Tire Force Distribution Research Articles

Integrated Chassis Control for Multi-Axle Vehicles: A Comprehensive Review

Multi-axle vehicles (MAVs) are used to transport heavy loads, navigate challenging terrain, and perform specific tasks. However, designing vehicle control systems for such vehicles is challenging. MAVs, such as trucks, buses, military vehicles, and multi-purpose vehicles, require sophisticated control techniques to increase the stability and ride comfort of such vehicles. This paper provides a comprehensive review of standalone control systems and integrated control systems (ICSs) for the steering, driving/braking, and suspension systems of MAVs, with a particular focus on the optimal tyre force distribution (TFD) in ICSs for MAVs. It also discusses various objective functions and optimisation methods used for the TFD. The findings indicate that optimising TFD significantly improves the stability of MAVs. As such, future studies may consider examining optimising three-axis TFD for MAVs to further improve vehicle stability.

Optimized Longitudinal and Lateral Control Strategy of Intelligent Vehicles Based on Adaptive Sliding Mode Control

To improve the tracking accuracy and robustness of the path-tracking control model for intelligent vehicles under longitudinal and lateral coupling constraints, this paper utilizes the Kalman filter algorithm to design a longitudinal and lateral coordinated control (LLCC) strategy optimized by adaptive sliding mode control (ASMC). First, a three-degree-of-freedom (3-DOF) vehicle dynamics model was established. Next, under the fuzzy adaptive Unscented Kalman filter (UKF) theory, the vehicle state parameter estimation and road adhesion coefficient (RAC) observer were designed to estimate vehicle speed (VS), yaw rate (YR), sideslip angle (SA), and RAC. Then, a layered control concept was adopted to design the path-tracking controller, with a target VS, YR, and SA as control objectives. An upper-level adaptive sliding mode controller was designed using RBF neural networks, while a lower-level tire force distribution controller was designed using distributed sequential quadratic programming (DSQP) to obtain an optimal tire driving force. Finally, the control strategy was validated using Carsim and Matlab/Simulink software under different road adhesion coefficients and speeds. The findings indicate that the optimized control strategy is capable of adaptively adjusting control parameters to accommodate various complex conditions, enhancing the tracking precision and robustness of vehicles even further.

Active rack control of steer-by-wire systems for vehicle lateral stability

This paper describes a stability control strategy based on a steer-by-wire system to improve the lateral stability and manoeuvrability of vehicles by integrating individual chassis control modules, such as electronic stability control (ESC) and active front steering (AFS). Because of the uncertainty of cornering stiffness, an adaptive sliding-mode control is implemented without using the cornering stiffness value. An adaptive parameter is used instead of the cornering stiffness in the slip angle estimation and the lateral stability control. An unscented Kalman filter is used to estimate the slip angle and adaptive sliding mode control is used in lateral stability control. An equivalent desired command is calculated in lateral stability control. An integrated AFS and four individual wheel-braking controls were utilised to achieve an optimal distribution of longitudinal and lateral tyre forces, aiming to attain the desired command for lateral stability. Optimal coordination of the control authority for the AFS and the ESC has been chosen to minimise the force of each tyre. Computer simulations and vehicle tests of a closed-loop driver–vehicle–controller system subjected to a double-lane change have been carried out to verify that the proposed control strategy works.

Coordinated Longitudinal and Lateral Motion Control for Distributed Drive Electric Vehicles With Mechanical Elastic Wheels

The distributed drive electric vehicle (DDEV) with active front wheel steering is an over-actuated system. For such a system, more optimization targets should be considered to make the system better in addition to meeting the driving command of drivers and keeping the vehicle stable. The slip energy generated by excessive tire slipping reduces the utilization of the output energy of the motor, resulting in a reduction of electric vehicle mileage. In order to improve the vehicle performance, a coordinated longitudinal and lateral controller is designed for DDEV with mechanical elastic wheels (MEWs). The motion control layer of the hierarchical controller adopts the integral sliding mode control (ISMC) to determine the desired longitudinal force, lateral force and yaw moment as virtual inputs of the vehicle. Then, a novel tire force distribution strategy is proposed to dynamically assign the virtual inputs among front wheels and four motors with the goal of optimizing the vehicle stability and longitudinal tire slip energy dissipation. To characterize tire slip energy more accurately, the brush model matching MEW is deduced in the combined slip conditions. The proposed controller is evaluated on the hardware-in-the-loop (HIL) test platform under different driving conditions. Simulation results demonstrate that this controller not only ensures the vehicle handling stability performance, but also improves the utilization of motor output energy and reduces tire wear.

Research on tyre mechanics model for multi-axle coordinated steering of heavy vehicles

Compared with passenger cars, heavy vehicles have larger loads, longer bodies, more steering modes, and are more likely to cause improper steering angle relationships among the wheels, resulting in uncoordinated steering. This uncoordinated steering makes the tyres roll and drag, which results in abnormal lateral and longitudinal slips, changing the lateral and longitudinal mechanical characteristics of tyres and leading to low path tracking accuracy and poor steering performance of vehicles. Therefore, a tyre model containing lateral and longitudinal mechanical characteristics under heavy load is the key to solving the problem of uncoordinated steering in heavy vehicles. Firstly, with the physical tyre model, the lateral and longitudinal slip is described as carcass deflections. With the carcass deflections and contact pressure distribution of heavy load, the tyre forces under uncoordinated steering conditions are derived. Then, the tyre imprint parameters are obtained with a test bench, and a two-dimensional contact pressure distribution model is established to reproduce the contact pressure distribution of tyre under heavy loads and dynamic slips. The comparison results with Magic Formula (MF) and Trucksim are generally consistent, proving the effectiveness of the model. Finally, a lateral and longitudinal tyre force distribution control of vehicles is carried out based on the established model. The results of the Trucksim-Simulink co-simulation show that the path tracking accuracy of vehicles is significantly improved, which demonstrates that the tyre model incorporating lateral and longitudinal mechanical characteristics under heavy loads can provide a theoretical basis for solving the problem of uncoordinated steering in heavy vehicles.

Trajectory Tracking Control of Intelligent X-by-Wire Vehicles

Vehicle intelligence is an effective way to improve driving safety and comfort and reduce traffic accidents. The trajectory tracking control of unmanned vehicles is the core module of intelligent vehicles. As a redundant system, the X-by-wire electric vehicle has the advantage that the turning angles and driving torque of the four wheels can be precisely controlled and it has a higher degree of controllability and flexibility. In this paper, a trajectory tracking control algorithm based on a hierarchical control architecture is designed based on x-by-wire vehicles. The hierarchical control algorithm architecture includes the trajectory tracking layer, tire force distribution layer, and actuator control layer. The trajectory tracking layer uses the longitudinal force, lateral force, and yaw moment as the control variables; the model predictive control algorithm controls the vehicle to follow the desired trajectory. The tire force distribution layer is solved by transforming the tire force distribution problem into a quadratic programming problem with constraints. Based on the expected resultant force and resultant moment, the longitudinal force and lateral force of each tire in the vehicle coordinate system are obtained. The actuator control layer converts the coordinate system to obtain the longitudinal force and lateral force in the tire coordinate system, which uses the arctangent function tire model to solve the desired tire slip angle, and then obtains the vehicle steer angle and driving torque. To verify the effectiveness of the trajectory tracking control algorithm of the hierarchical control architecture, the proposed trajectory tracking control algorithm is simulated and verified through the variable speed double line change condition and the low road friction coefficient double line change condition. The simulation results show that the control algorithm proposed in this paper has the accuracy to follow the desired trajectory.Definition:

A novel integrated control framework of AFS, ASS, and DYC based on ideal roll angle to improve vehicle stability

The current research on vehicle stability control mainly focuses on following the ideal yaw rate and sideslip angle, without considering the potential of ideal roll angle in improving the vehicle stability. In addition, the mutation of tire-road friction coefficient promotes a great challenge to the stability control. To improve the vehicle stability, in this study, firstly, the three-dimensional stability region of “lateral speed-yaw rate-roll angle” was studied, and a method to determine the ideal roll angle was proposed. Secondly, a novel integrated control framework of AFS, ASS, and DYC based on ideal roll angle was proposed to actively control the front tire slip angles, suspension forces, and motor torques: In the upper-level controller, model predictive control and tire force distribution algorithm were used to obtain the optimal four-tire longitudinal forces, front tire lateral forces and additional roll moment under constraints; In the lower-level controller, the upper virtual target was realized by the optimal allocation algorithm of actuators and the tire slip controller. Finally, the proposed control framework was verified on the varied-µ road. The results indicated that compared with the two existing control strategies, the proposed framework can significantly improve the vehicle following performance and stability.

Integrated Path Tracking Control of Steering and Differential Braking Based on Tire Force Distribution

Integrated Path Tracking Control of Steering and Differential Braking Based on Tire Force Distribution

Incorporated vehicle lateral control strategy for stability and enhanced energy saving in distributed drive hybrid bus

Vehicle stability and energy efficiency are important considerations in vehicle engineering. In this context, the current paper presents an energy saving strategy for hybrid electric vehicles that incorporates vehicle lateral dynamic control in conjunction with energy efficiency. To this end, we first model the nonlinear vehicle lateral dynamics of a hybrid electric bus via a Takagi–Sugeno approach and combine this model with an H_{\\infty } state-feedback controller via parallel distributed compensation. The controller matrices are obtained using linear matrix inequalities through an optimal energy-to-energy performance norm of the nonlinear vehicle model. Second, we propose a reference side-slip angle generating method and a set of tire force distribution rules, which under the premise of ensuring vehicle stability, minimize the overall energy consumption of the vehicle. Finally, we put forward a new speed prediction method based on vehicle lateral dynamics for hybrid electric vehicle energy saving. Human-in-the-loop simulated driving experiments are conducted where the bus performs lane-changing maneuvers with enhanced control properties under various driving conditions, demonstrating the reliability of the proposed energy-saving performance measures.

Unified Chassis Control of Electric Vehicles Considering Wheel Vertical Vibrations.

In the process of vehicle chassis electrification, different active actuators and systems have been developed and commercialized for improved vehicle dynamic performances. For a vehicle system with actuation redundancy, the integration of individual chassis control systems can provide additional benefits compared to a single ABS/ESC system. This paper describes a Unified Chassis Control (UCC) strategy for enhancing vehicle stability and ride comfort by the coordination of four In-Wheel Drive (IWD), 4-Wheel Independent Steering (4WIS), and Active Suspension Systems (ASS). Desired chassis motion is determined by generalized forces/moment calculated through a high-level sliding mode controller. Based on tire force constraints subject to allocated normal forces, the generalized forces/moment are distributed to the slip and slip angle of each tire by a fixed-point control allocation algorithm. Regarding the uneven road, H∞ robust controllers are proposed based on a modified quarter-car model. Evaluation of the overall system was accomplished by simulation testing with a full-vehicle CarSim model under different scenarios. The conclusion shows that the vertical vibration of the four wheels plays a detrimental role in vehicle stability, and the proposed method can effectively realize the tire force distribution to control the vehicle body attitude and driving stability even in high-demanding scenarios.

State estimation and experimental verification of a robotic vehicle with six in-wheel drives using Kalman filter

In this research we present an algorithm for a six-wheeled robotic vehicle with articulated suspension (RVAS) to estimate the vehicle velocity and acceleration states, slip ratio and the tire forces. The estimation algorithm consists of six parts. In the first part, a wheel state estimator estimates the wheel rotational speed and its angular acceleration using Kalman filter, which is used to estimate the longitudinal tire force distribution in the second part. The third part is to estimate respective longitudinal, lateral, and vertical speeds of the vehicle and wheels. Based on these speeds, the slip ratio and slip angle are estimated in the fourth part. In the fifth part, the vertical tire force is then estimated. In the sixth part, the lateral tire force is then estimated. For a simulation test environment, the RVAS dynamic model is developed using Matlab and Simulink. The estimation algorithm is then verified in simulation using the vehicle test data and different test scenarios. It is found from simulation results that the proposed estimation algorithm can estimate the vehicle states, longitudinal tire forces efficiently. Moreover, a small prototype of the robotic vehicle is fabricated for experimental verification of the estimation algorithm. Various experiments are executed in pavement and off-road driving to estimate the wheel angular position, velocity and acceleration states and finally the slip ratio is estimated in these situations.

Lateral Tyre Force Distribution for Four-Wheel Steer-by-Wire Vehicles

In a four-wheel independent steering vehicle, all the tyres have the capability of being steered independently. The traditional steering assemblies are mechanically limited because their inner and outer wheel’s steering angles are interrelated which makes it difficult to extract the maximum possible traction from the ground. Such steering systems are unable to take the advantage of the load transfer which occurs during the cornering. This work proposes a novel method of lateral tyre force distribution between the inner and outer wheels by making use of load transfer during the cornering of the vehicle. The distribution is obtained by using a function which maps the lateral acceleration of the vehicle to the distribution of the forces between the wheels. The function can be tailored according to the requirements of the driving. The control strategy involves simple equations to allow for an easy hardware implementation. The simulations performed through numerical solution of vehicle dynamics model using the computer program in MATLAB/Simulink show an improvement in the cornering performance of the vehicle and a significant reduction in workload of tyres.

Robust path control for an autonomous ground vehicle in rough terrain

Typically, it is not trivial for an autonomous ground vehicle (AGV) to navigate in rough terrain due to lots of unexpectable uncertainties. Because the performance of the autonomous navigation can be degraded by the uncertainties, the AGV requires a robust control system against them. To handle the necessity, this study proposes the robust path controller by utilizing a disturbance observer (DOB)-based control method. The proposed controller is developed by two steps: the first step is to design a controller for handling a nominal system of the AGV, and the other is to add the DOB to the nominal controller. Then, the determined control input is distributed into tire forces because the tire forces are final resource enabling the AGV to move. The tire force distribution is defined as an optimization problem with some constraints, and the solution is obtained by the CVXGEN. Finally, numerical simulations and field tests with a skid-type ground vehicle, developed by the authors’ laboratory, are conducted to validate the performance of the proposed method.

Robust adaptive backstepping sliding mode control for motion mode decoupling of two‐axle vehicles with active kinetic dynamic suspension systems

SummaryA mode decoupling control strategy is proposed for the active Kinetic Dynamic Suspension Systems (KDSS) with electrohydrostatic actuator (EHA) to improve the roll and warp mode performances. A matrix transfer method is employed to derive the modes of body and wheel station motions for full vehicle with active KDSS. The additional mode stiffness produced by the active KDSS is obtained and quantitatively described with the typical physical parameters. A new hierarchical feedback control strategy is proposed for the active KDSS to improve the roll and warp motion performances and simultaneously accounting for nonlinear dynamics of the actuators with hydraulic uncertainties. H∞ static output‐feedback control is employed to obtain the desirable mode forces, and a new projection‐based adaptive backstepping sliding mode tracking controller is designed for EHA to deal with address the nonlinearity and parameters uncertainty. This controller is used to realize the desirable pressure difference of EHA required from the target mode forces. Numerical simulations are presented to compare the roll and warp performances between the active KDSS, conventional spring‐damper suspension, and suspension with antiroll bar under typical excitation conditions. The evaluation indices are normalized and compared with radar chart. The obtained results illustrate that the proposed active KDSS with proposed controller does not produce additional warp motion for vehicle body, and has achieved more reasonable tire force distribution among wheel stations, the roll stability, road holding, and significantly improved ride comfort simultaneously.

Study on Control Strategy of Handling Stability for an Eight In-Wheel Motor Drive AWS Electric Vehicle

This paper took an eight in-wheel motor independent driven and all-wheel independent active steering vehicle as research object, and proposed a hierarchical optimized tire force distribution control strategy (8WD8WS+) based on sliding mode control and control allocation to coordinate the output torques and steering angle of eight wheels. The hierarchical control strategy included an upper vehicle motion controller, a lower tire force distribution controller, and a tire force tracking controller. The upper controller adopted the sliding mode control algorithm focusing on the vehicle motion state control. The lower controller used the optimal control allocation method to realize the tire force distribution control under the constraint condition, and proposed the error approximation objective function and performance objective function. And the tire force distribution was solved by the active set method. The desired tire force tracking controller used the sliding mode control algorithm to realize the tracking of the desired slip ratio and sideslip angle calculated by the inverse tire model, and calculates the actuator output. Finally, the control strategy was verified by simulation based on the MATLAB/Simulink model, and the closedloop slalom test at high speed verified the effectiveness of the control strategy.

Modular Integrated Longitudinal, Lateral, and Vertical Vehicle Stability Control for Distributed Electric Vehicles

There is a nonlinear coupling relationship between the vehicle in the longitudinal, lateral, and vertical directions, which brings great difficulties to the design of the controller. To tackle the chattering problem, a hierarchical integrated controller for distributed electric vehicle is proposed to improve driving safety, handling stability, ride comfort, and road tracking capabilities. The proposed algorithm has been developed to overcome a major challenge of the conventional method, which can improve only partial dynamic performance of the vehicle. The optimal pre-pointing lateral acceleration model is used to simulate the operator's expected reaction to the vehicle. The body control layer decouples complex problems to achieve multi-target independent tracking through a nonlinear sliding-mode control algorithm, and calculates the expected total body force to meet the upper level instructions. The tire force distribution layer is designed to optimize the function by reducing the tire load ratio and balancing the vertical dynamic load coefficient to improve the vehicle's driving stability and ride comfort. The lower actuator control layer controls the corresponding actuator to achieve the optimal tire force output from the middle layer. Finally, the effectiveness of the chassis integrated control system is verified in CarSim and MATLAB co-simulation.

A Trajectory Tracking Control Strategy of 4WIS/4WID Electric Vehicle with Adaptation of Driving Conditions

The Four Wheel Independent Steering/Driving (4WIS/4WID) electric vehicle has the advantage that the rotation angle and driving torque of each wheel can be independently and accurately controlled. In this paper, a trajectory tracking strategy based on the hierarchical control method is designed. In the path tracking layer, the nonlinear state feedback controller is used, and the neural network Proportion Integration Differentiation (NNPID) controller is designed to track the desired path and to obtain the desired yaw rate. By tracking the desired yaw rate and vehicle speed, the terminal sliding mode controller in vehicle dynamics control layer calculates the desired resultant tire force. In the tire force distribution layer, the multiple optimization objectives, including vehicle stability performance objective, energy-saving performance objective, and tire wear energy consumption objectives are determined and the weight coefficient is adaptive to different working conditions based on fuzzy logic theory. Finally, the wheel steering angle and driving torque of each wheel are calculated by the nonlinear three-degree-of-freedom vehicle model. Simulation results show that it realizes the adaptive control of tire force while tracking the desired trajectory, improves the stability and energy saving of the vehicle, and effectively reduces tire wear.

Tire Force Distribution Method With the Constraints of Executable Drive Space Consideration

Tire force distribution with the consideration of practical constraints is a key part of automatic driving. This paper is intended to improve the operational capability of the vehicle under low friction coefficient. The speed and front wheel angle are restricted within a specific range caused by the limitation of executable drive space, which is defined as an input constrained problem of the nonlinear system. The hierarchical design concept is adopted in this paper, including algorithms of both control and allocation to determine the driving performance cooperatively. The methodology of multi-input and multi-output sliding mode control (MIMO SMC) is applied in the high-level controller to guarantee the vehicle system stable. Confronted with circumstances that the vehicle may be seriously unstable due to longitudinal forces and lateral forces beyond the feasible region in the friction circle, the scheme of dynamic adjustment of control target is provided owing to there is no reasonable solution for tire force distribution in the low-level controller. The coefficients of reconstruction and attenuation are introduced to reconstruct the optimized controller and weaken inputs of the closed loop system, respectively. The simulation results verify that the proposed design can redistribute generalized forces and moments between the wheels especially for the poor road condition.

Coordinated fault tolerant control of over-actuated electric vehicles based on optimal tyre force distribution

Actuator faults of the driving/steering/suspension subsystems may lead to instability in over-actuated electric vehicles. Though many fault tolerant control methods that rely on partial subsystems exist, a novel coordinated fault tolerant control (CFTC) method based on optimal longitudinal/lateral/vertical tyre force distribution is proposed. First, the coordination principle of all the actuator subsystems is explained using vehicle dynamics control equations. Then, an optimal longitudinal/lateral/vertical tyre force distribution method is established. Results of simulations and hardware-in-the-loop (HIL) experiments show that the CFTC method successfully coordinates all the subsystems to compensate actuator faults and effectively improve vehicle stability and safety.

Multi-Objective Coordination Control Strategy of Distributed Drive Electric Vehicle by Orientated Tire Force Distribution Method

In order to improve the extension mileage and ensure the yaw stability of the distributed drive electric vehicle simultaneously, a multi-objective coordination control strategy is presented in this paper, in which the optimal vehicle-state estimation method and the orientated tire force distribution method are designed. The longitudinal force estimation is designed using the unknown input observer Kalman filter, a novel yaw rate and a vehicle sideslip angle estimation scheme is proposed by an observer error compensation method. A multi-objective hierarchical vehicle motion control strategy is developed to monitor the yaw stability and improve the energy efficiency of vehicle in real time. In the upper layer controller design, a sliding mode controller is proposed to track the desired yaw rate. In the lower layer controller design, the orientated tire force distribution scheme is presented to improve the motor efficiency and reduce the energy loss caused by vehicle steering resistance while ensuring the yaw stability of vehicle. Finally, the effectiveness of the proposed estimation method and the global coordination control strategy is validated by simulation in CarSim-Simulink joint platform and road test.