Vehicle Dynamics Model

This paper proposes a novel unified structure to estimate tire forces. The proposed structure uses estimation modules to calculate/estimate tire forces by means of nonlinear observers. The novelty in the proposed approach lies in the independence of the estimates from the vehicle tire model, thereby making the structure robust against variations in vehicle mass, tire parameters due to tire wear, and, most importantly, road surface conditions. In the proposed structure, we have a dedicated module to estimate the longitudinal tire forces and another to calculate the vertical tire forces. Subsequently, these forces are fed into a third module that utilizes a nonlinear observer to estimate lateral tire forces. The proposed structure is validated through experimental studies. Index Terms-Extended Kalman filter (EKF), identification, observer, tire force estimation, unscented Kalman filter (UKF). V EHICLE control systems such as electronic stability pro- grams and antilock braking systems (ABSs) have been used to improve vehicle stability and handling performance. However, the effectiveness of such control systems can be further improved with the ability to measure/estimate tire vertical, lateral, and longitudinal forces in real time. Currently, direct measurement of these forces is prohibited in vehicles due to high costs. Therefore, estimation of tire forces is considered as the sole alternative. There are various studies on estimation of vehicle tire forces in the literature using analytical tire models such as linear [1], Dugoff's model , or semiempirical models including Pacejka's tire model . It is noted that tire models include different parameters that should be tuned using experimental data. These parameters however change with the aging of the tire. There are other studies for estimating the tire forces independent of tire models. In these studies, vertical tire forces Manuscript

A modern railway train is a complex mechanical system, the movement of which is determined by mechanical, dynamic, electrical, and thermodynamic processes. It is necessary to consider analytical models of varying degrees of complexity of their oscillations and interaction with the railway track to solve numerous problems regarding the dynamics of rail vehicles. Often there is a need to take into account the longitudinal forces transmitted to the railcar from neighboring railcars, as well as their components in the vertical and horizontal transverse directions. These forces can be obtained from the solution of the train dynamics problem and then used to study the dynamics of a single railcar. However, in a number of papers, analytical models appear in which the problems of train dynamics and spatial oscillations of a railcar are combined together. When combining the problems solved in the dynamics of the train and the spatial oscillations of a single railcar, the studied rail vehicle is considered according to the full design scheme and neighboring ones according to the simplified one. The spatial oscillations of a train of freight railcars moving along a section of the track with vertical and horizontal irregularities are described in the presented analytical model.

The article is devoted to the study of the influence of flexural deformation of the body of a freight wagon on the indicators of the interaction of rail fleet with rails. The considered indicators depend both on the design of the rail fleet, its condition and speed, and on the design and condition of the railroad track. A theoretical study was carried out using a model of spatial vibrations of a freight wagon as part of a homogeneous train. When carrying out calculations, the wagon body was considered as an absolutely rigid body and as a discrete multi-mass system with elastic connections between the masses. When choosing a design scheme, it was assumed that the wagon body is a deformable body and, when bending, has finite rigidity in the vertical and horizontal planes. As a result of the research, the dependences of the dynamic indicators of a freight wagon on the flexural deformation of the body and the speed of movement were obtained. Based on theoretical calculations, the influence of the deformability of the body on the interaction of rail fleet with the railroad track on a tangent level track and curved section with irregularities was assessed.

The task of mastering and improving practical skills is one of the most difficult tasks in the process of education and training of specialists in any brunch of industry. Thanks to the rapid development of computer and information technologies, this problem could be solved through the use of multimedia simulators realised using software simulators or by application of hybrid simulators using the equipment of a real train. The paper describes the possibilities of training drivers and students to effective driving modes of train using the developments of universities. Streszczenie. Zadanie opanowania i doskonalenia umiejętności praktycznych jest jednym z najtrudniejszych zadań w procesie edukacji i szkolenia specjalistów w dowolnej branży. Dzięki szybkiemu rozwojowi technologii komputerowych i informatycznych, problem ten można rozwiązać poprzez zastosowanie symulatorów multimedialnych realizowanych za pomocą symulatorów programowych lub przez zastosowanie symulatorów hybrydowych z wykorzystaniem wyposażenia prawdziwego pociągu. W pracy opisano możliwości szkolenia maszynistów i studentów w zakresie efektywnych trybów jazdy pociągów z wykorzystaniem opracowań uniwersytetów. (Komputerowe i sprzętowe trenażery do szkolenia maszynistów pociągów: przegląd możliwości i efektów wdrożenia)

The influence of flexural deformation of the freight car body on the stability indicator is studied. A theoretical study was carried out using a model of spatial vibrations of a freight car as part of a homogeneous train. When carrying out calculations, the car body was considered as an absolutely rigid body and as a discrete multi-mass system with elastic connections between the masses. When choosing a design scheme, it was assumed that the car body is a deformable body and, when bending, has finite rigidity in the vertical and horizontal planes. As a result of the research, the dependence of the wheel stability indicator from derailment on the flexural deformation of the body and the speed of movement was obtained. The presented study makes it possible to estimate the permissible speed of movement of the car based on the elastic characteristics of the body in the vertical and horizontal plane, the displacement of the center of mass of the cargo in the car, and also to take into account the longitudinal quasi-static forces arising under operating conditions.

Lane departure collisions have contributed to the traffic accidents that cause millions of injuries and tens of thousands of casualties per year worldwide. Due to vision-based lane departure warning limitation from environmental conditions that affecting system performance, a model-based vehicle dynamics framework is proposed for estimating the lane departure event by using vehicle dynamics responses. The model-based vehicle dynamics framework mainly consists of a mathematical representation of 9-degree of freedom system, which permitted to pitch, roll, and yaw as well as to move in lateral and longitudinal directions with each tire allowed to rotate on its axle axis. The proposed model-based vehicle dynamics framework is created with a ride model, Calspan tire model, handling model, slip angle, and longitudinal slip subsystems. The vehicle speed and steering wheel angle datasets are used as the input in vehicle dynamics simulation for predicting lane departure event. Among the simu...

In this paper, we address the enhanced state estimation and prediction system for automobile applications by fusing relatively low-cost and noisy Inertial Navigation System (INS) sensing with Global Positioning System (GPS) measurements. An unscented Kalman filter is used to merge multi-rate measurements from GPS and INS sensors together with a high-fidelity vehicle-dynamics model for state-predictions. The high-fidelity motion model (including suspension-effects) for the vehicle motion trajectory on uneven terrain is captured by a 20-state system of nonlinear differential equations. Computer simulation results illustrate the effectiveness of sensor-fusion (building upon the merger of an inexpensive INS sensing with GPS based measurements) to accurately estimate the full system-state. The relative ease of implementation, accuracy and predictive performance with low-cost sensing will facilitate its use in various electronic control and safety-systems, such as Electronic Stability Pro...

This paper presents a state-of-the-art estimation technique by cross-combining a number n of filters for high-precision, reliable and robust vehicle sideslip angle state estimation, over a full range of vehicle operations irrespective of the driving mission and disruptions that may occur in the system. A machine-learning algorithm based on decision trees connects several filters together to switch between them according to the driving context, ensuring the best possible state estimate for relatively small and large sideslip angle values. In conjunction with the above-mentioned aspects, a seamless transition between different vehicle models is attained by observing the key parameters characterizing the lateral motion of the vehicle. The tests conducted using a prototype vehicle on a snow-covered track confirm the effectiveness and reliability of the proposed approach.

A theoretical background to pneumatic suspension in semi-trailers is put forward which can be used for the calculation of the total weight of a vehicle and its axle. This information is essential for both static and dynamic analyses, and is an important factor in safety. The response of an air spring with a height control valve is characterised and the problem of different axle loads in a pneumatic suspension without a mechanical equaliser is studied in a triaxial tandem. An expression for the dynamic spring rate (stiffness coefficient) versus pressure and length is obtained for a commercial air spring.

Vehicle stability control systems called ESP, vehicle dynamics control (VDC), yaw stability control (YSC), and so forth are important active safety systems used for maintaining lateral stability of the vehicles under such adverse conditions. This paper investigates the notion of virtual sensing which is a promising concept for yaw stability control and is an attractive option for vehicle manufactures as it reduces sensor cost, maintenance, and machine downtime. A frequent situation in automotive control applications is when an unknown input needs to be estimated from available state measurements. The virtual sensor proposed use measurements of lateral acceleration, steering angle as unknown input signals and provide the yaw rate angle estimate as output. Stability conditions of this virtual sensor are given in terms of Linear Matrix Inequalities (LMI). To illustrate the proposed methodology, a linear bicycle model is considered. The observer(virtual sensor) is confronted to data iss...

Information about vehicle dynamics states is indispensable for modern dynamics control system on a vehicle today. Instead of using the expensive physical sensor to measure directly the states of a vehicle, this paper proposes a "virtual sensor" which bases on the dynamical model of vehicle and an observation algorithm. An observer based on Luenberger method is developed in Matlab/Simulink. To make the dynamics model consistent with a virtual vehicle in CarSim, the model parameters are identified at a pre-defined velocity using Parameter Identification toolbox of Simulink. The whole system is constructed by connecting Matlab/Simulink to CarSim to simulate a complete real system. The simulation results show the good performance of the observer when the estimated values are well converged to real values given by CarSim. The precision of results depends on what extent the velocity of the vehicle whether it is near the velocity of parameters identification or not.

To develop an effective vehicle control system, it is needed to estimate vehicle mot ions accurately. In the absence of commercially available transducers to measure the tire forces direct ly, various types of estimation methods have been investigated in the past. Most models in the literature usually use lowdegrees of freedom. In this paper, a new estimation process is proposed to estimate tire forces based on extended Kalman filter. These methods use the measurements fro m currently available standard sensors. For such estimat ion, a ten degree-o f-freedom nonlinear vehicle model was developed. The estimated results are compared with the results obtained fromCarsim using the same parameter values to verify the proposed model.

In this paper, we propose the use of a neural network to identify lateral skidding events of road vehicles used during winter driving conditions. Firstly, data from a simulation model was used to identify the essential vehicle dynamics variables needed and to create the network structure. Then this network was retrained to classify real-world vehicle skidding events. The final network consists of a 3 layer network with 10, 5 and 1 output neurons 13 inputs, 4 outputs and a 5 step time delay. The retrained network was used on a limited set of real vehicle data and confirmed the effectiveness of the network classifying lateral skidding events.

This study presents a scheme to detect and isolate faults in over-actuated electric vehicles. Although this research work is still emerging, it already provides a view of the main challenges on the problem and discusses some possible approaches that can be useful to overcome the key difficulties. This paper intends to present a fault detection algorithm based on Unknown Input Observer (UIO). The residuals are built through the difference of signals between the measured outputs and the output estimations from the observer. The main idea is to detect fault in the electric motors and steering wheel actuator. The algorithm is presented and tested with some fault scenarios using the co-simulation tool between Simulink/MATLAB and the high-fidelity model from Carsim software.

This paper investigates the lateral stability and maneuverability in long combination vehicles (LCVs), namely semi-trucks with 28-ft doubles, 28-ft triples, and 33ft doubles, using TruckSim. In recent years, due to the rapid increase of E-commerce cargo transport demands, trucks with multiple trailers have been used with increasing frequency on U.S. highways. The most common configuration is 28-ft doubles, although in some states, 28-ft triples and longer doubles, such as 33-ft trailers, are also allowed. LCVs provide operational advantages in terms of loading and unloading, ease of distribution, and other key logistics that are superior to the conventional 53-ft trailers that are commonly used for bulk cargo over long hauls. The vast proliferation of LCVs on U.S. highways heightens awareness of their dynamics, including lateral stability and maneuverability which are strongly tied to highway safety. This study provides a comparative evaluation of the lateral characteristics for tractors with 28-ft double, 28-ft triple, and 33-ft double trailers. In particular, the likelihood of rollovers, rearward amplification, and off-tracking are analyzed among those LCVs using the multi-domain dynamic models developed in TruckSim. The efforts to validate the truck dynamic model against test results are also included. The simulation results show that trucks with triple trailers exhibit a larger rearward amplification, higher likelihood of rollovers, and larger off-tracking than trucks

Driving safety enhancement could be achieved by better understanding of risk situations from the knowledge of vehicle dynamic states as well as road geometry. Among the parameters of the road that have an impact on vehicle dynamics, one can find the bank and the slope angles, which can not however be measured by mean of low cost onboard sensors. This work of this paper is aimed to improve the controllability of the vehicle and the development of a low cost mapping system of the roadway. Two observers are developed firstly to estimate these two variables and secondly to localize the vehicle. The road attributes are estimated using an extended Kalman filter (EKF) and a Proportional Integral (PI) observer with unknown inputs based vehicle models and the measurements obtained from inertial (INS) and ABS sensors. The vehicle localization is performed at each time sample using an algorithm based on the IMM technique (Interacting Multiple Models), it allows to reconstruct the road shape in 3 dimensions. Testing on measurements obtained with a prototype vehicle show the good behavior of the proposed estimation scheme.

Analysis of the fatigue life of a semitrailer structure necessitates identification of the loads and dynamic solicitations in the structure. These forces can be introduced in computer simulation software (multibody + finite element) for analysing the response of different design solutions to them. These numerical models must be validated and some parameters need to be measured directly in a field test with real vehicles under various driving conditions. In this study, a low-cost monitoring system is developed for application to a real fleet of semitrailers. According to the definition of the numerical model, the guidance of a virtual vehicle is defined by the three-dimensional kinematics of the kingpin. For characterisation of these movements, a monitoring system having a low-cost inertial measurement unit (IMU) and global positioning system (GPS) antennas is developed with different configurations to enable analysis of the best cost-benefit (result accuracy) solution, and an extend...

Driving safety enhancement could be achieved by better understanding of risk situations from the knowledge of vehicle dynamic states as well as road geometry. Among the parameters of the road that have an impact on vehicle dynamics, one can find the bank and the slope angles, which can not however be measured by mean of low cost onboard sensors. This work of this paper is aimed to improve the controllability of the vehicle and the development of a low cost mapping system of the roadway. Two observers are developed firstly to estimate these two variables and secondly to localize the vehicle. The road attributes are estimated using an extended Kalman filter (EKF) and a Proportional Integral (PI) observer with unknown inputs based vehicle models and the measurements obtained from inertial (INS) and ABS sensors. The vehicle localization is performed at each time sample using an algorithm based on the IMM technique (Interacting Multiple Models), it allows to reconstruct the road shape in 3 dimensions. Testing on measurements obtained with a prototype vehicle show the good behavior of the proposed estimation scheme.

Analysis of the fatigue life of a semitrailer structure necessitates identification of the loads and dynamic solicitations in the structure. These forces can be introduced in computer simulation software (multibody + finite element) for analysing the response of different design solutions to them. These numerical models must be validated and some parameters need to be measured directly in a field test with real vehicles under various driving conditions. In this study, a low-cost monitoring system is developed for application to a real fleet of semitrailers. According to the definition of the numerical model, the guidance of a virtual vehicle is defined by the three-dimensional kinematics of the kingpin. For characterisation of these movements, a monitoring system having a low-cost inertial measurement unit (IMU) and global positioning system (GPS) antennas is developed with different configurations to enable analysis of the best cost-benefit (result accuracy) solution, and an extend...

Robust estimation of vehicle states (e.g., vehicle sideslip angle and roll angle) is essential for vehicle stability control applications such as yaw stability control and roll stability control. This paper proposes novel methods for estimating sideslip angle and roll angle using real-time lateral tire force measurements, obtained from the multi-sensing hub (MSHub) units, for practical applications to vehicle control systems of inwheel-motor-driven electric vehicles. In vehicle sideslip estimation, a recursive least squares (RLS) algorithm with a forgetting factor is utilized based on a linear vehicle model and sensor measurements. In roll angle estimation, the Kalman filter is designed by integrating available sensor measurements and roll dynamics. The proposed estimation methods, RLS-based sideslip angle estimator and the Kalman filter are evaluated through field tests on an experimental electric vehicle. The experimental results show that the proposed estimator can accurately estimate the vehicle sideslip angle and roll angle. It is experimentally confirmed that the estimation accuracy is improved by more than 50% comparing to conventional method's one (see RMS error shown in Fig. ). Moreover, the feasibility of practical applications of the lateral tire force sensors to vehicle state estimation is verified through various test results.

Recent developments in vehicle stability control and active safety systems have led to an interest in reliable vehicle state estimation on various road conditions. This paper presents a novel method for tire force and velocity estimation at each corner to monitor tire capacities individually. This is entailed for more demanding advanced vehicle stability systems and especially in full autonomous driving in harsh maneuvers. By integrating the lumped LuGre tire model and the vehicle kinematics, it is shown that the proposed corner-based estimator does not require knowledge of the road friction and is robust to model uncertainties. The stability of the time-varying longitudinal and lateral velocity estimators is explored. The proposed method is experimentally validated in several maneuvers on different road surface frictions. The experimental results confirm the accuracy and robustness of the state estimators.

Information fusion from multiple sensors ensures the accuracy and robustness of a navigation system, especially in the absence of global positioning system (GPS) data which gets degraded in many cases. A way to deal with multi-mode estimation for a small fixed wing unmanned aerial vehicle (UAV) localization framework is proposed, which depends on utilizing a Luenberger observer-based linear matrix inequality (LMI) approach. The proposed estimation technique relies on the interaction between multiple measurement modes and a continuous observer. The state estimation is performed in a switching environment between multiple active sensors to exploit the available information as much as possible, especially in GPS-denied environments. Luenberger observer-based projection is implemented as a continuous observer to optimize the estimation performance. The observer gain might be chosen by solving a Lyapunov equation by means of a LMI algorithm. Convergence is achieved by utilizing the linear matrix inequality (LMI), based on Lyapunov stability which keeps the dynamic estimation error bounded by selecting the observer gain matrix (L). Simulation results are presented for a small UAV fixed wing localization problem. The results obtained using the proposed approach are compared with a single mode Extended Kalman Filter (EKF). Simulation results are presented to demonstrate the viability of the proposed strategy.

Onboard attitude estimation for a ground vehicle is persuaded by its application in active anti-roll bar design. Conventionally, the attitude estimation problem for a ground vehicle is a complex one, and computationally, its solution is very intensive. Lateral load transfer is an important parameter which should be taken in account for all roll stability control systems. This parameter is directly related to vehicle roll angle, which can be measured using devices such as dual antenna global positioning system (GPS) which is a costly technique, and this led to the current work in which we developed a simple and robust attitude estimation technique that is tested on a ground vehicle for roll mitigation. In the first phase Luenberger and Sliding mode observer is implemented using simplest roll dynamics model to measure the roll angle of a vehicle and the validation of results is carried using commercial software, CarSim® (CarSim, Ann Arbor, MI, USA). In the second phase of research, co...

In-wheel drive systems which combine with the permanent magnet synchronous motors (PMSM) and tires are highly electromechanical-coupled. This paper studies the dynamic characteristics of this system to estimate the tire-road friction condition. After a dynamic tire model and a PMSM model is studied, a transfer function from control signal of the motor to the wheel dynamics is obtained. As a result of analyses about longitudinal dynamics in the frequency domains, motor-wheel resonance frequency is observed, which is related to the tire-road friction. Based on this feature, the friction estimation method combining a system identification technique to find dominant resonance frequency and recursive least square filtering, is applied for simulation. The simulation result shows that the proposed approach can detect road friction in the case that the tire is freely rolling, which is not sensitive to the noise and error of wheel speed signal.

In this work, two high order sliding mode observers under cascade form are proposed in order to estimate the important states and inputs affecting the lateral dynamics of twowheeled vehicles. The first observer is based on a vision system and is used to estimate the lateral velocity of the vehicle. This velocity is considered as an additional measure for the second observer which is designed to estimate the tire forces, the roll angle and torque applied to the handle-bar. The main contribution of this work is the estimation of the tire forces even with the variation of the longitudinal velocity and without the prior knowledge of the pneumatic coefficients.

In recent years, autonomous vehicles development reached certain milestones and now it is the time to optimize the performance of those vehicles and to add more features to improve the comfort level and safety measures. Artificial Intelligence (AI) in this space playing vital role to estimate the vehicle output parameters by observing the required inputs. Machine learning algorithms and deep learning algorithms are widely applied in fully automated applications such autonomous vehicles, elevators, bullet trains, etc., In this paper, authors propose a fully connected neural network (FNN) based deep learning algorithm for autonomous vehicle in order to identify the driving conditions dynamically and issue control commands for braking and steering control. Authors have also identifying algorithm for surface recognition to determine the friction and slip. In the proposed research work, slip based tire – road friction estimation algorithm is integrated to proposed FNN algorithm for achieving the dynamic control has been executed and the results are presented analysed in this paper. Based on the results captured, it is evident that proposed algorithm is the simplest, straight forward and the efficient one when compare to other deep learning and machine learning algorithms.

The article presents the results of works aimed at developing a train travel simulator on a selected route with a multi-criteria optimization module, the set of objective functions of which allows for the minimization of time, energy consumption, total costs or reduction of the negative impact on the natural environment. The optimization module also allows the determination of travel parameters to achieve the optimum of the function created from the combination of these goals, taking into account the weights proving their importance for the railway undertaking. The simulation tool presented in the article, together with the optimization module, gives completely new possibilities to the railway carrier, as it allows it to increase the economic efficiency of the travel while taking care of the human factor and safety as well as the natural environment. The basis of the system presented in the article is a simulator of a railway vehicle running along a defined route, for which it was required to define a mathematical model that would allow for consideration a number of input data allowing for the full formulation of the equation of train motion together with resistance to motion, traction characteristics, braking curves, and mapping of the railway infrastructure, but also taking into account rail traffic control, legal restrictions and the human factor. The article describes the mathematical model of a vehicle travel together with the basic assumptions of its implementation in the numerical version.

W artykule przedstawiono wyniki prac ukierunkowanych na opracowanie symulatora przejazdu pociągu na wybranej trasie wraz z modułem optymalizacji wielokryterialnej, której zbiór funkcji celu pozwala na minimalizację czasu, zużycia energii, kosztów całkowitych czy też redukcję niekorzystnego wpływu na środowisko naturalne. Moduł optymalizacji pozwala również na wyznaczanie parametrów przejazdu dla osiągnięcia optimum funkcji utworzonej z kombinacji tych celów z uwzględnieniem wag świadczących o ich istotności dla przewoźnika kolejowego. Przedstawione w artykule narzędzie symulacyjne wraz z modułem optymalizacyjnym daje zupełnie nowe możliwości przewoźnikowi kolejowego, gdyż pozwala mu na zwiększenie efektywności

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.

In this work, two high order sliding mode observers under cascade form are proposed in order to estimate the important states and inputs affecting the lateral dynamics of twowheeled vehicles. The first observer is based on a vision system and is used to estimate the lateral velocity of the vehicle. This velocity is considered as an additional measure for the second observer which is designed to estimate the tire forces, the roll angle and torque applied to the handle-bar. The main contribution of this work is the estimation of the tire forces even with the variation of the longitudinal velocity and without the prior knowledge of the pneumatic coefficients.

A model-based estimator design and implementation is described in this paper to undertake combined estimation of vehicle states and tire-road friction coefficients. The estimator is designed based on a vehicle model with three degrees of freedom (3-DOF) and the dual extended Kalman filter (DEKF) technique is employed. Effectiveness of the estimation is examined and validated by comparing the outputs of the estimator with the responses of the vehicle model in CarSim in three typical road adhesion conditions (high-friction, low-friction, and joint-friction roads). Simulation results demonstrate that the DEKF estimator algorithm designed is able to obtain vehicle states (e.g., yaw rate and roll angle) as well as road friction coefficients with reasonable accuracy.