Mathematical Models of Tire-Lateral Road Adhesion for Use in Road Vehicle Dynamics Studies

Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad adhesion revolutionize the Pacejka's model in concept and therefore make it possible for applications in vehicle dynamics studies by the expression of lateral adhesion coefficient as a function of wheel slip ratio,instead of the wheel slip angle,taking into account in the mean time the influences of mad surface condition, vehicle velocity,vertical load,tire slip angle,and wheel camber angle.

Mathematical Models of Tire-Longitudinal Road Adhesion and Their Use in the Study of Road Vehicle Dynamics

Mathematical models of tire-longitudinal road adhesion for use in the study of road vehicle dynamics are set up so as to express the relations of longitudinal adhesion coefficients with the slip ratio. They perfect the Pacejka's models in practical use by taking into account the influences of all essential parameters such as road surface condition. vehicle velocity. slip angle. vertical load and slip ratio on the longitudinal adhesion coefficients. The new models are more comprehensive more concise. simpler and more convenient in application in all kinds of simulations of car dynamics in various sorts of braking modes.

Real-time Tire Parameters Observer for Vehicle Dynamics Stability Control

The performance of the vehicle dynamics stability control system（DSC） is dominated by the accurate estimation of tire forces in real-time.The characteristics of tire forces are determined by tire dynamic states and parameters,which vary in an obviously large scope along with different working conditions.Currently,there have been many methods based on the nonlinear observer to estimate the tire force and dynamic parameters,but they were only used in off-line analysis because of the computation complexity and the dynamics differences of four tires in the steering maneuver conditions were not considered properly.This paper develops a novel algorithm to observe tire parameters in real-time controller for DSC.The algorithm is based on the sensor-fusion technology with the signals of DSC sensors,and the tire parameters are estimated during a set of maneuver courses.The calibrated tire parameters in the control cycle are treated as the elementary states for vehicle dynamics observation,in which the errors between the calculated and the measured vehicle dynamics are used as the correcting factors for the tire parameter observing process.The test process with a given acceleration following a straight line is used to validate the estimation method of the longitudinal stiffness;while the test process with a given steering angle is used to validate the estimated value of the cornering stiffness.The ground test result shows that the proposed algorithm can estimate the tire stiffness accurately with an acceptable computation cost for real-time controller only using DSC sensor signal.The proposed algorithm can be an efficient algorithm for estimating the tire dynamic parameters in vehicle dynamics stability control system,and can be used to improve the robustness of the DSC controller.

Vehicle Dynamics Modeling and Simulation for ACC

A 7 degree-of-freedom （DOF） 4 wheels vehicle dynamics model based on Matlab-Simulink is established,and 7 DOF vehicle dynamics equations in the form of nonlinear state-space standards are given.The characters of the electronic throttle and the active braking system have been analyzed.And the electronic throttle model and the active braking system model are built according to the test results respectively.Off-line simulation results indicate that the model is suitable for the vehicle adaptive cruise control system,and both of the electronic throttle and the active braking system work in a reasonable way.An adaptive cruise control （ACC） example illustrates that the model has a good performance in cruise and distance keeping.

Model-Based Approach to Investigate the Influences of Different Load States to the Vehicle Dynamics of Light Electric Vehicles

The need to find alternative urban mobility solutions for delivery and transport has led mobility companies to devote enormous resources for research-based solutions to increase vehicle safety. This paper documents a virtual approach to investigate the influences of different load states to the vehicle dynamic of light electric vehicle. A model basing on a three-dimensional multibody system was used, which consists of five bodies. By applying methods of multibody modelling the generalized equations of motion were generated. To include the behavior within the contact point between road and vehicle a simplified tire models was added. The implementation of the equations allowed a first validation of the model via simulations. In a final modeling step the simulation results were interpreted in respect of plausibility. Afterwards, the model was simulated numerically to investigate different load states of the vehicle, by applying constant steering stimuli and variable velocities. In sum, the investigated model approach is useful to identify safety relevant parameters and shows the effects of load states to the vehicle dynamics. Furthermore, it behaves plausibly regarding general vehicle dynamics. These results prove the general usability of the model for the development controllers and estimators in driver assistances systems.

Integrated Control of Lateral and Vertical Vehicle Dynamics Based on Multi-agent System

The existing research of the integrated chassis control mainly focuses on the different evaluation indexes and control strategy. Among the different evaluation indexes, the comprehensive properties are usually not considered based on the non-linear superposition principle. But, the control strategy has some shortages on tyre model with side-slip angle, road adhesion coefficient, vertical load and velocity. In this paper, based on belief, desire and intention（BDI）-agent model framework, the TYRE agent, electric power steering（EPS） agent and active suspension system（ASS） agent are proposed. In the system（SYS） agent, the coordination mechanism is employed to manage interdependences and conflicts among other agents, so as to improve the flexibility, adaptability, and robustness of the global control system. Due to the existence of the simulation demand of dynamic performance, the vehicle multi-body dynamics model is established by SIMPACK. And then the co-simulation analysis is conducted to evaluate the proposed multi-agent system（MAS） controller. The simulation results demonstrate that the MAS has good effect on the performance of EPS and ASS. Meantime, the better road feeling for the driver is provided considering the multiple and complex driving traffic. Finally, the MAS rapid control prototyping is built to conduct the real vehicle test. The test results are consistent to the simulation results, which verifies the correctness of simulation. The proposed research ensures the driving safety, enhances the handling stability, and improves the ride comfort.

Multi-Body Dynamics Modeling of Heavy Goods Vehicle-Rail Interaction

Based on the principle of vehicle-track coupling dynamics, SIMPACK multi-body dynamics software is used to establish a C80 wagon line-coupled multi-body dynamics model with 73 degrees of freedom. And the reasonableness of the line-coupled dynamics model is verified by using the maximum residual acceleration, the nonlinear critical speed of the wagon. The experimental results show that the established vehicle line coupling dynamics model meets the requirements of vehicle line coupling dynamics modeling.

Implementation of MPC-Based Path Tracking for Autonomous Vehicles Considering Three Vehicle Dynamics Models with Different Fidelities

Model predictive control(MPC)algorithm is established based on a mathematical model of a plant to forecast the system behavior and optimize the current control move,thus producing the best future performance.Hence,models are core to every form of MPC.An MPC-based controller for path tracking is implemented using a lower-fidelity vehicle model to control a higher-fidelity vehicle model.The vehicle models include a bicycle model,an 8-DOF model,and a 14-DOF model,and the reference paths include a straight line and a circle.In the MPC-based controller,the model is linearized and discretized for state prediction;the tracking is conducted to obtain the heading angle and the lateral position of the vehicle center of mass in inertial coordinates.The output responses are discussed and compared between the developed vehicle dynamics models and the CarSim model with three different steering input signals.The simulation results exhibit good path-tracking performance of the proposed MPC-based controller for different complexity vehicle models,and the controller with high-fidelity model performs better than that with low-fidelity model during trajectory tracking.

Dynamics Modeling and Simulation of Autonomous Underwater Vehicles with Appendages

To provide a simulation system platform for designing and debugging a small autonomous underwater vehicle＇s （AUV） motion controller, a six-degree of freedom （6-DOF） dynamic model for AUV controlled by thruster and fins with appendages is examined. Based on the dynamic model, a simulation system for the AUV＇s motion is established. The different kinds of typical motions are simulated to analyze the motion performance and the maneuverability of the AUV. In order to evaluate the influences of appendages on the motion performance of the AUV, simulations of the AUV with and without appendages are performed and compared. The results demonstrate the AUV has good maneuverability with and without appendages.

Review on dynamic analysis of road pavements under moving vehicles and plane strain conditions

This paper reviews works on the dynamic analysis of flexible and rigid pavements under moving vehicles on the basis of continuum-based plane strain models and linear theories.The purpose of this review is to provide in-formation about the existing works on the subject,critically discuss them and make suggestions for further research.The reviewed papers are presented on the basis of the various models for pavement-vehicle systems and the various methods for dynamically analyzing these systems.Flexible pavements are modeled by a homogeneous or layered half-plane with isotropic or anisotropic and linear elastic,viscoelastic or poroelastic material behavior.Rigid pavements are modeled by a beam or plate on a homogeneous or layered half-plane with material properties like the ones for flexible pavements.The vehicles are modeled as concentrated or distributed over a finite area loads moving with constant or time dependent speed.The above pavement-vehicle models are dynamically analyzed by analytical,analytical/numerical or purely numerical methods working in the time or frequency domain.Representative examples are presented to illustrate the models and methods of analysis,demonstrate their merits and assess the effects of the various parameters on pavement response.The paper closes with con-clusions and suggestions for further research in the area.The significance of this research effort has to do with the presentation of the existing literature on the subject in a critical and easy to understand way with the aid of representative examples and the identification of new research areas.

Hydrodynamics Research on Amphibious Vehicle Systems:Modeling Theory

For completing the hydrodynamics software development and the engineering application research on the amphibious vehicle systems, hydrodynamic modeling theory of the amphibious vehicle systems is elaborated, which includes to build up the dynamic system model of amphibious vehicle motion on water, gun tracking-aiming-firing, bullet hit and armored check-target, gunner operating control, and the simulation computed model of time domain for random sea wave.

Vehicle Dynamic State Estimation： State of the Art Schemes and Perspectives

Next-generation vehicle control and future autonomous driving require further advances in vehicle dynamic state estimation. This article provides a concise review, along with the perspectives, of the recent developments in the estimation of vehicle dynamic states. The definitions used in vehicle dynamic state estimation are first introduced, and alternative estimation structures are presented. Then, the sensor configuration schemes used to estimate vehicle velocity, sideslip angle, yaw rate and roll angle are presented. The vehicle models used for vehicle dynamic state estimation are further summarized, and representative estimation approaches are discussed. Future concerns and perspectives for vehicle dynamic state estimation are also discussed.

Collision mitigation and vehicle transportation safety using integrated vehicle dynamics control systems

The aim of this paper is to investigate the effect of vehicle dynamics control systems （VDCS） on both the collision of the vehicle body and the kinematic behaviour of the ve- hicle＇s occupant in case of offset frontal vehicle-to-vehicle collision. A unique 6-degree-of- freedom （6-DOF） vehicle dynamics/crash mathematical model and a simplified lumped mass occupant model are developed. The first model is used to define the vehicle body crash parameters and it integrates a vehicle dynamics model with a vehicle front-end structure model. The second model aims to predict the effect of VDCS on the kinematics of the occupant. It is shown from the numerical simulations that the vehicle dynamics/crash response and occupant behaviour can be captured and analysed quickly and accurately. Yurthermore, it is shown that the VDCS can affect the crash characteristics positively and the occupant behaviour is improved.

Coupled dynamic model of state estimation for hypersonic glide vehicle

Aiming at handling complicated maneuvers or other unpredicted emergencies for hypersonic glide vehicle tracking,three coupled dynamic models of state estimation based on the priori information between guidance variables and aerodynamics are presented. Firstly, the aerodynamic acceleration acting on the target is analyzed to reveal the essence of the target’s motion.Then three coupled structures for modeling aerodynamic parameters are developed by different ideas: the spiral model with a harmonic oscillator, the bank model with trigonometric functions of the bank angle and the guide model with the changing rule of guidance variables. Meanwhile, the comparison discussion is concluded to show the novelty and advantage of these models.Finally, a performance assessment in different simulation cases is presented and detailed analysis is revealed. The results show that the proposed models perform excellent properties. Moreover, the guide model produces the best tracking performance and the bank model shows the second; however, the spiral model does not outperform the maneuvering reentry vehicle(MaRV) model markedly.

Development and Validation of a Scaled Electric Combat Vehicle Tire Model

Pneumatic tire modeling and validation have been the topic of several research papers, however, most of these papers only deal with pneumatic passenger and truck tires. In recent years, wheeled-scaled vehicles have gained lots of attention as a feasible testing platform, nonetheless up to the authors’ knowledge there has been no research regarding the use of scaled tires and their effect on the overall vehicle performance characteristics. This paper presents a novel scaled electric combat vehicle tire model and validation technique. The pro-line lockdown tire size 3.00 × 7.35 is modeled using the Finite Element Analysis (FEA) technique and several materials including layered membrane, beam elements, and Mooney-Rivlin for rubber. The tire-rim assembly is then described, and the rigid body analysis is presented. The tire is then validated using an in-house custom-made static tire testing machine. The tire test rig is made specifically to test the pro-line tire model and is designed and manufactured in the laboratory. The tire is validated using vertical stiffness and footprint tests in the static domain at different operating conditions including several vertical loads. Then the tire is used to perform rolling resistance and steering analysis including the rolling resistance coefficient and the cornering stiffness. The analysis is performed at different operating conditions including longitudinal speeds of 5, 10, and 15 km/h. This tire model will be further used to determine the tractive and braking performance of the tire. Furthermore, the tire test rig will also be modified to perform cornering stiffness tests.

Dynamic Modeling and Analysis of 9-DOF Omnidirectional Legged Vehicle

The omnidirectional legged vehicle with steering-rails has a specific mechanism feature, and it can be controlled flexibly and accurately in omnidirectional motion. Currently there lacks further research in this area. In this paper, the mechanical characteristics of independent walking control and steering control and its kinematics principle are introduced, and a vehicle has a composite motion mode of parallel link mechanism and steering mechanism is presented. The motion direction control of the proposed vehicle is only dependant on its steering rails, so its motion is simple and effective to control. When the relative motion between the walking and steering is controlled cooperatively, the vehicle can walk perfectly. By controlling the steering rails, the vehicle can walk along arbitrary trajectory on the ground. To achieve a good result of motion control, an equivalent manipulator model needs to be built. In terms of the mechanism feature and the kinematic principle, the simplified manipulator model consists of a rail in stance phase, a rail in swing phase, and an equivalent leg. Considering the ground surface slope during walking, a parameter of inclination angle is added. Based on such a RPP manipulator model, the equations of motion are derived by means of Lagrangian dynamic approach. To verify the dynamic equations, the motion of the manipulator model is simulated based on linear and nonlinear motion planning. With the same model and motion parameters, the dynamic equations can be solved by Matlab and the calculation data can be gained. Compared with the simulation data, the result confirms the manipulator dynamic equations are correct. As a result of such special characteristics of the legged mechanism with steering rails, it has a potential broad application prospects. The derivation of dynamics equation could benefit the motion control of the mechanism.

Dynamic Modeling and Investigation of Maneuver Characteristics of A Deep-Sea Manned Submarine Vehicle

A deep-sea Manned Submarine Vehicle （MSV） is usually required to move at a low forward speed and a low rotational speed when it executes investigation tasks. In this condition, the motion is in large drift angles, and the maneuverability hydrodynamic forces cannot be expressed properly in the conventional mathematical model of submersible motion. In this paper, firstly, a general equation of MSV with six-freedom motion is presented, and the numerical simulation of descent/ascent motion and helix motion is conducted to reveal the general maneuver characteristics of MSV. Secondly, according to the data of captive model tests of large drift angles of MSV, the regression analysis of position hydrodynamic forces and rotation hydrodynamic forces is carried out, and the results of regression analysis of maneuverability hydrody- namic characteristics are analyzed to reveal the special maneuver characteristics. Thirdly, a special new mathematical model of MSV with the whole range of drift angles motion is presented, which can be used to predict hydrodynamic performance of motion in the 0° - 180° range of drift angles. The results are applied to the design of maneuverability hydrodynamic forces, development of control system and simulator of a practical MSV.

A New Application of Multi-Body System Dynamics in Vehicle-Road Interaction Simulation

In vehicle-road interaction simulation, multibody system (MBS) dynamics as well as the corresponding software ADAMS has been employed to model the nonlinear vehicle in more detail. The simulation method has been validated by the test data, and been compared to the former simple models. This method can be used for estimating the effects of dynamic tire forces and other vehicle features on road damage so that the “road-friendliness” can be assessed in vehicle design process.

Identification of dynamic model parameters for lithium-ion batteries used in hybrid electric vehicles

An electrical equivalent circuit model for lithium-ion batteries used for hybrid electric vehicles （HEV） is presented. The model has two RC networks characterizing battery activation and concentration polarization process. The parameters of the model are identified using combined experimental and extended Kalman filter （EKF） recursive methods. The open-circuit voltage and ohmic resistance of the battery are directly measured and calculated from experimental measurements, respectively. The rest of the coupled dynamic parameters, i.e. the RC network parameters, are estimated using the EKF method. Experimental and simulation results are presented to demonstrate the efficacy of the proposed circuit model and parameter identification techniques for simulating battery dynamics.

Study on modeling of vehicle dynamic stability and control technique

In order to solve the problem of enhancing the vehicle driving stability and safety,which has been the hot question researched by scientific and engineering in the vehicle industry,the new control method was investigated.After the analysis of tire moving characteristics and the vehicle stress analysis,the tire model based on the extension pacejka magic formula which combined longitudinal motion and lateral motion was developed and a nonlinear vehicle dynamical stability model with seven freedoms was made.A new model reference adaptive control project which made the slip angle and yaw rate of vehicle body as the output and feedback variable in adjusting the torque of vehicle body to control the vehicle stability was designed.A simulation model was also built in Matlab/Simulink to evaluate this control project.It was made up of many mathematical subsystem models mainly including the tire model module,the yaw moment calculation module,the center of mass parameter calculation module,tire parameter calculation module of multiple and so forth.The severe lane change simulation result shows that this vehicle model and the model reference adaptive control method have an excellent performance.