Complex Vehicle Model Research Articles

Non-Invasive Identification of Vehicle Suspension Parameters: A Methodology Based on Synthetic Data Analysis

In this study, we introduce an innovative approach for the identification of vehicle suspension parameters, employing a methodology that utilizes synthetic and experimental data for non-invasive analysis. Central to our approach is the application of a basic local optimization algorithm, chosen to establish a baseline for parameter identification in increasingly complex vehicle models, ranging from quarter-vehicle to half-vehicle (bicycle) models. This methodology enables the accurate simulation of the vehicle dynamics and the identification of suspension parameters under various conditions, including road perturbations such as speed bumps and curbs, as well as in the presence of noise. A significant aspect of our work is the ability to process real-world data, making it applicable in practical scenarios where data are obtained from onboard sensor equipment. The methodology was developed in MatLab, ensuring portability across platforms that support this software. Furthermore, the study explores the application of this methodology as a tool for denoising, enhancing its utility in real-world data analysis and predictive maintenance. The findings of this research provide valuable insights for vehicle suspension design, offering a cost-effective and efficient solution for dynamic parameter identification without the need for physical disassembly.

A consensus-based alternating direction method of multipliers approach to parallelize large-scale minimum-lap-time problems

Minimum-lap-time planning (MLTP) problems, which entail finding optimal trajectories for race cars on racetracks, have received significant attention in the recent literature. They are commonly addressed as optimal control problems (OCPs) and are numerically discretized using direct collocation methods. Subsequently, they are solved as nonlinear programs (NLPs). The conventional approach to solving MLTP problems is serial, whereby the resulting NLP is solved all at once. However, for problems characterized by a large number of variables, distributed optimization algorithms, such as the alternating direction method of multipliers (ADMM), may represent a viable option, especially when multicore CPU architectures are available.This study presents a consensus-based ADMM approach tailored to solving MLTP problems through a distributed optimization algorithm. The algorithm partitions the problem into smaller subproblems based on different sectors of a track, distributing them among multiple processors. ADMM is then used to ensure consensus among the distributed computational processes. In particular, here the term “consensus” denotes the requirement for each subproblem to achieve mutual agreement across the junction areas. The paper also outlines specific strategies leveraging domain knowledge to improve the convergence of the distributed algorithm. The ADMM approach is validated against the serial approach, and numerical results are presented for both single-lap and multilap scenarios. In both cases, the ADMM approach proves superior for problem dimensions of 70k+ variables compared to serial methods. In planning scenarios with complex vehicle models on long track horizons, i.e., for problems with 1M+ variables, the efficiency gain of the ADMM approach is substantial, and it becomes the only viable option to maintain computational times within acceptable limits.

Global stability of road vehicle motion with driver control

The paper contributes to unveil how drivers—either human or not—may lose control of road vehicles after a disturbance. First, a simple vehicle-and-driver model is considered: Its motion is characterized by the existence of limit cycles whose amplitude depend on vehicle forward velocity (both oversteering and understeering vehicles may exibit this property). Such limit cycles are originated by a Hopf bifurcation occurring at a relatively high vehicle forward velocity. A mathematical proof of the existence of Hopf bifurcations is given. The existence of Hopf bifurcations and saddle limit cycles is confirmed by experimental tests performed by a dynamic driving simulator with a complex vehicle model and human in the loop. By a Zubov method, a Lyapunov function is derived to compute the region of asymptotic stability for the simple vehicle-and-driver model. A necessary and sufficient condition is derived for global asymptotic stability. Such a condition refers to the variation of the kinetic energy which must vanish at the end of the disturbed motion. This occurrence has been detected at the driving simulator too. Just a single stable equilibrium has been found inside the domain of attraction in all of the examined cases.

Dynamic Analysis of Wind–Vehicle–Bridge Systems: An Advanced Hybrid Method

To investigate the dynamics of the wind–vehicle–bridge (WVB) system in the multi-body dynamics framework, which avoids the large computation cost of programming the motion equation of complex vehicle models and improves the calculation efficiency, an advanced hybrid method is proposed to optimize the WVB system coupling vibration analysis model. The dummy body coupling (DBC) method is integrated to build the connection between the MBS and the FE model, which cannot change the mechanical characteristics of the MBS vehicle model and the bridge FE model. The proposed method makes full use of the high efficiency of the established structure modeling, the powerful wheel–rail analysis function, and vehicle modeling in the multi-body dynamics framework. The complex bridge is modeled by a number of elements to reflect the actual dynamic characteristics of structure, which cannot satisfy the requirement of calculation in the multi-body dynamics framework. Thus, to avoid forming the wheel–rail relationship function, the bridge modeling as a finite element model would be transferred into multi-body dynamics coupling model of the WVB system as a flexible body. The verification of the relationship among the sub-systems of the multi-body model of the WVB system is investigated by analysis of the wind–vehicle, wind–bridge, and vehicle–bridge sub-systems. Finally, a dynamic analysis of the WVB system based on the proposed method is carried out for a double-track railway continuous bridge, in which the effects of different vehicle speeds and the incoming wind directions are studied. The simulation of the WVB system by the hybrid method has a high computational efficiency and strong practicability.

Machine Learning-Based Vehicle Model Construction and Validation—Toward Optimal Control Strategy Development for Plug-In Hybrid Electric Vehicles

Advances in machine learning inspire novel solutions for the validation of complex vehicle models and spur an easy manner to promote energy management performance of complexly configured vehicles, such as plug-in hybrid electric vehicles (PHEVs). A constructed PHEV model, based on the four-wheel-drive passenger vehicle configuration, is validated through an efficient virtual test controller (VTC) developed in this article. The VTC is designed via a novel approach based on the least-square support vector machine and random forest with the inner-interim data filtered by the ReliefF algorithm to validate the vehicle model as necessary. This article discusses the process and highlights the accuracy improvements of the PHEV model that is achieved by implementing the VTC. The validity of the VTC is addressed by examining the PHEV model to mimic the characteristics of internal combustion engine, motor, and generator behaviors observed through the benchmark test. Sufficient simulations and hardware-in-loop test are employed to demonstrate the capability of the novel VTC-based model validation method in practical applications. The major novelty of this article lies in the development of a VTC, by which the vehicle model can be efficiently developed, providing solid framework and enormous convenience for control strategy design.

An Optimal Control Strategy for Plug-In Hybrid Electric Vehicles Based on Enhanced Model Predictive Control With Efficient Numerical Method

Advances in machine learning inspire novel solutions for the validation of complex vehicle models and spur an easy manner to promote energy management performance of complexly configured vehicles, such as plug-in hybrid electric vehicles (PHEVs). A constructed PHEV model, based on the four-wheel-drive passenger vehicle configuration, is validated through an efficient virtual test controller (VTC) developed in this article. The VTC is designed via a novel approach based on the least-squares support vector machine and random forest with the inner-interim data filtered by the ReliefF algorithm to validate the vehicle model as necessary. This article discusses the process and highlights the accuracy improvements of the PHEV model that is achieved by implementing the VTC. The validity of the VTC is addressed by examining the PHEV model to mimic the characteristics of the internal combustion engine, motor, and generator behaviors observed through the benchmark test. Sufficient simulations and hardware-in-the-loop tests are employed to demonstrate the capability of the novel VTC-based model validation method in practical applications. The major novelty of this article lies in the development of a VTC, by which the vehicle model can be efficiently developed, providing a solid framework and enormous convenience for control strategy design.

Intrinsic Characteristics of Forward Simulation Modeling Electric Vehicle for Energy Analysis

The forward method for modeling electric vehicles is one of the most suitable for estimating energy consumption in different imposed driving cycles. However, a detailed description of the methodology used for the development of electric vehicle models is necessary and is scarce in the current literature. To fill this gap, this study focuses on highlighting the intrinsic characteristics through a theoretical study with a mathematical model, complemented by demonstrative simulations in Matlab/Simulink. The results show that the forward method can be estimated more accurately based on the energy consumption of the electric vehicle. Moreover, this paper aims to be explicitly descriptive for the development of more complex electric vehicle models to incorporate real driving cycles, being able to size the drivetrain of the vehicle itself or develop ecological routes.

Effective adoption of vehicle models for autonomous vehicle path tracking: a switched MPC approach

Efficient path tracking plays a key role in the overall ride experience of Autonomous Vehicles (AVs). Model Predictive Control (MPC) is one of the most competent techniques which is capable of handling multiple variables and constraints. The performance of this controller heavily relies on the proper choice of the vehicle model used to predict future states. This work proposes a novel MPC framework for the effective adoption of vehicle models to achieve a compromise between MPC’s performance and computational cost. To this aim, a Switched MPC (SMPC) using vehicle models with different levels of complexity and fidelity is developed. The SMPC uses a novel supervision scheme to adopt the appropriate vehicle model based on the models’ prediction error and MPC’s solution time. Two different configurations of SMPC are implemented: (1) A Fuzzy Logic System (FLS), and (2) An adaptive switching supervisor. The outcomes show that both approaches can perform path tracking accurately on roads with varying curvatures for different AV speeds. Moreover, comparisons with the conventional MPCs show that the proposed controllers can perform comparably with selective use of a complex vehicle model. Notably, they benefit from a higher computation efficiency from sidestepping the most complex models during path tracking.

Motion Control of a 4WS4WD Path-Following Vehicle: Dynamics-Based Steering and Driving Models

This paper deals with a four-wheel-steering four-wheel-driving (4WS4WD) vehicle under the path-following control. Focuses are placed on the motion control of the vehicle, and the drive forces and steering angles for achieving accurate path-following by the vehicle are determined. In this research, a nonlinear vehicle model of three degrees of freedom (DOFs) is used. The vehicle path-following dynamics are modeled using the classical mass-damper-spring vibration theory, which is described by three ordinary differential equations of second order with lateral, heading and velocity deviations, and control parameters. Combined with the vehicle path-following dynamic model, the nonlinear vehicle dynamic model is decoupled in generalized coordinate space. The required drive forces and steering angles for the vehicle path-following controllers are thus calculated and control models are obtained. Theoretical analysis for steering and driving control models is also carried out. It discloses that control models can maintain good performance against uncertainties. The vehicle path-following control is exhibited by dynamic simulation in CarSim with consideration of a complex vehicle model and a variable-curvature planned path. Numerical results obtained are analyzed and show control models have capable of dealing with a complex path-following problem. This paper provides a new insight into understanding path-following control of a 4WS4WD vehicle at the generalized vibration level.

Performance Review of Three Car Integrated ABS Types: Development of a Tire Independent Wheel Speed Control

This study concerns the development and testing of three types of Anti-lock Brake Systems (ABS): a standard on-off wheel’s acceleration control; a wheel’s longitudinal slip controller based on a discrete Proportional-Integral-Derivative (PID) control; and a novel type of ABS that involves controlling the wheel’s speed through a discrete PID. This work was developed inside a wider project that will lead to the implementation of stability control systems in a prototype car. For this reason, the typologies of ABS must not require extra sensors compared to those in standard vehicles: Inertial Measurement Unit (IMU) and 4-wheel speed sensors. Furthermore, they must be easily integrated with other controls and electronic components in terms of sampling time and values. The standard ABS seems more appropriate than the others two because it uses only parameters defined by sensors and it has a simple architecture that does not have the problem of computational time. However, in recent years, cars have been equipped with Electro-Hydraulic-Braking (EHB) units that improve the performance of the system controls. In fact, it is possible to use a control that allows actuators to follow a continuous target and smooth out pressure actions. Even if the longitudinal Slip Controller has a simple architecture and uses a PID control, it is limited to using quantities estimated instead of measured: the tires’ friction coefficient, the tires’ longitudinal stiffness, and the car’s speed. Therefore, the use of a Wheel Speed Controller is the right compromise to link the advantages of both controllers by following the braking pressure continuously and not needing to know the condition and properties of the tires. The results of tests carried out in a Hardware-In-the-Loop (HiL) system are showed and involved a complex vehicle model implemented in real-time.

Simulation-based assessment of a road surface condition aware adaptive cruise control

One of the major research and development efforts in the automotive industry worldwide is the introduction of highly automated driving functions. Due to the high level of complexity, suppliers and manufacturers often wonder whether and to what extent the potential or the effectiveness of newly developed systems can already be estimated a priori in terms of the different requirements in order to make the development process more targeted and thus timelier and also more cost-efficient. In the context of a current research project, that is developing a sensor system for the detection of the road surface condition, it shall be investigated how such a system can be used to improve high-level driving functions. In this paper, as an example to this end, the algorithm of a state-of-the-art adaptive cruise control (ACC) is first extended by a friction coefficient awareness and then tested and examined based on simulations within a complex vehicle model. Subsequently, the system is implemented in a traffic flow simulation and analysed for its impact on road safety via the analysis of corresponding parameters.

Simulation-based assessment of a road surface condition aware adaptive cruise control

One of the major research and development efforts in the automotive industry worldwide is the introduction of highly automated driving functions. Due to the high level of complexity, suppliers and manufacturers often wonder whether and to what extent the potential or the effectiveness of newly developed systems can already be estimated a priori in terms of the different requirements in order to make the development process more targeted and thus timelier and also more cost-efficient. In the context of a current research project, that is developing a sensor system for the detection of the road surface condition, it shall be investigated how such a system can be used to improve high-level driving functions. In this paper, as an example to this end, the algorithm of a state-of-the-art adaptive cruise control (ACC) is first extended by a friction coefficient awareness and then tested and examined based on simulations within a complex vehicle model. Subsequently, the system is implemented in a traffic flow simulation and analysed for its impact on road safety via the analysis of corresponding parameters.

Vehicle modeling for the analysis of the response of detectors based on inductive loops.

Magnetic loops are one of the most popular and used traffic sensors because of their widely extended technology and simple mode of operation. Nevertheless, very simple models have been traditionally used to simulate the effect of the passage of vehicles on these loops. In general, vehicles have been considered simple rectangular metal plates located parallel to the ground plane at a certain height close to the vehicle chassis. However, with such a simple model, it is not possible to carry out a rigorous study to assess the performance of different models of vehicles with the aim of obtaining basic parameters such as the vehicle type, its speed or its direction in traffic. For this reason and because computer simulation and analysis have emerged as a priority in intelligent transportation systems (ITS), this paper aims to present a more complex vehicle model capable of characterizing vehicles as multiple metal plates of different sizes and heights, which will provide better results in virtual simulation environments. This type of modeling will be useful when reproducing the actual behavior of systems installed on roads based on inductive loops and will also facilitate vehicle classification and the extraction of basic traffic parameters.

Real-time control for at-limit handling driving on a predefined path

ABSTRACTAutonomous driving at at-limit handling represents a big challenge due to the nonlinear behaviour of a vehicle. In this paper, a hierarchical control scheme composed of two Nonlinear Model Predictive Controls (NMPCs) for path following is proposed. This structure allows for real-time feasibility without having to simplify excessively the vehicle model. The higher level NMPC operates on a long prediction horizon with a point-mass model which constraints are given by a tyre dependant ‘g–g diagram’. The output of the higher level is a velocity profile which is used as terminal constraint by the lower level NMPC. This operates on a short horizon and is based on a seven degrees of freedom vehicle model with full Pacejka Magic Formula tyre formulation on all tyres, load transfers and Limited Slip Differential. Because of the terminal set computed by the higher level, it is possible to use a short horizon and exploit the vehicle performance in real-time. For both controllers, the full Nonlinear Optimisation Problem is solved at each step. The algorithm is tested in a Model-in-the-Loop environment where a validated Vi-Grade vehicle model is controlled in co-simulation. The results show the effectiveness and feasibility of real-time control with complex vehicle models.

Chrono::Vehicle: template-based ground vehicle modelling and simulation

Chrono::Vehicle is a module of the open-source multi-physics simulation package Chrono, aimed at modelling, simulation, and visualisation of wheeled and tracked ground vehicle multi-body systems. Its software architecture and design was dictated by the desire to provide an expeditious and user friendly mechanism for assembling complex vehicle models, while leveraging the underlying Chrono modelling and simulation capabilities, allowing seamless interfacing to other optional Chrono modules (e.g., its granular dynamics and fluid-solid interaction (FSI) capabilities), and providing a modular and expressive API to facilitate its use in third-party applications. Vehicle models are specified as a hierarchy of subsystems, each of which is an instantiation of a predefined subsystem template. Written in C++, Chrono::Vehicle is offered as a middleware library. In this paper, we provide an overview of the Chrono::Vehicle software design philosophy, its main capabilities and features, describe the types of ground vehicle mobility simulations it enables, and outline several directions of future development and planned extensions.

Analysis of Factors Influencing the Characteristics of the Tire and its Model Used in MSC.ADAMS/Car

The tire model validity factors are listed and discussed when using tires in complex multi-mass vehicle models. Complex vehicle system models are used to estimate (to forecast) their handling and stability properties (including Electronic Stability Control (ESC) performance). It should be as less as possible discrepancy between vehicle virtual computational and experimental tests results. The objective forces to create more complex vehicle models. A tire is known to be the one of the most significant elements in the model and to influence considerably on vehicle handling and stability factors transmitting all road reactions. The paper describes factors to be able to get influence on the PAC2002 pneumatic tire model validity when simulating it in MSC.ADAMS/Car Software. The tire model creating begins by conducting studies of rolling tire characteristics. The studies are examined on tire benches. Conducting experimental studies there are the set of factors to be able to bring a measurement error into study results. The analysis of various literary sources has permitted to choose three basic factors to be able to get influenced on tire model and all the vehicle model validity. Among these factors there are following: tire pressure, tire temperature и tire tread wear. The most significant of these factors is the tire pressure. For providing required study accuracy it needs to apply tight restrictions on each factor changing range influencing on rolling tire characteristics. The ranges are to be determined for each certain tire model by using study results.

CRONE Cruise Control System

This paper deals with vehicle longitudinal control performed by a cruise control (CC) system using the CRONE approach. A comparison between this approach, a classical proportional-integral (PI) controller, and an H-infini (Hinf) controller is presented. Simulations with these controllers are performed considering a complex vehicle model obtained from simulator software taking mass uncertainties, aerodynamic drag, gravity, and wind forces into account. This model also accounts for wheel dynamics with tire-road interactions that allow the analysis of the adherence effect. Results show better robustness to uncertainties with the second-generation CRONE controller, as already demonstrated with the CRONE suspension system and the CRONE ABS system.

Optimal control of steer-braking systems: Non-existence of minimizing trajectories

Summary In this paper, we investigate an optimal control problem in which the objective is to decelerate a simplified vehicle model, subject to input constraints, from a given initial velocity down to zero by minimizing a quadratic cost functional. The problem is of interest because, although it involves apparently simple drift-less dynamics, a minimizing trajectory does not exist over the admissible input trajectories. This problem is motivated by a minimum-time problem for a fairly complex car vehicle model on a race track. Numerical computations run on the car trajectory optimization problem provide evidence of convergence issues and of an apparently unmotivated ripple in the steer angle. Characterizing this ripple behavior is important to fully understand and exploit minimizing vehicle trajectories. We are able to isolate the key features of this chattering behavior in a very simple dynamics/objective setting. We show that the cost functional has an infimum, but an admissible minimizing input trajectory does not exist. We also show that the infimum can be arbitrarily approximated by bang-bang inputs with a sufficiently large number of switches. We reproduce this phenomenon in numerical computations and characterize it by means of non-existence of admissible minimizing trajectories. Copyright © 2015 John Wiley & Sons, Ltd.

Integration of Geometry and Analysis for Vehicle System Applications: Continuum-Based Leaf Spring and Tire Assembly

The development of new and complex vehicle models using the absolute nodal coordinate formulation (ANCF) and multibody systems (MBS) algorithms is discussed in this paper. It is shown how a continuum-based finite element (FE) leaf spring and tire assembly can be developed at a preprocessing stage and integrated with MBS algorithms, allowing for the elimination of dependent variables before the start of the dynamic simulations. Leaf springs, which are important elements in the suspension system of large vehicles, are discretized using ANCF FEs and are integrated with ANCF tire meshes to develop new models with significant details. To this end, the concept of the ANCF reference node (ANCF-RN) is used in order to systematically assemble the vehicle model using linear algebraic constraint equations that can be applied at a preprocessing stage. These algebraic constraint equations define new FE connectivity conditions that include the leaf spring shackle/chassis assembly, tire flexible tread/rigid rim assembly, tire/axle assembly, and revolute joints between different vehicle components. The approach presented in this paper allows for using both gradient deficient and fully parameterized ANCF FEs to develop the new models. In order to develop accurate leaf spring models, the prestress of the leaves and the contact forces between leaves are taken into consideration in the ANCF models developed in this investigation. Numerical results are presented in order to demonstrate the use of the computational framework described in this paper to build continuum-based leaf spring/tire assembly that can be integrated with complex vehicle models. The results of this paper also demonstrate the feasibility of developing a CAD (computer-aided design)/analysis system in which the geometry and analysis mesh of a complete vehicle can be developed in one step, thereby avoiding the incompatibility and costly process of using different codes in the flexible MBS analysis.

Vibration analysis of a multi-span continuous bridge subject to complex traffic loading and vehicle dynamic interaction

A numerical analysis of the dynamic behavior of multi-span continuous bridges subject to traffic loadings and vehicle dynamic interactions is presented in this paper using the finite element program ANSYS. The proposed numerical model is capable of: (1) analyze “complex bridge systems”, “complex vehicle models”, and “complex traffic conditions”; (2) predict the vehicle-bridge coupled vibration response under various complex traffic loadings and vehicle dynamic conditions including the passage of multiple vehicles, vehicles changing lanes, vehicles subject to constant acceleration, and vehicles overtaking; and, (3) investigate the effect of girder stiffness decay on the coupled vibration of the vehicle-bridge system. Analytical and experimental results indicate that decay in the girder stiffness has a major effect on the coupled vibrations between the vehicles and bridge. The established method could be extended to analyze the vehicle-bridge coupled vibrations of many different types of bridges subject to complex vehicle loadings, which potentially could have a broad impact in the field of Bridge Engineering.