Rear Steering Research Articles

Research on the potential of integrated vehicle control with closed-loop phase portrait analysis

The phase portrait is an important tool for analyzing vehicle stable region widely utilized in vehicle dynamic control systems. At handling limits, traditional open-loop vehicle stable region constraints will restrict the vehicle control ability, while the closed-loop actuator interventions can help states outside the open-loop stable region converge back to stable origin, which is more suitable for constraining vehicle states under extreme working conditions. This article systematically analyzes the potential of integrated vehicle control with closed-loop phase portrait. Firstly, a vehicle dynamic model considering actuator dynamics and tire transient characteristics is established. Then, a numerical optimal control method for calculating closed-loop controllability region is introduced. The controllability region under different friction coefficients, vehicle speeds, convergence time, vehicle steering response characteristics, actuator time constants, and tire transient characteristics are discussed and analyzed. In terms of different control inputs combinations, this article displays the controllability regions under different front steering angles, rear steering angles, direct yaw moments, and their synergistic performances. Control input laws derived from numerical optimization are summarized in two specific directions. Finally, a comparative analysis of open-loop stable regions and closed-loop controllability regions confirms the superiority of the proposed method. Potential applications of the systematic analysis are also discussed.

Investigating off-road vehicle lateral stability with integrated chassis control

This study investigates the improvement of off-road vehicle lateral stability by integrated control of active rear steering (ARS) and rear differential braking (RDB) and how the performance of such systems compares on smooth and rough roads. The ARS and RDB controllers comprise a sliding mode controller (SMC) for which critical design choices are the SMC reference model, SMC gain and integration rule. Findings include that the kinematic model reference error is preferred over the phase plane location error on both terrains, the SMC gain is terrain dependent, and the rear axle slip angle is the preferred integration rule over the stability index (SI) on both terrains. The study also found that RDB, and to a lesser degree ARS, tends to improve on the baseline vehicle path-following ability for a double lane change (DLC) manoeuvre on both terrains, but RDB has a larger loss of speed compared to ARS. The Rear axle slip angle was found to be a terrain-dependent tuneable integration rule to combine ARS and RDB, and this resulted in a control system that has the good path-following ability of RDB but the low loss of speed associated with ARS after tuning.

Multi input multi output lateral dynamics control of an electric vehicle

Full electric vehicles with multiple and independently controlled powertrains allow for an improvement of vehicle handling capabilities both in steady state and in transient manoeuvres. This paper focuses on active lateral dynamics control of an electric vehicle equipped with 4 in-wheel motors and active rear steering. An integral terminal sliding mode controller (ITSMC) is derived starting from the linearized single track model with the addition of the rear wheel steering angle. The controller has a multi-input multi-output structure and is designed to track vehicle yaw rate and sideslip angle reference quantities through torque vectoring and active rear steering actuation. A novel approach for calculating reference sideslip angle and yaw rate using a logistic function is also presented in this paper. The ITSMC relies on real time knowledge of sideslip angle which cannot be measured in the real vehicle, thus it is estimated through the addition of an extended Kalman filter to the control loop. The performance of the controller is tested with VI-CarRealTime 14 degrees of freedom nonlinear model both for steady state and transient manoeuvres. Simulation results show a good tracking of the reference value with no chattering issues and with an improved behaviour if compared to a sliding mode controller from literature.

Coordinated Control for the Trajectory Tracking of Four-Wheel Independent Drive–Four-Wheel Independent Steering Electric Vehicles Based on the Extension Dynamic Stability Domain

In order to achieve multi-objective chassis coordination control for 4WID-4WIS (four-wheel independent drive–four-wheel independent steering) electric vehicles, this paper proposes a coordinated control strategy based on the extension dynamic stability domain. The strategy aims to improve trajectory tracking performance, handling stability, and economy. Firstly, expert PID and model predictive control (MPC) are used to achieve longitudinal speed tracking and lateral path tracking, respectively. Then, a sliding mode controller is designed to calculate the expected yaw moment based on the desired vehicle states. The extension theory is applied to construct the extension dynamic stability domain, taking into account the linear response characteristics of the vehicle. Different coordinated allocation strategies are devised within various extension domains, providing control targets for direct yaw moment control (DYC) and active rear steering (ARS). Additionally, a compound torque distribution strategy is formulated to optimize driving efficiency and tire adhesion rate, considering the vehicle’s economy and stability requirements. The optimal wheel torque is calculated based on this strategy. Simulation tests using the CarSim/Simulink co-simulation platform are conducted under slalom test and double-lane change to validate the control strategy. The test results demonstrate that the proposed control strategy not only achieves good trajectory tracking performance but also enhances handling stability and economy during driving.

Path Tracking Control with Constraint on Tire Slip Angles under Low-Friction Road Conditions

This paper presents a method to design a path tracking controller with a constraint on tire slip angles under low-friction road conditions. On a low-friction road surface, a lateral tire force is easily saturated and decreases as a tire slip angle increases by a large steering angle. Under this situation, a path tracking controller cannot achieve its maximum performance. To cope with this problem, it is necessary to limit tire slip angles to a value where the maximum lateral tire force is achieved. The most commonly used controllers for path tracking, linear quadratic regulator (LQR) and model predictive control (MPC), are adopted as a controller design methodology. The control inputs of LQR and MPC are front and rear steering angles and control yaw moment, which have been widely used for path tracking. The constraint derived from tire slip angles is imposed on the steering angles of LQR and MPC. To fully verify the performance of the path tracking controller with the constraint on tire slip angles, a simulation is conducted on vehicle simulation software. From the simulation results, it is shown that the path tracking controller with the constraint on tire slip angles presented in this paper is quite effective for path tracking on low-friction road surface.

Personalized Collision Avoidance Control for Intelligent Vehicles Based on Driving Characteristics

Collision avoidance has been widely researched in the field of intelligent vehicles (IV). However, the majority of research neglects the individual driver differences. This paper introduced a novel personalized collision avoidance control (PCAC) strategy for IV based on driving characteristics (DC), which can better satisfy various scenarios and improve drivers’ acceptance. First, the driver’s DC is initially classified into four types using K-means clustering, followed by the application of the analytic hierarchy process (AHP) method to construct the DC identification model for the PCAC design. Then, a novel PCAC is integrated with a preview-follower control (PFC) module, an active rear steering (ARS) module, and a forward collision control (FCC) module to ensure individual requirements and driving stability. Moreover, simulations verified the validity of the developed PCAC in terms of path tracking, lateral acceleration, and yaw rate. The research results indicate that DC can be identified effectively through APH, and PCAC based on DC can facilitate the development of intelligent driving vehicles with superior human acceptance performance.

Comparative Study on Effects of Input Configurations of Linear Quadratic Controller on Path Tracking Performance under Low Friction Condition

This paper presents a comparative study on the effects of the input configurations of linear quadratic (LQ) controllers on path tracking performance under low friction conditions. For the last decade, the path tracking controller has adopted several control inputs, input configurations, and actuators. However, these have not been compared with one another on a single frame in terms of common measures. For this reason, this paper compares input configurations of LQ controllers and available actuators in terms of common measures. For this purpose, the control inputs of the LQ controller were composed of front and rear steering and control yaw moment. By combining these control inputs, five input configurations of the LQ controller were set. If the control yaw moment is selected as a control input, then an actuator is needed to generate a control allocation, which should be adopted to convert the control yaw moment into longitudinal and lateral tire forces of actuators. As an actuator for control yaw moment generation, front/rear and 4-wheel steering, 4-wheel independent steering, braking, and driving were adopted. By applying the weighted least square based method, control allocation was formulated as a quadratic programming problem, which can be algebraically solved. For comparison on path tracking performance, new measures were adopted. To check the path tracking performance of each input configuration, a simulation was conducted on vehicle simulation software. From the simulation results, it was shown that front or 4-wheel steering itself is enough for path tracking on low friction roads and that the control yaw moment or an additional actuator is not recommended as a control input for path tracking on low friction roads.

The Effect of Nonlinear Feature of Tire on the Control of Active Rear Steering at High Speed

The two-degree-of-freedom model of the vehicle is more accurate with considering of the nonlinear feature of tire. Based on the model, the active rear steering control strategy for achieving zero sideslip angle is yielded. Simulation results show that both of the two cases, constant and variable cornering stiffness, are useful in the control of sideslip motion, and using the variable stiffness due to the effect of load transfer in control strategy is more effective.

Emergency collision avoidance strategy for autonomous vehicles based on steering and differential braking

This paper develops a novel integrated collision avoidance strategy for autonomous vehicles in an emergency based on steering and braking. Specifically, the framework of the collision avoidance strategy is composed of two parts: an up-level decision-making layer and a low-level controller layer. The purpose of the up-level is to select the appropriate control strategy based on the vehicle information, and the low-level is to drive the vehicle according to the instructions generated by the up-level. More concretely, a novel control strategy is proposed by integrating four-wheel steering, active rear steering, and differential braking with guaranteed path-tracking accuracy and driving stability by adaptive model predictive control (AMPC). Finally, extensive co-simulations in MATLAB/Simulink and CarSim are conducted to verify the effectiveness of the proposed collision avoidance strategy in terms of tracking error, yaw rate, and roll angle.

High clearance four-wheel independent electric drive sprayer path tracking control based on self-correction controller

Most traditional agricultural machines use traditional mechanical transmission with fuel drive and front wheel steering, and most of them are manned, with low transmission efficiency, poor flexibility and low level of intelligence. This paper proposes a new high ground clearance sprayer with four-wheel independent drive (4WID) with dual front and rear steering axles. This sprayer is an oil-electric hybrid that not only saves energy, but also reduces the pollution to crops. In this study, a path tracking controller and a self-correcting controller are constructed based on the kinematic model of the sprayer, respectively. The model prediction controller is used as the main controller, and it outputs the desired steering angle and speed of the sprayer based on the current state of the sprayer and the desired path to achieve path tracking control. The self-correcting controller, as an auxiliary controller, adopts fuzzy control method and designs fuzzy control rules based on the driver’s experience to correct the wheel turning angle at the current moment, which not only retains the advantages of model prediction control in linear path tracking, but also improves the control effect in curved path tracking and enhances the path tracking accuracy in large curvature roads. The simulation shows that the maximum lateral deviation of 0.03 m can be achieved by the model predictive control alone, and the maximum lateral deviation is reduced to 0.0141 m after adding the self-correcting controller.

Autonomous Vineyard Tracking Using a Four-Wheel-Steering Mobile Robot and a 2D LiDAR

The intensive advances in robotics have deeply facilitated the accomplishment of tedious and repetitive tasks in our daily lives. If robots are now well established in the manufacturing industry, thanks to the knowledge of the environment, this is still not fully the case for outdoor applications such as in agriculture, as many parameters are varying (kind of vegetation, perception conditions, wheel–soil interaction, etc.) The use of robots in such a context is nevertheless important since the reduction of environmental impacts requires the use of alternative practices (such as agroecological production or organic production), which require highly accurate work and frequent operations. As a result, the design of robots for agroecology implies notably the availability of highly accurate autonomous navigation processes related to crop and adapting to their variability. This paper proposes several contributions to the problem of crop row tracking using a four-wheel-steering mobile robot, which straddles the crops. It uses a 2D LiDAR allowing the detection of crop rows in 3D thanks to the robot motion. This permits the definition of a reference trajectory that is followed using two different control approaches. The main targeted application is navigation in vineyard fields, to achieve several kinds of operation, such as monitoring, cropping, or accurate spraying. In the first part, a row detection strategy based on a 2D LiDAR inclined in front of the robot to match a predefined shape of the vineyard row in the robot framework is described. The successive detected regions of interest are aggregated along the local robot motion, through the system odometry. This permits the computation of a local trajectory to be followed by a robot. In a second part, a control architecture that allows the control of a four-wheel-steering mobile robot is proposed. Two different strategies are investigated, one is based on a backstepping approach, while the second considers independently the regulation of front and rear steering axle position. The results of these control laws are then compared in an extended simulation framework, using a 3D reconstruction of actual vineyards in different seasons.

Towards Active Safety Driving: Controller Design of an Active Rear Steering System for Intelligent Vehicles

To advance the active safety performance for vehicles, especially in extreme conditions, an active rear steering (ARS) control system is designed in this paper. A driver model is established to simulate the driving behaviour of a human driver who is in charge of the front steering control. In the ARS control system, the sliding mode predictive control (SMPC) approach is applied to the ARS controller design based on a 3 degrees of freedom (DoF) nonlinear vehicle model. In the ARS controller design, four kinds of active safety performances are considered, namely, path-tracking performance, handling performance, lateral stability, and rollover prevention. Furthermore, the priority of the four kinds of active safety performance is defined. According to the control priority, an event-triggered mechanism (ETM) is designed to adjust the SMPC controller of the ARS system to address different driving conditions. Finally, two simulation cases are conducted to evaluate the performance of the proposed ARS system. The results show that the ARS system is in favour of the active safety performance advancement for human drivers. Additionally, the comparative simulation indicates that the SMPC algorithm is superior to the fast terminal sliding mode control (FTSMC) algorithm.

A numerical simulation of vehicle dynamics behavior for a four-wheel steering vehicle with the passive control system

The Advanced Driver Assistance System (ADAS) is a technology in the vehicle to assist drivers in mitigating road risk and improving maneuverability. The system is capable of providing warnings to drivers and even executing an action if necessary. However, these systems are limited to the sensors and capability of the vehicle. Increasing the degree of freedom of a vehicle could potentially develop new ADAS with more efficiency. Along with the X-By-Wire technology, a four-wheel drive and independent steering (4WDIS) can be produced as a part of ADAS, especially for electric vehicles. In this research, an understanding of the steering characteristic of a 4WDIS during steady-state cornering (SSC) is presented using numerical simulation in MATLAB. An actual Segment B type vehicle is used as a simulation model and a preliminary two-wheel steering SSC simulation was performed to determine the steering characteristics. The model is modified to include a rear steer angle with a passive control system and the SSC simulation was repeated. The results show that the vehicle can perform SSC by increasing the yaw rate at high speed using the opposite steering mode. Meanwhile, parallel steering mode is suitable during low-speed cornering which can increase the yaw rate while maintaining stability.

Integration sliding mode control for vehicle yaw and rollover stability based on nonlinear observation

An active rear steering and direct yaw moment (ARS-DYC) coordination control is conducted on the basis of nonlinear fuzzy observation to improve yaw and roll stability control of vehicles under extreme conditions. First, a Takagi–Sugeno (T-S) model of yaw and roll motion is established, and tire nonlinearity at emergency steering is approximated with sector domain. A nonlinear fuzzy observation model is established on the basis of the extended Kalman filter (EKF) to observe the sideslip angle, yaw rate, and roll state accurately under extreme conditions in real time. Second, an improved ideal yaw reference model under the T-S framework is constructed in accordance with the effect of yaw rate on roll stability, and the feedforward control of roll stability is achieved through yaw motion tracking. A fuzzy sliding mode controller is designed on the basis of nonlinear fuzzy observation considering tire sideslip stiffness and actuator constraints, and the coordinated control strategy of layered sliding mode surface for yaw and roll is constructed. Finally, the parameters of sub-sliding mode surface are adjusted with the 4-wire phase plane stability domain, the main sliding mode surface parameters are adjusted following the roll stability index, and the stability of the fuzzy sliding mode controller is proven in the Lyapunov framework. A hardware-in-loop simulation test is established with Carsim-Labview software, and results show that the proposed controller significantly enhances the yaw and roll stability of vehicles under the extreme steering process, due to the accuracy of nonlinear dynamic observation and the flexibility of layered sliding surface coordinated control.

Active Obstacle Avoidance Control Strategy Based on Four-Wheel Steering

Active obstacle avoidance control strategy is the main question of intelligent vehicles, and active four-wheel steering is gradually used in the intelligent control system. Considering both tracking performance and driving characters, an active controller with four-wheel steering (4WS) and active rear steering (ARS) based on adaptive model predictive theory (AMPC) is designed. The control architecture is composed a supervisor and an AMPC controller. The supervisor is used to select the appropriate control mode and the AMPC is used to calculate the expected steering angle when the stability indexes over the safety threshold. Finally, the proposed control strategy is simulated via Carsim-Simulink co-simulation. The results show that the integrated controller can track the obstacle avoidance path and has good driving performance.

A model predictive control approach for highly automated vehicles in urban environments

AbstractIn this paper, a model predictive control (MPC) approach for the lateral and longitudinal control of a highly automated electric vehicle with all-wheel drive and dual-axis steering is presented. For the prediction of state trajectories a two-track vehicle model is used. The MPC problem for trajectory tracking is formulated by controlling the front and rear steering angle as well as the individual drive torques with respect to actuator and design constraints. Beside the steering angles, the MPC controller computes the individual drive torques to not only match the reference velocity but also to support the lateral dynamics of the vehicle using torque vectoring. The MPC problem is solved using ACADOS, a software package for efficiently solving optimal control problems. The effectiveness of the proposed MPC scheme is demonstrated via simulation.

Optimal path tracking control for intelligent four-wheel steering vehicles based on MPC and state estimation

Four-wheel steering (4WS) vehicles have better stability control and path following performance than front-wheel steering (FWS) vehicles. Aiming at this characteristic, a new four-wheel active steering control strategy is proposed. For intelligent vehicle path tracking and nonlinear vehicle system state estimation, a path tracking control algorithm based on the MPC algorithm is designed to analyze the stability of the vehicle and set up constraints to achieve accurate tracking of the reference path. Automotive dynamic control systems require information on system variables. For example, the sideslip angle of electric vehicles cannot be measured directly. Based on UKF theory and the information input of low-cost sensors on the vehicle, an estimator is designed to estimate vehicle sideslip angle and yaw rate. According to the difference between the estimated value and the ideal value of the vehicle state, the LQR optimal controller is designed to realize the optimal control of the front and rear steering. And compared with the dynamic simulation results of front-wheel steering, proportional control four-wheel steering and yaw rate feedback four-wheel steering. The experimental results of the simulation platform show that the path tracking 4WS state feedback optimal control method has good lateral control stability and path tracking accuracy.

Path-following enhancement of an 8×8 combat vehicle using active rear axles steering strategies

Active rear steering has been used in many research work to enhance ground vehicles’ lateral stability. However, there is a shortage in the published research studies that consider the incorporation of active rear steering for autonomous vehicles applications, especially in case of multi-axle combat vehicles. In this paper, various H∞ controllers are developed to actively steer rear axles of a multi-axle combat vehicle using a linearized bicycle model. The proposed controllers are incorporated with a 22 degrees of Freedom nonlinear Trucksim full vehicle model to study and compare the developed controllers’ performance on a hard surface. Moreover, a frequency-domain analysis is conducted to investigate the influence of the active rear steering on the path-following controllers’ robustness in terms of stability and performance. Three path-following controllers are designed, where the first controller is applied on the front two axles of the vehicle, while the rear two axles are fixed. The second is applied to all-wheel steering vehicle. The third controller is an integration between the designed front steering path-following controller and a developed lateral stability active rear steering controller. Eventually, a series of virtual maneuvers are performed to evaluate the effectiveness of the intended controllers to present the advantages and limitations of each controller at different driving conditions.

A novel adaptive-rear axles steering controller for an 8 × 8 combat vehicle

Multi-axle vehicles are widely used in several applications such as transportation, industrial, and military field, because of its higher reliability in comparison with conventional two axles vehicles. Despite that, there is a paucity of research studies that consider lateral stability enhancement of these vehicles, especially on rough terrain. This simulation-based research study fills this gap and introduces a new adaptive Active Rear Steering (ARS) controller that improves the lateral stability of an 8x8 combat vehicle for rough-terrain operation. The developed controller is designed utilizing the Integral Sliding Mode Control theory (ISMC) based on Gain-Scheduled Linear Quadratic Regulator (GSLQR). Besides, the GSLQR control gains are optimized by a Genetic Algorithm (GA) toolbox using a new synthesized cost function to ensure asymptotic stability. Furthermore, a new Adaptive-ISMC (AISMC) is introduced by using genetic programming to generate control equations that can replace the developed high-dimension GSLQR gains and facilitate future hardware implementation. The developed controller is evaluated by performing a series of simulation-based Double Lane Change (DLC) maneuvers on several rough terrains. The evaluation is conducted for both high friction and slippery surfaces at high and moderate speed, consequently. The results show high fidelity and robustness of the developed controller in comparison with a previously designed optimal LQR controller.

A cooperative control strategy for yaw rate and sideslip angle control combining torque vectoring with rear wheel steering

ABSTRACT Automobiles are becoming more and more complex as multiple control systems are integrated into the vehicle platform. This paper investigates the coordination of active rear steering (RWS) and torque vectoring (TV) – which is enabled by independent electric motors at the rear axle – in controlling vehicle lateral dynamics. The proposed controller aims at enhancing vehicle handling performance and stability while cornering. The coordination of the two actuators is achieved by weighting their contribution based on their impact on vehicle dynamics according to the working condition. The impact of each control system is assessed by means of phase portraits. These plots are a very powerful tool for analysing vehicle nonlinear dynamics as they readily display vehicle stability properties and map equilibrium point locations and movement to changing parameters and control inputs. Based on phase portrait analysis, a performance index is thus proposed, which weights more the control action (TV or RWS) capable of leading the vehicle at the nearest equilibrium point with the fastest rate. The controller performance is assessed through numerical simulations carried out using a nonlinear 14 dofs vehicle model. Results are compared with ones of the two controllers alone (RWS and TV) in different manoeuvers and adherence conditions.