay and High Frequency Gain of Vehicle Behavior Corresponding to Steering Angle Input on Ease of Driving

This paper describes an investigation of the nonlinear filter that can design for gain and phase independently. In the driver-vehicle closed-loop system, it is reported that the phase delay of vehicle has an optimal value and reduces vehicle maneuverability if too large or too small. However, there is a deep relationship between the gain and phase delay in a linear system. It is difficult to evaluate the gain and phase delay of vehicle response independently. In this investigation, we tried to design a non-linear filter that can resolve the deep relationships between the gain and phase delay. We investigate the each effect of the gain and phase delay corresponding to the steering angle input on the ease of driving by using driving simulator, and evaluate the sensory evaluation and control performance on the lane change task. We verified the improvement of ease of driving by reducing a phase delay and decreasing a high frequency gain.

Comprehensive lateral driver model for critical maneuvering conditions

A new comprehensive driver model is presented for critical maneuvering conditions with more accurate dynamic control performance. In order to achieve a safe maneuvering mode, a new path planning scheme to maintain stability of the vehicle was designed. A new steering strategy, considering the errors of vehicle position and yaw angle between the real track and the planned path, was established to obtain the steering angle. Therefore, the vehicle can be adjusted to accurately follow the desired path with the driver model, and the stability of the vehicle and the smoothness of the steering angle input were comprehensively considered. Simulation results were used to validate the control performance in comparison with the optimal preview driver model proposed by Macadam.

3114 ドライバ操舵に対する車両挙動の位相遅れと高周波ゲインが運転しやすさに及ぼす影響(OS10-2 シミュレータの応用,OS10 ビークルシミュレータの開発と応用,オーガナイズド・セッション(OS))

3114 ドライバ操舵に対する車両挙動の位相遅れと高周波ゲインが運転しやすさに及ぼす影響(OS10-2 シミュレータの応用,OS10 ビークルシミュレータの開発と応用,オーガナイズド・セッション(OS))

Handling Stability Performance Simulation and Analysis of Three Different Vehicle Models

In order to obtain accurate vehicle handling stability performance, 2 DOF nonlinear vehicle model and multi-body dynamics vehicle model are established. Selecting the same vehicle parameters, step steering angle input simulations of three vehicle model (include 2DOF linear vehicle model) are carried out under the same driving conditions, simulation results are analyzed and compared. The simulation results show that 2DOF linear model can characterize the steering states of vehicle when vehicle lateral acceleration is small, but when vehicle lateral acceleration is big, Nonlinear vehicle model and multi-body dynamics model is accurate.