Browse Topic: Four wheel steering

Items (78)
The Active Wheel-Corner (AWC) integrates driving, braking, steering, and suspension systems into the wheel end, forming a fully drive-by-wire, four-wheel independent steering and four-wheel independent driving (4WIS&4WID) vehicle platform. While improving vehicle control performance, the full by-wire architecture also places higher demands on system reliability and fault tolerance. The steer-by-wire system has electrical, communication, and software failure risks, which may cause the vehicle to lose steering capability and trigger severe traffic accidents. This article proposes a hierarchical active fault-tolerant control strategy based on fault information reconstruction (FAST-FTC), enabling fault diagnosis and active fault-tolerant control when the steer-by-wire system fails, effectively ensuring the steering maneuverability and lateral stability of the vehicle under fault conditions. First, the strategy designs an adaptive observer combined with the Dugoff tire model to estimate nonlinear tire forces, while introducing a fault factor to achieve quantitative grading of steering system faults. Second, a hierarchical controller is designed for steering system faults. The upper-level controller, based on Adaptive Super-Twisting Sliding Mode Control (AST-SMC), determines the generalized forces required to track the desired trajectory under different fault conditions. The lower-level controller, based on the Fault-Aware Model Predictive Control (FA-MPC) strategy, dynamically adjusts weight matrices according to the fault factor and tire reconstructed stiffness, coordinating the allocation of four-wheel driving and the steering of healthy wheels to ensure lateral stability. Finally, the effectiveness of the proposed active fault-tolerant control strategy is validated through Hardware-in-the-Loop (HIL) simulation and real-vehicle tests.
Xiao, FengJiang, YueyongCheng, RuiXu, ChangheTang, XiangjiaoGao, FenglingLi, Jianhua
To improve the handling stability of four-wheel steering/drive vehicles under complex high-speed maneuvers, this study proposes a coordinated control strategy that incorporates Active Rear Steering (ARS) and Direct Yaw Moment Control (DYC) based on a dynamic stability region. Firstly, a four-wheel steering vehicle dynamics model including lateral motion and yaw motion is established, and the ideal values of the control variables are determined. Secondly, combined with the fuzzy control theory and double-line method, the boundary of the dynamic stability region is obtained in the sideslip angle-sideslip angle rate β−β̇ phase plane, and the vehicle state is categorized into stable, unstable, and critical stable region. Then, A hierarchical control architecture is designed based on the stability boundary. The upper controller comprehensively solves the target rear wheel angle and additional yaw moment through feedforward feedback control; the coordinated control layer allocates control weights according to the stable state of the vehicle; the lower controller optimizes torque distribution through quadratic programming. Finally, the control strategy is validated by MATLAB/Simulink and CarSim co-simulation platform. The results show that the proposed control strategy reduces the RMS values of yaw rate and sideslip angle by 23.1% and 28.5% respectively, significantly improving the handling stability of the vehicle.
Nie, KeheChen, JinWang, FalongLi, RenBai, Xianxu
Wheel-corner brake failures can significantly deteriorate vehicle stability and safety, since unbalanced braking forces may introduce an undesired yaw moment. This work investigates a fault-tolerant control strategy for Active Wheel-Corner Systems, exploiting Four-Wheel Independent Steering (4WIS) to mitigate such effects and preserve vehicle stability when brake actuator malfunctions occur. Unlike many existing approaches, the proposed framework does not require explicit fault detection or quantification as a prerequisite for corrective action, eliminating potential delays and uncertainties associated with fault-diagnosis schemes. A reference model for yaw rate and sideslip angle, incorporating combined longitudinal and lateral dynamics, is proposed, and a Weighted Pseudo-Inverse Control Allocation (WPCA) scheme is employed to distribute corrective actions among the four steering angles according to each tire’s capability, compensating for yaw moment imbalances caused by degraded braking performance. The overall control framework is evaluated using a high-fidelity vehicle model implemented through VI-CarRealTime, with control algorithms and fault scenarios integrated via MATLAB/Simulink, providing a flexible and realistic platform for systematic analysis. The strategy is tested in cornering maneuvers with fault injection representing the worst-case scenario of a complete failure of the outer-front wheel brake. Results demonstrate that 4WIS can effectively recover the desired vehicle response, reducing deviations in yaw rate and sideslip compared to a baseline vehicle without reconfiguration. The study highlights the potential of steering redundancy as a complementary solution to braking and torque-vectoring systems for improving fault tolerance in future Active Wheel-Corner systems.
Sonnino, SamuelMelzi, StefanoCaresia, PietroManzoni, AlessandroVaini, Gianluca
This paper briefly introduces the vehicle characteristics of four-wheel steering. Based on the parameters of an electric SUV, a linear two-degree-of-freedom vehicle dynamics model is established, and the transfer function of the rear wheel steering angle is derived to keep the sideslip angle at the center of gravity(CoG) constant at zero and proportional to the front wheel steering angle under steady state. The active rear wheel steering control strategy based on zero sideslip angle is established by MATLAB/Simulink, and a co-simulation model is built with CarSim and the HIL test bench to simulate and analyze the proposed control strategy. Subsequently, through classic handling stability test conditions such as the snake test, steering angle step test, and double lane change test, the influence of active rear wheel steering on vehicle dynamic response indicators such as sideslip angle, lateral acceleration, and yaw rate is studied, and the control effect is compared with that of the feedforward control rear wheel steering strategy. Test results demonstrate that the rear-wheel steering technology based on zero sideslip angle control improves the vehicle's low-speed maneuverability and high-speed stability. Under the double lane change test condition at 80 km/h, the sideslip angle is reduced by approximately 30%, and the yaw rate gain is decreased by about 25% compared to the feedforward control strategy. These enhancements significantly improve the overall dynamic performance of the vehicle.
Xu, XiangfeiQu, YuanLiu, Jiabao
Four-wheel independent steering four-wheel independent drive electric vehicles have an independent steering motor and an independent driving motor for each wheel, for a total of eight motors. About 28 works in this emerging field have shown path-tracking control algorithms for these vehicles, 18 of them explicitly or implicitly aspire for a condition known as optimal tire usage. This article first defines this optimality condition and explains its significance. Second, this article identifies three indicators of tire usage that aid in assessing the existing algorithms. Third, this article performs block diagram examination of four of the 18 works, revealing significant commonalities across the 28 works and identifying areas for improvement in three of the four algorithms. Lastly, this article suggests motor control systems to fill these gaps. Furthermore, it employs these motor control systems in one of the four algorithms, and illustrates path-tracking and achievement of the optimality condition in simulation. This shows that the motor control systems are sufficient (in simulation) to meet the optimality condition in one work. They are likely sufficient for all path-tracking algorithms employing appropriate control allocation to achieve the optimality condition.
Kumar, DileepPotluri, Ramprasad
This research addresses the issues of permanent - magnet synchronous motor parameter matching and sudden - load compensation in four - wheel independent steering systems and proposes a composite control strategy. By analyzing their dynamic characteristics, it is found that traditional rotational inertia identification methods and existing load observers have deficiencies. The research uses the gradient correction algorithm to construct an online rotational inertia identification model, achieving real - time parameter identification with the characteristics of adjustable parameters and low computational complexity. At the same time, a load observer is designed based on the terminal sliding - mode control theory to solve the problem of observation lag in sudden - load conditions and provide timely compensation. Simulation and experimental results show that after a sudden load is applied, the angle - tracking error of this method is reduced to ±0.12°, the convergence time of rotational inertia identification is shortened by 140 ms, and the response time of sudden - load observation is stable within 50 ms, improving the dynamic response characteristics and control robustness of the system.
Zhou, LitaoHuang, YanLi, Huichen
When the vehicle system performs trajectory tracking control, it presents relatively complex nonlinear coupling dynamics characteristics. The traditional coordination algorithm relying on a simplified linear model is mostly unable to deal well with the actual nonlinear dynamic behaviors. In contrast, reinforcement learning (RL) method will derive the optimal strategy by means of interaction with the environment. This eliminates the need for accurate vehicle modeling. These methods use all of the nonlinear approximation capabilities of deep neural networks and can effectively reflect the complex relationship between vehicle state and control actions. The framework itself supports multidimensional input processing and continuous operation space optimization because of the development of parallel processing architectures. In order to reduce the motion jitter caused by the direct generation of front and rear wheel angles by the network, this article uses steering angle increments as control commands and effectively reduces motion jitter through differential action formulas. To accelerate policy convergence, behavioral cloning (BC) technology was integrated into the deep reinforcement learning (DRL) training pipeline and initial policy parameterization was performed using expert demonstration data. The combination of four-wheel independent steering and DRL improves operational flexibility and enables precise trajectory compliance under different operating conditions.
Ren, GaotianWang, Yangyang
This paper presents a methodology for optimizing the steering system of a multi-purpose agricultural vehicle (MPAV) equipped with four-wheel steering (4WS) and a symmetrically configured double-wishbone suspension on both axles. The MPAVs are often prone to bump steer issues due to their narrow track width and the need for long suspension travel. The objective is to define and dimension the steering geometry while maintaining the existing suspension kinematics and preserving the hard points of the wheel hubs. In the scientific literature, this issue is typically addressed by adjusting the hard points of both the steering mechanism and the suspension kinematics. The proposed optimization framework begins with a sensitivity analysis of key design parameters: the position and length of the steering actuator. Based on this analysis, the problem is formulated as an optimization task with two different objective functions, whose solutions are then compared. The functions aim to minimize bump steer and replicate the kinematic steering geometry for both front wheel steering (FWS) and all-wheel steering (AWS) configurations. The steering system is modeled using a multibody (MB) approach, and a genetic algorithm is employed for optimization. Finally, the optimized solutions are evaluated and compared using a full-scale MB vehicle model.
Belloni, MattiaVignati, MicheleSabbioni, Edoardo
The motion control system, as the core executive component of the automatic hierarchical framework, directly determines whether autonomous vehicles can reliably and stably follow planned trajectories, making it crucial for driving safety. This article focuses on steering lock faults and proposes a cross-system fault-tolerant control (C-FTC) algorithm based on dynamic model reconstruction. The algorithm uses a classic hierarchical collaborative architecture: the upper-level controller employs an MPC algorithm to solve lateral velocity and yaw rate reference values in real-time, while the lower-level controller, designed based on the reconstructed dynamic model, uses an MPC algorithm to adaptively adjust actuator control quantities. In cases where four-wheel steering vehicles lose steering ability due to locked steering axles, the locked axle’s steering angle is treated as a state variable, and healthy actuator outputs are used as control variables to dynamically reconstruct the vehicle dynamic model. The required lateral force for steering is then allocated to healthy actuators to achieve fault-tolerant control. To verify the algorithm’s effectiveness, validation combines hardware and real-vehicle testing, conducting high-speed obstacle-avoidance tests under three fault conditions: front axle lock, rear axle lock, and both axles locked. Results show that under all three conditions, the proposed algorithm keeps lateral trajectory tracking errors within 0.35 m, ensuring vehicle safety even with steering system faults.
Hu, HongyuTang, MinghongChen, GuoyingGao, ZhenhaiWang, XinyuGao, Fei
A large-scale logistics transport vehicle composed of two skateboard chassis is investigated in this paper. This unmanned vehicle with dual-modular chassis (VDUC) is suitable for transporting varying size of goods. The two chassis can be used jointly or driving separately as needed, which enhancing the reconfigurability of transport vehicle. Considering the road environment uncertainty and the rollover safety problem associated with large transport vehicle, this paper proposes the path planning of VDUC using the Artificial Potential Field(APF)+Model Predictive Control(MPC) while incorporating the rollover stability index. Due to the independent operation of the two modular chassis, based on the hierarchical control approach, the path following controller of the two modular chassis are designed separately according to the vehicle’s planned path. Distributed model predictive control is applied to coordinate the front and rear modular chassis, so it can realize the path following for the VDUC. A multi-body model of VDUC is built in Matlab/Simscape, and its path planning and tracking control are simulated in specific obstacle avoidance scenario. Simulation results demonstrate that the VDUC can avoid obstacles with smaller lateral displacement error while maintaining roll stability along the planned path, which shows that the proposed motion planning framework is suitable for the VDUC’s safe and efficient operation.
Liu, ZuyangShen, YanhuaWang, Kaidiwang, Haoshuai
Single lane changing is one of the typical scenarios in vehicle driving. Planning an appropriate lane change trajectory is crucial in autonomous and semi-autonomous vehicle research. Existing polynomial trajectory planning mostly uses cubic or quintic polynomials, neglecting the lateral jerk constraints during lane changes. This study uses seventh-degree polynomials for lane change trajectory planning by considering the vehicle lateral jerk constraints. Simulation results show that the utilization of the seventh-degree method results in a 41% reduction in jerk compared to the fifth-degree polynomial. Furthermore, this study also proposes lane change trajectory schemes that can cater to different driving styles (e.g., safety, efficiency, comfort, and balanced performance). Depending on the driving style, the planned lane change trajectory ensures that the vehicle achieves optimal performance in one or more aspects during the lane change process. For example, with the trajectory that provides the best comprehensive performance under given constraints (initial speed of 20 m/s, lane width of 3.5 m, and a longitudinal distance of 50 m to the obstacle in front), the four-wheel steering model predictive control can effectively track the planned trajectory, with the maximum jerk value being 6.4 m/s3 and the longitudinal speed after lane change being approximately 12.6 m/s. Although this study assumes specific longitudinal displacement before and after the lane change, the methodology is applicable to other scenarios. For example, it can determine the shortest longitudinal displacement and the optimal lane change trajectory given predefined vehicle speeds and maximum lateral acceleration conditions. The lane change trajectories developed in this study can be directly applied to the system design of autonomous vehicles.
Lai, FeiHuang, Chaoqun
Path planning in parking scenarios for vehicles with Ackermann steering characteristics is a well studied problem in the literature. However, the recent emergence of four-wheel steering (4WS) chassis has brought new opportunities to the field of motion planning. Compared with front-wheel steering (2WS), 4WS vehicles offer higher flexibility and new maneuver modes such as CrabWalk. To utilize such new potential to further improve parking efficiency, this paper proposes a four-wheel steering oriented planning algorithm for parking scenarios. First, Hybrid A*-4WS is proposed to search for a coarse trajectory from the starting pose to the parking slot, with improved node expansion mechanism to incorporate four-wheel steering characteristics. Then a nonlinear programming (NLP) problem is formulated with four-wheel steering kinematic model to fully utilize the maneuver capability of 4WS vehicles, with OBCA used for collision avoidance constraints. Finally, the two algorithms are sequentially integrated, using the coarse trajectory obtained from Hybrid A*-4WS as the initial guess for optimization. Simulation results demonstrate that our proposed algorithm achieves higher parking efficiency in narrow space, and the efficiency is improved as maximum rear steering angle increases.
Song, YufeiLiu, YuanzhiXiong, LuTang, Chen
With the modernization of agriculture, the application of unmanned agricultural special vehicles is becoming increasingly widespread, which helps to improve agricultural production efficiency and reduce labor. Vehicle path-tracking control is an important link in achieving intelligent driving of vehicles. This paper designs a controller that combines path tracking with vehicle lateral stability for four-wheel steer/drive agricultural special electric vehicles. First, based on a simplified three-degrees-of-freedom vehicle dynamics model, a model predictive control (MPC) controller is used to calculate the front and rear axle angles. Then, according to the Ackermann steering principle, the four-wheel independent angles are calculated using the front and rear axle angles to achieve tracking of the target trajectory. For vehicle lateral stability, the sliding mode control (SMC) is used to calculate the required direct yaw moment control (DYC) of the vehicle, and wheel torque distribution is carried out considering the front and rear axle loads and road adhesion coefficient. CarSim and MATLAB/Simulink were chosen to build a joint simulation platform, and simulation experiments were conducted under two working conditions: high adhesion road surface and low adhesion road surface. The simulation results showed that the controller designed in this paper can improve the lateral stability of the vehicle while ensuring good path-tracking accuracy.
Huang, BinYang, NuorongMa, LiutaoWei, Lexia
Vehicles equipped with articulated steering systems have advantages such as low energy consumption, simple structure, and excellent maneuverability. However, due to the specific characteristics of the system, these vehicles often face challenges in terms of lateral stability. Addressing this issue, this paper leverages the precise and independently controllable wheel torques of a hub motor-driven vehicle. First, an equivalent double-slider model is selected as the dynamic control model, and the control object is rationalized. Subsequently, based on the model predictive control method and considering control accuracy and robustness, a weight-variable adaptive model predictive control approach is proposed. This method addresses the optimization challenges of multiple systems, constraints, and objectives, achieving adaptive control of stability, maneuverability, tire slip ratio, and articulation angle along with individual wheel torques during the entire steering process of the vehicle. Finally, the effectiveness of the controller is validated through hardware-in-the-loop testing, and the data indicates that the proposed adaptive model predictive controller significantly enhances the vehicle’s handling stability.
Huang, BinMa, MinruiMa, LiutaoCui, KangyuWei, Xiaoxu
In order to improve the trajectory tracking accuracy and yaw stability of vehicles under extreme conditions such as high speed and low adhesion, a coordinated control method of trajectory tracking and yaw stability is proposed based on four-wheel-independent-driving vehicles with four-wheel-steering. The hierarchical structure includes the trajectory tracking control layer, the lateral stability control decision layer, and the four-wheel angle and torque distribution layer. Firstly, the upper layer establishes a three-degree-of-freedom vehicle dynamics model as the controller prediction model, the front wheel steering controller is designed to realize the lateral path tracking based on adaptive model predictive control algorithm and the longitudinal speed controller is designed to realize the longitudinal speed tracking based on PID control algorithm. Then, the middle layer decides the rear wheel steering angle and the additional yaw moment to maintain the vehicle's yaw stability based on the super-twisting sliding mode control algorithm and the improved particle swarm PID (IPSO-PID) control algorithm, respectively. Next, the lower layer allocates the four wheel steering angle according to the Ackermann Angle relation of four-wheel-steering vehicle, and optimally assigns the four wheel hub motor torques using sequential least squares planning with the objective function of minimizing the sum of the four tires' adhesion utilization. Finally, the CarSim/Simulink co-simulation platform is built to carry out the simulation test of medium-speed low-adhesion and high-speed high-adhesion double-lane-change conditions respectively. The simulation results show that the coordinated control strategy of trajectory tracking and yaw stability designed in this paper can improve the path tracking accuracy of the vehicle and meet the yaw stability of the vehicle under dangerous working conditions.
Fu, YaoXie, RenminKaku, ChuyoZheng, Hongyu
Multiple actuators equipped in electric vehicles, such as four- wheel steering (4WS) and four-wheel drive (4WD), provide more degrees of freedom for chassis motion control. However, developing independent control strategies for distinct actuator types could result in control conflicts, potentially degrading the vehicle's motion performance. To address this issue, a model predictive control (MPC) based steering-drive cooperated control strategy for enhanced agility and stability of electric vehicles with 4WD and 4WS is proposed in this paper. By designing the control constraints within the MPC framework, the strategy enables single-drive control, single-steering control, and steering-drive cooperative control. In the upper control layer, a linear time-varying MPC (LTV-MPC) is designed to generate optimal additional yaw moment and additional steering angles of front and rear wheels to enhance vehicle agility and lateral stability. In the lower control layer, a linear MPC (LMPC) based torque vectoring optimization allocation strategy is implemented to track the desired additional yaw moment. Furthermore, tire slip ratios are taken into account within this layer to enhance vehicle longitudinal stability. Hardware-in-the-loop (HIL) experiments are conducted under diverse test conditions to assess the proposed cooperated control strategy. The results indicate that steering-drive cooperated control strategy can simultaneously enhance vehicle agility and stability performance compared to single-drive control and single-steering control.
Sun, HaoboZhang, LinZhao, ChunlaiWang, NianZhang, ZeyangChen, Hong
The pursuit of maintaining a zero-sideslip angle has long driven the development of four-wheel-steering (4WS) technology, enhancing vehicle directional performance, as supported by extensive studies. However, strict adherence to this principle often leads to excessive understeer characteristics before tire saturation limits are reached, resulting in counter-intuitive and uncomfortable steering maneuvers during turns with variable speeds. This research delves into the phenomenon encountered when a 4WS-equipped vehicle enters a curved path while simultaneously decelerating, necessitating a reduction in steering input to adapt to the increasing road curvature. To address this challenge, this paper presents a novel method for dynamically regulating the steady-state yaw rate of 4WS vehicles. This regulation aims to decrease the vehicle's sideslip angle and provide controlled understeer within predetermined limits. As a result, the vehicle can maintain a zero-sideslip angle during turns with constant speed and exhibit a neutral or slightly understeer behavior during turns with varying speeds. The relationship between vehicle speed, yaw rate, and the understeer gradient is rigorously analyzed, following the definition of the understeer gradient in the Guiggiani’s formulation. Yaw rate is influenced by vehicle speed and steering wheel angle during turns, resulting in a moderate understeer gradient and a slight deviation from the baseline—i.e., the zero-sideslip angle condition. To address this, a regression algorithm is developed to facilitate the realignment of the steady-state yaw rate with the baseline as speed and steering wheel inputs change, thereby maintaining minimal sideslip angles. Simulations validate the proposed method, demonstrating its effectiveness in achieving a moderate understeer gradient and eliminating counter-intuitive and discomforting steering actions. Ultimately, this dynamic regulation of steady-state yaw rate promises to enhance the handling performance
Guan, YihangZhou, HongliangJing, HouhuaMiao, Weiwei
Compared to traditional vehicles, four-wheel independent drive and four-wheel independent steering (4WID-4WIS) vehicles have gained significant attention from researchers due to their enhanced control flexibility and superior handling performance. The steering angle deviation caused by dynamic toe angle changes in two-wheel steering (2WS) systems is often minimal and hence overlooked. However, the impact becomes notably significant in 4WIS systems. This article contrasts the tire slip angle differences between 2WS and 4WIS, and delves into the effects of dynamic toe angle variations on 4WIS control. Solutions are proposed both in terms of steering angle control and suspension design. Firstly, a dynamic model for the 4WID-4WIS vehicle is established. Secondly, a hierarchical tire force distribution strategy is designed for trajectory tracking. The upper layer utilizes a sliding mode controller and PID controller to determine the total required longitudinal, lateral forces, and yaw moment for tracking. The middle layer allocates these combined forces and moments to individual tires based on constraint optimization, while the lower layer determines vehicle torques and steering angles according to the longitudinal and lateral forces exerted by each tire. In terms of steering control, feedforward control with bump steer compensation is implemented to improve wheel steering precision and lateral tire force control accuracy. Considering the toe angle variations during cornering, critical hardpoint coordinates are identified and optimized through sensitivity analysis in the suspension design, aiming to reduce dynamic toe angle changes. Lastly, the effectiveness of these proposed strategies is validated under constant radius and slalom scenarios using the co-simulation of Carsim and Matlab/Simulink. Simulation results highlight that toe angle changes due to suspension kinematic characteristics play a significant role in 4WIS control. The strategies proposed in this article notably improved tire slip angle errors, demonstrating superior yaw rate responses and lateral tracking accuracy during trajectory following.
Lu, AoLi, RunfengYu, YunchangJi, WenfeiHou, YufengTian, Guangyu
An automatic collision avoidance control method integrating optimal four-wheel steering (4WS) and direct yaw-moment control (DYC) for autonomous vehicles on curved road is proposed in this study. Optimal four-wheel steering is used to track a predetermined trajectory, and DYC is adopted for vehicle stability. Two single lane change collision avoidance scenarios, i.e., a stationary obstacle in front and a moving obstacle at a lower speed in the same lane, are constructed to verify the proposed control method. The main contributions of this article include (1) a quintic polynomial lane change trajectory for collision avoidance on curved road is proposed and (2) four different kinds of control method for autonomous collision avoidance, namely 2WS, 2WS+DYC, 4WS, and 4WS+DYC, are compared. In the design of DYC controller, two different feedback control methods are adopted for comparison, i.e., sideslip angle feedback and yaw rate feedback. The simulation results demonstrate significant improvements in the path tracking performance and stability of the 4WS+DYC control system compared to other control systems. Furthermore, the performance of the DYC control system with yaw rate feedback outperforms that of the DYC control system with sideslip angle feedback.
Lai, Fei
Vehicle dynamic control could improve vehicle performance. Vehicle stability is vital to the determination of vehicle dynamic control strategy. The phase plane method is one of the most common methods to judge vehicle stability. To determine the 4WS (four-wheel steering) vehicle stability status faster and more accurately, a novel method to assess the vehicle stability is based on the vehicle sideslip angle and angular velocity ( β-β˙) phase plane. At first, the 2 DOF (degree of freedom) model with a nonlinear tire model is established to acquire β-β˙ phase plane. Then the boundary of the stability region generated by the current method is compared. A crosspoint-ellipse method is provided based on the boundary comparison with the ideal boundary. The boundary function determined by the crosspoint-ellipse method is fitted based on vehicle dynamic theory and the boundary analysis with different steering angles, velocity, and road adhesion coefficient. At last, the transition area between the stable and unstable region is acquired by considering the uncertainty of the road adhesion coefficient. The provided method could describe the stable boundary closer to the ideal region with a relatively simple function, which could lay a good foundation for vehicle dynamic control.
Peng, DengzhiXia, ZuguoWang, LongLiu, Qing
Vehicular automation in the form of a connected and automated vehicle platoon is demanding as it aims to increase traffic flow and driver safety. Controlling a vehicle platoon on a curved path is challenging, and most solutions in the existing literature demonstrate platooning on a straight path or curved paths at constant speeds. This article proposes an algorithmic solution with leader-following (LF) communication topology and constant distance (CD) spacing for platooning homogeneous position-controlled vehicles (PCVs) on a curved path, with each vehicle capable of cornering at variable speeds. The lead vehicle communicates its reference position and orientation to all the follower vehicles. A follower vehicle stores this information as a virtual trail of the lead vehicle for a specific period. An algorithm uses this trail to find the follower vehicle’s reference path by solving an optimization problem. This algorithm is feasible and maintains a constant inter-vehicle distance. The PCVs can be holonomic or nonholonomic. For simulations, this article considers a holonomic four-wheel independent steering four-wheel independent drive (4WIS4WID) PCV for platooning. This vehicle has superior maneuverability and traction and can extend the applications of vehicle platoons from highways to paths with smaller radii of curvature. Simulation of a five-vehicle platoon suggests a satisfactory performance of the proposed approach. This article also presents an alternate curved platooning approach where the lead vehicle communicates its reference longitudinal and lateral velocities and yaw rate to a follower vehicle. The follower vehicle directly follows these communicated signals for platooning. This approach does not store the communicated signals and also cuts the cost of the position controller for the follower vehicles. Simulation results show that this alternative approach is applicable to constant-speed motion.
Bhaskar, RintuPotluri, RamprasadWahi, Pankaj
This work investigates the steering and wheel speed control of a completely custom built 8x8 scaled electric combat vehicle (SECV) which has been constructed to meet the Ackermann condition at low speeds. During remote control operation the scaled vehicle is capable of continuously maintaining and varying the individual wheel speed and individual wheel steering angles of all eight wheels in real time. Several steering scenarios have been developed including traditional (front 2-axle steering), fixed third axle (first, second and fourth axle steering), all wheel steering and crab steering (all wheels are parallel with same steering angle). The traditional, two axle steering scenario is experimentally tested for accuracy in this work with planned future research for experimental analysis of the other steering configurations. This work is conducted using Arduino software to control the physical SECV and TruckSim software to simulate the dynamics of the vehicle. The results obtained from the physical testing of the wheel angular velocity were validated using a handheld tachometer device. The steering angle measurement of each wheel was validated using linear actuator sensors. It was seen that the physical results from the SECV are within acceptable range of the theoretical data calculated and simulated in Trucksim Software. The continuous steering method is applied by investigating the relationship between the steering angles of all eight wheels while operating the steering system from zero to the maximum steering angle of the 1st axle inner wheel during a turn. A major contribution of this work is a novel physical experimentation of the continuous Ackermann relationship for eight wheels. During testing of the traditional two-axle steering configuration the metrics of performance that were reviewed include: wheel speed, center velocity, yaw rate, and eight-wheel steering angles. With these metrics being compared with the Trucksim simulation, the experimental results obtained from the scaled 8x8 electric combat vehicle are a solid foundation for the development of future full-size 8x8 electric combat vehicles.
Kim, JunwooEl-Gindy, MoustafaEl-Sayegh, Zeinab
To tackle the over-actuated and highly nonlinear characteristics that four-wheel-independent-steering and four-wheel-independent -driving (4WIS/4WID) vehicles exhibit when tracking aggressive trajectory, a hierarchical controller with layers of computation-intensive modules is commonly adopted. The high-level linear motion controller commands the desired state derivatives of the vehicle to meet the overall trajectory tracking objectives. Then the system dynamic is inversed by the mid-level control allocation layer and the low-level wheel control layer to map the target state derivatives to steering angle and motor torque commands. However, this type of controller is difficult to implement on the embedded hardware onboard since the nonlinear dynamic inversion is typically solved by nonlinear programming. This article refines the dynamic inversion part of current hierarchical trajectory tracking controller for 4WIS/4WID vehicles with consideration of the nonlinear tyre/vehicle dynamics and of computational complexity. First, the mid-level control allocation layer distributes target resultant forces to each tyre via the less computationally troublesome direct allocation method. The current method to determine the attainable generalised force subset (AFS) in direct allocation cannot incorporate the tyre friction circle constraints, leading to an inaccurate AFS. The inaccuracy of AFS will either introduce inversion error or fail to return controls for theoretically-attainable generalised force. Hence, a means of determining the refined AFS, which considers the actual tyre force limits and uses polygons to approximate tyre friction circles, is designed. Second, the low-level wheel control layer steers and drives the wheel to achieve the target tyre forces. An iterative method with proofed convergence is proposed to inverse the nonlinear tyre model. The effectiveness of the refinements is validated by Carsim and MATLAB/Simulink co-simulation. Simulation results demonstrate that the vehicle can well follow an obstacle avoidance trajectory. Comparisons with the direct allocation using the AFS determined by the current method are made. The refined AFS we proposed can not only enlarge the envelope of vehicle controllability, but also preserve the desired direction of the generalised force vector if it is beyond the vehicle’s capability, highlighting the importance of accounting for the nonlinearities we considered during the design.
Yu, YunchangLi, RunfengJi, WenfeiLu, ZiwangTian, Guangyu
The rapid development of city traffic makes the driving conditions faced by vehicles increasingly complex. The drive-by-wire chassis vehicle has the characteristics of four-wheel independent steering, four-wheel independent drive and four-wheel independent braking, which has become a current research hotspot because that can meet various complex working conditions. However, it is precisely because of the high degree of controllability of the drive-by-wire chassis that the research on the control strategy has become difficult. In this paper, an integrated control strategy based on the hierarchical algorithm framework is designed for the drive-by-wire chassis vehicle, which includes a centralized control layer, a tire force distribution layer and an actuator control layer. The centralized control layer is based on the model predictive control algorithm, which takes the vehicle longitudinal speed, lateral speed and yaw rate as the control objectives, and solves the total longitudinal force, total lateral force and total yaw moment required by the vehicle. The tire force distribution layer assigns the control objectives to the four wheels, which adopts the optimal control method to transform the tire force distribution problem into a quadratic programming problem, and solves the problem with the tire utilization efficiency as the optimization objective to obtain the longitudinal force and lateral force of each wheel. The actuator control layer obtains the wheel angle and driving torque through the tire inverse model. The performance with the proposed strategy is demonstrated by steering wheel angle step input simulation test under the condition of low road friction coefficient which compared with the direct yaw moment control algorithm. In order to further verify the effectiveness of the strategy under various driving conditions, a simulation test of the sine input of steering wheel angle was carried out to verify that the strategy can improve the driving stability of the vehicle under various driving conditions.
Wang, ZixuZheng, HongyuZong, ChangfuKaku, Chuyo
In contrast to a normal vehicle, a 4-wheel steer (4WS) and 4-wheel independent drive (4WID) vehicle provides more flexibilities in vehicle dynamic control and better handling performance, since both the steer angle and drive torque of each wheel can be controlled. However, for motorsports, how much lap time can be improved with such a vehicle is a problem few discussed. So, this paper focuses on the racing line optimization and lap time improvement for a 4WS &4WID vehicle. First, we optimize the racing line and lap time of three given circuits with the genetic algorithm (GA) and interior-point method, and several objective functions are compared. Next, to evaluate the lap time improvement of 4WS & 4WID, a detailed vehicle dynamic model of our 4WS & 4WID platform vehicle is built in Carsim. To follow the racing line, a path following controller which contains a PID speed controller and a model predictive control (MPC) yaw rate controller is built. Moreover, a sliding mode (SMC) 4WS controller is designed to adjust the steer angle of wheels, meanwhile another SMC direct yaw moment (DYC) controller is proposed to track the target yaw rate and allocate the wheel torque considering the appropriate usage of tire friction. Results have demonstrated that the optimized racing line and lap time have tolerable error (<3%), and the proposed 4WS & 4WID method can reduce 3% of the lap time by enlarging the G-G diagram.
Sun, YiwenLi, RunfengLu, ZiwangTian, Guangyu
This research aims to model and assess autonomous vehicle controller while including a four-wheel steering and longitudinal speed control. Such a modeling process simulates human driver behavior with consideration of real vehicle dynamics’ characteristics during standard maneuvers. However, a four-wheel steering control improves vehicle stability and maneuverability as well. A three-degree of freedom bicycle model, lateral deviation, yaw angle, and longitudinal speed is constructed to describe vehicle dynamics’ behavior. Moreover, a comprehensive traction model is implemented which includes an engine, automatic transmission, and non-linear magic formula tire model for simulation of vehicle longitudinal dynamics. A combination of proportional integral derivative (PID) longitudinal controller and fuzzy lateral controller are implemented simultaneously to track the desired vehicle path while minimizing lateral deviation and yaw angle errors. Then, A linear quadratic regulator (LQR) based rear steering controller is introduced to represent a performance improvement over front steering only. The longitudinal controller tries to maintain the desired speed through control of the engine throttle while the lateral controller steers the vehicle wheels to follow the pre-defined path. Path tracking simulation is executed through enjoining a referenced safe path to pass a simulated track based on ISO 3888 double lane change maneuver. Both longitudinal and lateral controllers’ simulation results achieved the required performance based on lateral deviation, yaw angle, front steering angle, and vehicle speed. Additionally, the lateral deviation is minimized according to the reference simulated path through the rear steering controller while decreasing vehicle yaw rate and slip angles for front and rear tires.
Gafar, IbrahimOraby, WalidAly, Mahmoud Atef
Aiming at the test safety problems in the early stage of self-driving cars development, firstly the virtual vehicle on-board CAN data acquisition module of the present project was designed based on virtual LabVIEW. Then a wireless remote control system for the self-driving car was constructed, which integrated the built virtual vehicle on-board CAN data acquisition system, the remote real-time image monitoring module and the remote upper computer control module based on ZigBee wireless transmission. It can execute the environmental awareness training and continuous and complex motion manipulation testing of the vehicle without relying on the driver, which can solve the safety problems in the tests of initial development of self-driving cars. Finally, the four-wheel independent steering electric vehicle was used as the self-driving test vehicle, and the wireless remote control system was tested on the double lane change type path and S-type path. During the testing, the self-driving car performed better actions and followed the desired path, which verified the consistency of the test behaviors and the remote control operation instructions.
Zhou, SuXie, ZhengchunZhang, GangHirz, MarioShen, Wei
The articulated steering system is widely used in engineering vehicles due to its high mobility and low steering radius. The design parameters have a vital impact on the selection of the steering system assemblies, such as the operation stroke, pressure, and force of the hydraulic cylinders during the steering process, which will affect the system weight. The system energy consumption is also relevant to the geometry parameters. According to the kinetic analysis of the steering system and dynamic analysis of the steering process, the kinetic model of an engineering vehicle steering system is built, and the length and pressure variation of the cylinder is calculated and validated by the field test. The influence of the factors is analyzed based on the established model. To lower the system weight, needed pressure, and force, the multi-objective particle swarm optimization method is initiated to optimize the geometry parameter of the articulated steering system. After optimization, the weight of the system is decreased by 0.61kg, and the maximum force and pressure are decreased by 9.47% and 9.54% respectively.
Peng, DengzhiChen, LiTan, Gangfeng
Recently, customers' demands for future mobility have increased, such as movement in narrow spaces, increased driving freedom, and ease of parking. The key technology to meet these demands is the four-wheel independent steering system. In this study, we introduce the concept design process for a four-corner steering module and how to prove the design. In addition, we introduce a control method for basic driving modes, such as short U-turn, diagonal driving, crab driving, and zero radius turning. Finally, we propose a special driving mode using the instantaneous rotation center of the 4WS system.
Moon, Ha-KyungLee, Byung-KyuJeon, Gab-BaeSoon, HuhLee, Jae-WonSuh, Jee-YoonSeo, Mu-YeolOh, Kwang-Seok
In order to improve the performance of automatic emergency steering and collision avoidance of intelligent vehicle, two automatic steering control methods under ideal model following control are proposed. The two ideal reference models are the reference model with zero sideslip angle of vehicle gravity center and the reference model with no phase-lag in vehicle lateral acceleration. The control system adopts the combination of outer loop and inner loop. In the design of the outer loop controller, the optimal control is used to get the steering wheel angle needed to avoid collision. The inner loop controller uses feedforward and feedback control to get the required front and rear wheel steering angles. Taking vehicle two degrees of freedom (DOF) lateral dynamics model as the research object, the vehicle collision avoidance reference trajectory is obtained through the fifth-degree polynomial. The simulation test of automatic emergency steering and collision avoidance for vehicles equipped with the above control system is carried out on high and low adhesion roads respectively. The comparison with the control system without reference model is also carried out. The results show that the collision avoidance effect of the control systems with reference model are better than those without reference model. When avoiding collision on a high adhesion road, the reference model control system with zero sideslip angle has the best effect. While when avoiding collision on a low adhesion road, the reference model control system with no phase-lag in lateral acceleration has the best effect.
Lai, FeiHuang, ChaoqunChen, HuaTang, YuYang, HuiWang, Xiaoyu
Previous researches about vehicle lateral dynamics mainly focus on one or several specific working conditions and make simulation analysis in the time domain to compare the quality of the steering control system, which cannot compare the performance of the controller as a whole. In this article, an innovative concept was proposed to compare the vehicle steering controller. Combined with the bifurcation theory, the performance of three different steering control systems (front-wheel steering system, four-wheel steering system, and direct yaw-moment control [DYC] system) can be compared intuitively from the phase plane. First of all, taking the front-wheel steering system as the research object, the state phase trajectory of the vehicle under certain speed and different front-wheel steering angle inputs is analyzed, based on the established two degrees-of-freedom (2-DOF) model of vehicle lateral dynamics. Then the influence of the front-wheel steering angle and vehicle speed on the lateral dynamics is further studied, and the stable driving area of the front-wheel steering system on a high- and low-adhesion road is calculated, respectively. Finally, the phase plane and time-domain simulations of the four-wheel steering system and the DYC system are carried out. The results show that compared with the front-wheel steering system, the stable driving area of the four-wheel steering control system is significantly increased, and the stability of the DYC system is the best.
Lai, FeiHuang, ChaoqunJiang, Chengyue
Lane-changing is a typical traffic scene effecting on road traffic with high request for reliability, robustness and driving comfort to improve the road safety and transportation efficiency. The development of connected autonomous vehicles with V2V communication provide more advanced control strategies to research of lane-changing. Meanwhile, four-wheel steering is an effective way to improve flexibility of vehicle. The front and rear wheels rotate in opposite direction to reduce the turning radius to improve the servo agility operation at the low speed while those rotate in same direction to reduce the probability of the slip accident to improve the stability at the high speed. Hence, this paper established Four-Wheel-Steering(4WS) vehicle dynamic model and quasi real lane-changing scenes to analyze the motion constraints of the vehicles. Then, the polynomial function was used for the lane-changing trajectory planning and the extended rectangular vehicle model was established to get vehicle collision avoidance condition. Vehicle comfort requirements and lane-changing efficiency were used as the optimization variables of optimization function and the control of trajectory tracking can be obtained by using model predictive control (MPC) method. A lane-changing model based on steering characteristics and safety distance with the system of V2V communication and collaboration strategy was established. The lane-changing trajectory was simulated by MATLAB and the results showed that the lane-changing trajectory can safely realize the lane-changing behavior of 4WS autonomous vehicles.
Ma, FangwuShen, YuchengNie, JiahongLi, XiyuYang, YuWang, JiaweiWu, Guanpu
Steering movement is the most basic movement of the vehicle, in the car driving process, the driver through the steering wheel has always been to control the direction of the car, in order to achieve their own driving intention. Four Wheel Steering (4WS) is an advanced vehicle control technique which can markedly improve vehicle steering characteristics. Compared with traditional front wheel steering vehicles, 4WS vehicles can steer the front wheels and the rear wheels individually for cornering, according to the vehicle motion states such as the information of vehicle speed, yaw velocity and lateral acceleration. Therefore, 4WS can enhance the handling stability and improve the active safety for vehicles. Based on the theory of Vehicle Dynamics and Sliding Mode Control, this paper investigates the following issues, Firstly, a 2DOF 2WS vehicle model is built up by using the state-space equations, which will be used to compare the 4WS vehicle model containing vehicle lateral and yaw; Secondly, based on the 4WS vehicle model with nonlinear tire lateral force characteristics, the control algorithm is designed to use feed-forward plus feed-back control framework by following the reference model. And the simulation is processed in MATLAB/Simulink and CarSim to verify the control algorithm. By comparison and analysis of the simulation results, By following the reference model, the performances of the yaw velocity and lateral acceleration responses are largely different. When set the speed at 30 km/h, 50 km/h and 80 km/h in simulations, the traditional steering stability of 2WS vehicle is not more stable than the four-wheel steering vehicle at different speeds. Consequently, the use of sliding mode control can effectively improve the steering performance of the vehicle in the steering, a good way to track the target path, and 4WS car to improve the vehicle’s handling stability.
Zhang, JiaxuZheng, HongyuZhao, Mengdi
Compared with the traditional front-wheel- steering (FWS) vehicles, four-wheel-independent-steering (4WIS) vehicles have better handing stability and path-tracking performance. In view of this, a novel 4WIS electric vehicle (EV) with steer-by-wire (SBW) system is proposed in this paper. As to the 4WIS EV, a linear quadratic regulator (LQR) optimal controller is designed to make the vehicle track the target path based on the linear dynamic model. Taking the effect of uncertainties in vehicle parameters into consideration, a robust controller utilizing μ synthesis approach is designed and the controller order reduction is implemented based on Hankel-Norm approximation. In order to evaluate the performance of the designed controllers, numerical simulations of two maneuvers are carried out using the nonlinear vehicle model with 9 degrees of freedom (DOF) in MATLAB/Simulink. Simulation results show that the robust controller is superior to the LQR optimal controller in tracking accuracy in terms of the nominal vehicle model. Furthermore, the robust controller can make the vehicle track the target path well under the circumstances of different vehicle velocities and road friction coefficients, which indicates the robust controller has strong robust stability and good robust performance against parametric perturbations.
Hang, PengChen, XinboLuo, FengmeiFang, Shude
This paper presents an integrated chassis controller with multiple hierarchical layers for 4WID/4WIS electric vehicle. The proposed systematic design consists of the following four parts: 1) a reference model is in the driver control layer, which maps the relationship between the driver's inputs and the desired vehicle motion. 2) a sliding mode controller is in the vehicle motion control layer, whose objective is to keep the vehicle following the desired motion commands generated in the driver control layer. 3) By considering the tire adhesive limits, a tire force allocator is in the control allocation layer, which optimally distributes the generalized forces/moments to the four wheels so as to minimize the tire workloads during normal driving. 4) an actuator controller is in the executive layer, which calculates the driving torques of the in-wheel motors and steering angles of the four wheels in order to finally achieve the distributed tire forces. Experimental verification is made to show that the proposed integrated chassis controller is able to improve the vehicle's stability and handling performance through coordinating the steering and driving systems.
Li, ChunshanSong, PanChen, GuoyingZong, ChangfuLiu, Wenchao
Four-wheel independent control electric vehicle is a new type of x-by-wire EV with four wheels independent steering and four wheels independent drive/brake systems. In order to take full advantage of the vehicle's performance potential, this paper presents a novel integrated chassis control strategy. In the paper, the strategy is designed by the hierarchical control structure and divided into integrated control layer and allocation layer. By this method, the control logical can be modularized and simplified. In the integrated control layer, Model Prediction Control (MPC) is adopted to design the integrated control unit, which belongs to be a kind of local optimization algorithm with feedback correction features. Using this method could avoid the system performance degradation caused by the control model mismatch. The control allocation layer is to optimally distribute the vehicle control forces to the steering/driving/brake actuators on each wheel. In order to maximize the use of the tire adhesions, the algorithm sets the tire load rate minimized as the control target. Finally, based on the four-wheels-independent vehicle dynamic model, the feasibility of the proposed integrated chassis control strategy is verified under the condition of step steering angle response with two different road adhesion coefficients.
Chen, GuoyingZhang, Dong
The main characteristic of vehicle moving on road is related to its response to the drivers command and to environmental factors affecting the direction of motion of vehicle. The two basic problems in handling the vehicle are control of vehicle along the desired path and stabilization of the direction of motion of vehicle against external disturbances. The vehicle with best handling characteristics is the vehicle which can always be controlled by the driver. While parking the vehicle and doing sharp turnings the vehicle with two wheel steering cannot be more significant. The two wheel steering system takes large radius of turning and requires more space to take turn. Hence four wheel steering is preferable than two wheel steering systems. A multi-function four wheel steering system could improve directional stability at high speeds, sharp turning performance at low speeds, and parking performance of a vehicle. Generally there are three types of steering systems which include front wheel, rear wheel and four wheels. The paper deals with the mechanical steering system which can perform all these operations. The paper presents a new design of steering system which involves a connector, coupler and bevel gears. In a front wheel steering, only front wheels steer, and in a rear wheel steering only rear wheels will steer to get turning. In a four wheel steering system at low speeds, the front wheels and rear wheels are out of phase for low turning radius. However at high speeds, the front and rear wheels should be in phase to increase the stability of a vehicle. The paper presents a single steering mechanism arrangement offering three modes of steering operations possible which can be selected by the driver.
Vanamala, Uma Maheshwarkoganti, Raja Rao
Interaction of Vehicle Ride Vibration Control with Lateral Stability Using Active Rear Wheel Steering2009-01-10424/20/2009
In this work the effects of vehicle vertical vibrations on the tires/road cornering forces, and then consequently on vehicle lateral dynamics are studied. This is achieved through a ride model and a handling model linked together by a non-linear tire model. The ride model is a half vehicle with four degrees of freedom (bounce and pitch motions for vehicle body and two bounce motions for the two axles). The front and rear suspension are a hydro-pneumatic slow-active systems with 6 Hz cut-off frequency designed based on linear optimal control theory. Vehicle lateral dynamics is modeled as two degrees (yaw and lateral motions) incorporating a driver model. An optimal rear wheel steering control in addition to the front steering is considered in the vehicle model to represent a Four Wheel Steering (4WS) system. The tire non-linearity is represented by the Magic Formula tire model. The ride vibration control, vehicle lateral dynamics and tire/road cornering forces are interlinked together in order to study the effect of vertical vibration control on the vehicle lateral stability with active rear wheel steering. The results are time domain simulation of the vehicle response when performing lateral maneuvers while road wheels are subjected to vertical excitation. Vehicle lateral dynamics are compared with 2WS and 4WS systems taking into account the vehicle wheelbase correlation between front and rear active suspension systems.
Oraby, W. A. H.Aly, M. A.El-Demerdash, S.M.Selim, A. M.
Torque Vectoring Axle and Four Wheel Steering: A Simulation Study of Two Yaw Moment Generation Mechanisms2006-01-08194/3/2006
There is increasing demand for enhancement of stability and handling performance in modern automobiles. Active yaw moment generation mechanisms are essential for implementing intelligent stability control schemes. Two mechanisms being considered here are Torque Vectoring Rear Axle and Four Wheel Steering System. Torque Vectoring Axle allows active control of wheel speed ratio and torque distribution typically through the use of wet clutch/brake system and secondary gearing. Four wheel steer systems usually have conventional steering in the front axle and an active steering system in the rear axle. The steering logic is based on improved performance in terms of turning radius at low speeds and directional stability and response at higher speeds. In this study, a lumped parameter, large amplitude, non-linear vehicle model of a rear wheel drive, high-performance vehicle is used. The simulation is executed on a skid pad as well as on a prescribed test track using a closed loop driver-vehicle system. The operating characteristics under steady state situation on a skid pad and dynamic performance on Nurburgring Nordschleife track are evaluated. The investigation is limited to high speed driving on surfaces with high friction coefficient. The results are presented along with that of a baseline vehicle.
Mohan, Sankar KSharma, Anupam
This paper describes the use of a designed Fuzzy Logic Control for the purpose of integrating the driver’s steering input together with the four-wheel steering system (4WS) in order to improve the vehicle’s dynamic behavior with respect to yaw rate and body sideslip angle. The control objective is to obtain zero body sideslip angle by a two-dimensional rule table, which is created based on the error and on the change in the error of sideslip angle that is to be minimized. The dynamics of the model is developed with a three-degree of freedom nonlinear vehicle model including roll dynamics. The Magic Formula is applied in order to formulate the nonlinear characteristics of the tires. A lane change and steady state cornering simulations are performed to show the effectiveness of the control on transient motion body sideslip angle and yaw rate response time behaviors. During simulations, comparisons are done with the two-wheel steered vehicle and the control techniques studied previously.
Ozatay, EvrenUnlusoy, Samim Y.Yildirim, A. Murat
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