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The temperature of axle box bearing is always one of the indicators used to monitor whether the high-speed train is running safely. In this paper, a thermal model of axle box bearing considering the change of bearing lubrication state and the operating condition of the high-speed train was established. Based on the analysis of the generation mechanism of frictional heat inside the bearing, the influence of proportion of grease involved in lubrication was introduced for the first time and a detailed temperature transfer system of the axle box system was established. At the same time, through the axle box bearing-vehicle system dynamics model, the vertical and lateral loads of the axle box bearing under different operating condition were obtained as input parameters of the axle box bearing thermal model, the temperature distribution curve of the bearing under different operating conditions was obtained. Finally, based on the long-term wireless transmission device system (WTDS) temperature monitoring data, the calculation results of the established model were verified. The verification results showed the reliability of the model established in this paper, and showed the necessity of considering the change of the internal lubrication state of the bearing when evaluating the axle box bearing temperature. [ABSTRACT FROM AUTHOR]

Nowadays, control is pervasive in vehicles, and a full and accurate knowledge of vehicle states is crucial to guarantee safety levels and support the development of Advanced Driver-Assistance Systems (ADASs). In this scenario, real-time monitoring of the vehicle sideslip angle becomes fundamental, and various virtual sensing techniques based on both vehicle dynamics models and data-driven methods are widely presented in the literature. Given the need for on-board embedded device solutions in autonomous vehicles, it is mandatory to find the correct balance between estimation accuracy and the computational burden required. This work mainly presents different physical KF-based methodologies and proposes both mathematical and graphical analysis to explore the effectiveness of these solutions, all employing equal tire and vehicle simplified models. For this purpose, results are compared with accurate sensor acquisition provided by the on-track campaign on passenger vehicles; moreover, to truthfully represent the possibility of using such virtual sensing techniques in real-world scenarios, the vehicle is also equipped with low-end sensors that provide information to all the employed observers. [ABSTRACT FROM AUTHOR]

This study explores the effectiveness of vertical force control in in-wheel motors (IWMs) to enhance ride comfort in electric vehicles (EVs). A dynamic vehicle model and a proportional ride-blending controller were used to reduce vertical vibrations of the sprung mass. By converting the state-space model into a transfer function, the system's frequency response was evaluated using road profiles generated according to ISO 8608 standards and converted into Power Spectral Density (PSD) inputs. The frequency-weighted acceleration ( a w ) was calculated based on ISO 2631 standards to measure ride comfort improvements. The results showed that increasing the proportional gain ( K p ) effectively reduced the frequency-weighted acceleration and the RMS of the vertical acceleration of the sprung mass. However, the proportional gain could not be increased indefinitely due to the torque limitations of the IWMs. Optimal proportional gains for various road profiles demonstrated significant improvements in ride comfort. This study concludes that advanced suspension technologies, including the proportional ride-blending controller, can effectively mitigate the challenges of increased unsprung mass in IWM vehicles, thereby enhancing ride quality and vehicle dynamics. [ABSTRACT FROM AUTHOR]

The systems that are currently installed in autonomous vehicles are not designed to avoid obstacles on the road by manoeuvring at the limits of the vehicle and the road surface – the goal of the research presented was to develop such system. For these purposes, a universal test track based on ISO 3888-1 and ISO 3888-2 standards was adopted, which can be used to represent any situation in which there is an obstacle on the road in front of the vehicle that needs to be avoided. An analysis of the curves for generating the paths through the test track was carried out, on the basis of which the Bézier curves were chosen. In addition to them, the results of simulations in Adams Car software were used to generate the paths, which can be considered equivalent to real-world trials with a professional driver behind the wheel. A control model was developed for longitudinal and transverse control of the vehicle based on PID controllers, with the selection of optimal parameters – the ones that define PID controllers, and the others that define other characteristics of the model. The model proved to be successful in guiding the vehicle through the test track at all speeds at which manoeuvres are possible. Bézier curves are shown to be a better choice at lower speeds, while paths based on Adams Car simulations are a better choice at higher speeds. [ABSTRACT FROM AUTHOR]

We present a general approach to model the motion of a rigid body ground vehicle on a smooth nonplanar road surface. We generalise planar control-oriented models while preserving standard model states, inputs and outputs. We derive our approach from first principles, apply it to existing vehicle modelling approaches and test it through real-world experiments. We demonstrate that our approach improves upon the prediction accuracy of planar models. [ABSTRACT FROM AUTHOR]

The application of 'Target Cascading' in the product development process is well known to be effective in various industry fields, and it is a methodology that is already actively applied in various forms in the field of vehicle Ride & Handling (R&H) performance development. This paper proposes a model-based vehicle performance benchmarking methodology and a technology for setting system characteristics to achieve handling performance objectives as a means of utilization for this. Rather than introducing already well-known target deployment techniques, a process is proposed for practical use in the vehicle development phase through the development of interfaces between low degrees of freedom vehicle model and optimization software. The methodology presented in this study is expected to be available in a timely manner as a practical vehicle performance development tool. [ABSTRACT FROM AUTHOR]

Background: Hydraulically interconnected suspension (HIS) system has drawn wide attention in vibration control fields. The pressure difference problem due to long time use of HIS system will cause unsafe driving of the entire vehicle. Purpose: To solve the pressure difference problem and improve the anti-pitch and ride comfort performance of the HIS system, the displacement-sensitive grooves are added to the oil cylinder wall of the HIS system. The displacement-sensitive HIS (DSHIS) system has different damping characteristics depending on the position of the piston. Methods: The DSHIS system and a seven-DOF vehicle are modeled to lay a foundation for the simulation analysis. Then, the damping characteristics of the displacement-sensitive cylinder are studied. Next, the influence of the parameters on the DSHIS system's performance is studied. Finally, a full car simulation is performed to compare the performance of the proposed DSHIS system to the original suspension and the HIS system. Results: In the brake simulation, the pitch angles of vehicle 3 and vehicle 2 are reduced by 56% and 62.3% compared with that of vehicle 1, respectively. In the random road simulation, the acceleration RMS values of vehicle 3 and vehicle 2 are decreased by 48.17% and 26.73% than the original suspension, respectively. In the loading shock simulation, the maximum suspension deflection of vehicle 3 is decreased by 17.39% and 3.37% than vehicle 1 and vehicle 2, respectively. The maximum dynamic tire load of the vehicle 3 is decreased by 4.35% and 1.32% than vehicle 1 and vehicle 2, respectively. Conclusion: The full vehicle simulations prove that the proposed DSHIS system can effectively improve the ride comfort and anti-pitch performance of the mining vehicle. Besides, the pressure difference problem can also be solved by the additional grooves on the cylinder wall. [ABSTRACT FROM AUTHOR]

In this paper, we compared the linear and nonlinear motion prediction models of a long combination vehicle (LCV). We designed a nonlinear model predictive control (NMPC) for trajectory-following and off-tracking minimisation of the LCV. The used prediction model allowed coupled longitudinal and lateral dynamics together with the possibility of a combined steering, propulsion and braking control of those vehicles in long prediction horizons and in all ranges of forward velocity. For LCVs where the vehicle model is highly nonlinear, we showed that the control actions calculated by a linear time-varying model predictive control (LTV-MPC) are relatively close to those obtained by the NMPC if the guess linearisation trajectory is sufficiently close to the nonlinear solution, in contrast to linearising for specific operating conditions that limit the generality of the designed function. We discussed how those guess trajectories can be obtained allowing off-line fixed time-varying model linearisation that is beneficial for real-time implementation of MPC in LCVs with long prediction horizons. The long prediction horizons are necessary for motion planning and trajectory-following of LCVs to maintain stability and tracking quality, e.g. by optimally reducing the speed prior to reaching a curve, and by generating control actions within the actuators limits. [ABSTRACT FROM AUTHOR]

This article addresses a common issue in the design of battery electric vehicles (BEVs) by introducing a comprehensive methodology for the modeling and simulation of BEVs, referred to as the "PerfECT Design Tool". The primary objective of this study is to provide engineers and researchers with a robust and streamlined approach for the early stages of electric vehicle (EV) design, offering valuable insights into the performance, energy consumption, current flow, and thermal behavior of these advanced automotive systems. Recognizing the complex nature of contemporary EVs, the study highlights the need for efficient design tools that facilitate decision-making during the conceptual phases of development. The PerfECT Design Tool is presented as a multi-level framework, divided into four logically sequential modules: Performance, Energy, Currents, and Temperature. These modules are underpinned by sound theoretical foundations and are implemented using a combination of MATLAB/Simulink and the vehicle dynamics software VI-CRT. The research culminates in the validation of the model through a series of experimental maneuvers conducted with a Tesla Model 3, establishing its accuracy in representing the mechanical, electrical, and thermal behavior of BEVs. The study's main findings underscore the viability of the design tool as an asset in the initial phases of BEV design. Beyond its primary application, the tool holds promise for broader utilization, including the development of active control systems, advanced driver assistance systems (ADAS), and solutions for autonomous driving within the domain of electric vehicles. [ABSTRACT FROM AUTHOR]

Excessive vertical, roll, and pitch motions of the vehicle can cause discomfort for the driver and passengers. Mitigation of such motions can be done using active suspensions. In this paper, proportional-derivative controllers are used to reduce the vertical, roll, and pitch motions by using a 10 degree-of-freedom vehicle model. The vehicle model is verified by using CarSim for a double lane change maneuver. The verification results have showed that the vehicle model used in this study can emulate the motion of the vehicle model in CarSim. The proportional-derivative controllers are used to calculate the desired vehicle vertical force, roll moment, and pitch moment. These desired force and moments are converted into active suspension force inputs by using decoupling transformation. When the vehicle is given sine steer wave and braking torque inputs, the results have showed that the controllers can reduce the vertical, roll, and pitch motions considerably. [ABSTRACT FROM AUTHOR]

xComputational representation of real-world systems plays an important role in vehicle analysis. Aiming to improve mobility systems, this article presents the development of a chassis dynamometer and vehicle model describing the vehicle longitudinal dynamics considering the tire-bench contact. The model simulates the longitudinal vehicle-bench tests where the system is powered by the bench's electric motor and the gearbox in the neutral position, considering tire interaction forces, rolling resistance, and system losses. It was implemented in Matlab/Simulink™ and validated by coast-down experiments, starting at 60 km/h and 100 km/h, where the model result curves presented an appropriated representativity for the experimental data. A total movement resistance analysis resulted in a mean error of 6.71% when compared to experimental data, while the literature slip-independent equations presented mean errors between 31.94% and 77.61%. The developed model is a representative approximation of the vehicle-dynamometer set and can predict longitudinal experiments, helping the vehicle evaluation process, and saving time and resources. [ABSTRACT FROM AUTHOR]

In bridge structural health monitoring, the response of the bridge while the vehicle is on the bridge, is called a vehicle-bridge interaction (VBI) response. If the vehicle and the bridge are dynamically coupled, the VBI response depends on the bridge's and the vehicle's dynamic properties. Therefore, the damage detection techniques based on the bridge resonances become questionable due to the dynamic coupling between the bridge and the vehicle. This study investigates the influence of vehicle dynamics on the bridge's time-dependent resonances. Vehicle-Induced Delta Frequency (VIDF) represents the changes in the bridge's time-varying resonances resulting from the vehicle-bridge interaction, while Damage-Induced Delta Frequency (DIDF) accounts for the additional alterations caused by bridge damage. The dynamic interaction between vehicles and bridges (VBIs) is characterized by the frequency ratio between the vehicle (super-system) and the bridge (sub-system). The vehicle frequency is influenced by its dynamics, particularly the suspension systems. Two vehicle models, single suspension and dual suspension vehicles representing passenger trains and freight trains, respectively, are analyzed to assess the significance of vehicle dynamics on VIDF and DIDF. The results demonstrate that both vehicle models experience resonance, which magnifies the dynamic response to damage. However, not all types of vehicles possess the desired dynamic characteristics for effective bridge health monitoring. Trains with single suspension systems exhibit more pronounced changes in the bridge's frequency response. This characteristic makes them more suitable for effective bridge health monitoring and damage detection. [ABSTRACT FROM AUTHOR]

Relocating the electric motor to a position inside the wheel offers a variety of benefits, such as reduced overall vehicle weight, more efficient production of vehicles, more flexible design and better road handling because of the accurate torque control on each wheel. However, the motor also increases the unsprung mass, which can impair the ride comfort of the vehicle. In this paper, we propose and investigate a control strategy using the vertical component of the driving force provided by an in-wheel motor for better ride comfort and handling dynamics. In the next stage, a mathematical model of the vehicle with coupled longitudinal, lateral, and vertical dynamics was introduced. The parameters of the vehicle were measured and collected from an actual car equipped with in-wheel motors. To analyze the performance of the controller, a model of the vehicle was tested in a series of simulations. The straight-line acceleration test indicated an improvement to the ride comfort of 31.8% in terms of the RMS vertical vibrations of the sprung mass. The control is achieved without any deterioration of the tire load and the vehicle's longitudinal dynamics. The stable lateral dynamics of the controlled vehicle was confirmed using a sine-sweep steering excitation, conducted on a perfectly smooth road surface with a constant longitudinal acceleration. [ABSTRACT FROM AUTHOR]

Featured Application: The methodology presented in this paper can be applied to the design and evaluation of torque vectoring systems in hybrid electric vehicles. Comparison of different controllers is helpful in making design choices in these applications. In today's automotive industry, electrification is a major trend. In-wheel electric motors are among the most promising technologies yet to be fully developed. Indeed, the presence of multiple in-wheel motors acting as independent actuators allows for the implementation of innovative active systems and control strategies. This paper analyzes different design possibilities for a torque vectoring system applied to an originally compact front-wheel drive hybrid electric vehicle with one internal combustion engine for the front axle and two added electric motors integrated in the wheels of the rear axle. A 14 degrees of freedom vehicle model is present o accurately reproduce the nonlinearities of vehicle dynamic phenomena and exploited to obtain high-fidelity numerical simulation results. Different control methods are compared, a PID, an LQR, and four different sliding mode control strategies. All controllers achieve sufficiently good results in terms of lateral dynamics compared with the basic hybrid version. The various aspects and features of the different strategies are analyzed and discussed. Chattering reduction strategies are developed to improve the performance of sliding mode controllers. For a complete overview, control systems are compared using a performance factor that weighs control accuracy and effort in different driving maneuvers, i.e., ramp and step steering maneuvers performed under quite different conditions ranging up to the limits. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The introduction of more automation into our vehicles is increasing our ability to avoid or mitigate the effects of collisions. Early systems could brake when a likely collision was detected, while more advanced systems will be able to steer to avoid or reconfigure a collision during the same circumstances. This paper addresses how the post-impact motion of an impacted vehicle could be included in the decision-making process of severity minimisation motion planning. A framework is proposed that builds on previous work by the authors, combining models from motion planning, vehicle dynamics, and accident reconstruction. This framework can be configured for different contexts by adjusting its cost function according to relevant risks. Simulations of the unified system are carried out and analysed from the perspective of vehicle model complexity and collision parameters sensitivity. Additionally, effects are highlighted concerning different modelling decisions, with respect to vehicle dynamics models and collision models, that are important to consider in further research. [ABSTRACT FROM AUTHOR]

The automotive industry is experiencing increasing competition, and vehicle development is becoming increasingly complex. Manufacturers must therefore be able to rapidly compare the outcomes of experimental tests carried out under different conditions. Robust simulation tools that can adjust for external factors have the potential to save a significant amount of time. In this regard, the purpose of this paper is to propose a method for evaluating the effect of asphalt temperature on tire and vehicle lateral dynamic performance, based on empirical data. Because rubber is a viscoelastic material, its properties are heavily influenced by the operating conditions. Therefore, a corrective algorithm must be created to enable the transfer of results obtained from tests carried out under different asphalt temperature conditions to a reference temperature of 25 °C. This article presents an analytical model that accurately describes this phenomenon, as well as the methods employed to generalize and optimize the model. Generalizability represents a crucial aspect of this research, as the model must be widely applicable across several vehicle categories while requiring minimal data to perform the corrections effectively. Finally, the analytical compensatory tool was incorporated into a MATLAB bicycle model to update the numerical transfer function measurements that describe the vehicle's dynamic behavior during experimental maneuvers. These results indicate that modest data is needed to achieve good levels of accuracy, making the model and vehicle dynamics implementation promising. [ABSTRACT FROM AUTHOR]

Minimum lap-time planning (MLTP) is a well-established problem in the race car industry to provide guidelines for drivers and optimize the vehicle's setup. In this paper, we tackle the 3D nature of the problem in its full extension, making no simplifying assumptions on the mechanics of the system. We propose a multibody vehicle model, described by rigorous dynamical equations. To effectively handle the resulting complexity, we devised an efficient direct dynamics computational method based on Featherstone's articulated-body algorithm (ABA). To solve the MLTP, we employed a direct-collocation technique, discretizing the problem so that all information of the 3D track is pre-processed and directly embedded into the discrete problem. This discretization approach turns out to be perfectly compatible with our vehicle model, leading to a solution in accessible computational time frames. The high level of detail of the model makes the proposed approach most useful for in-depth vehicle dynamics analyses on complex tracks. To substantiate the analysis, we provide a comparison with the results obtained by a double-track model on the Nürburgring Nordschleife circuit. Consistently with the average trend defined by the double track, the proposed model features a more dynamically rich behavior, realistically capturing the higher-order effects elicited by the sharp corners and the highly variable slope of the track. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

For vehicle state estimation, the conventional Kalman filter performs well under the Gaussian assumption, but in the real non-Gaussian situation (especially when the noise is non-Gaussian heavy-tailed), it shows poor accuracy and robustness. In this paper, an extended Kalman filter (EKF) algorithm based on the maximum correntropy criterion (MCC) is proposed (MCCEKF), and a lateral-longitudinal coupled vehicle model is established, while a state observer containing the yaw rate, vehicle sideslip angle, and longitudinal vehicle speed is designed using the easily available measurement information of on-board sensors. After analyzing the complexity of the proposed algorithm, the new algorithm is verified on the Simulink/CarSim simulation experimental platform by Double Lane Change and Sine Sweep Steer Torque Input maneuver. Experimental results show that the MCC-based EKF algorithm has stronger robustness and better estimation accuracy than the traditional EKF algorithm in the case of non-Gaussian noise, and the MCCEKF is more applicable for vehicle state estimation in practical situations. [ABSTRACT FROM AUTHOR]

Heavy vehicles exiting (or entering) a tunnel at high speed under a strong crosswind is a particularly critical condition since the aerodynamic load changes drastically, greatly affecting the lateral stability of the vehicle. Often, active control systems (active suspensions, active front steering, etc.) and infrastructure elements (e.g., wind fences) are proposed to reduce the induced risks. To help the design of these devices, the present paper investigates the response of the vehicle–driver system in the case of a high-sided lorry exiting a tunnel under crosswind, by using Driver-In-the-Loop simulations. The study was performed using the dynamic driving simulator of Politecnico di Milano and 28 test drivers. Vehicle and aerodynamic models have been developed to reproduce the phenomenon in a highly immersive environment. During the tests, several combinations of vehicle and wind speed were considered. The effect of vehicle loading condition (Empty and Laden) was also investigated. The performed tests allowed us to gain information about the sequence of the driver's actions and associated delays, which may induce lane deviation or, in the worst case, rollover. It was found that lane invasion may happen for ratios of lateral aerodynamic force over vehicle weight force bigger than 0.1, while rollover could happen for ratios bigger than 0.3. Moreover, it was found that the driver's response typically happens with a delay of ∼0.25 s with respect to the onset of the crosswind stimulus. [ABSTRACT FROM AUTHOR]

To improve the real-time performance of the estimation method of road friction coefficient (RFC) based on moving horizon estimation (MHE), a hierarchical estimation method for RFC combining single-step MHE (S-MHE) and inverse tire model (ITM) based on lateral vehicle dynamics is proposed in this study. Firstly, a hierarchical estimation framework is designed to decouple vehicle and tire systems. Secondly, the S-MHE estimator is designed based on the nonlinear vehicle model to estimate the lateral tire force. Thirdly, the ITM is deduced based on the Pacejka model, and the estimator for the RFC based on the ITM is designed. Finally, the estimation accuracy, convergence speed, and real-time performance of the proposed method and the traditional MHE method are compared and discussed through different tests based on CarSim and Simulink. The results show that compared with the traditional MHE method, the proposed method reduces the average computation time to about 0.125 s and improves the real-time performance by more than 30% while ensuring the estimation accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

Vehicle mass is an important parameter for motion control of intelligent vehicles, but is hard to directly measure using normal sensors. Therefore, accurate estimation of vehicle mass becomes crucial. In this paper, a vehicle mass estimation method based on fusion of machine learning and vehicle dynamic model is introduced. In machine learning method, a feedforward neural network (FFNN) is used to learn the relationship between vehicle mass and other state parameters, namely longitudinal speed and acceleration, driving or braking torque, and wheel angular speed. In dynamics-based method, recursive least square (RLS) with forgetting factor based on vehicle dynamic model is used to estimate the vehicle mass. According to the reliability of each method under different conditions, these two methods are fused using fuzzy logic. Simulation tests under New European Driving Cycle (NEDC) condition are carried out. The simulation results show that the estimation accuracy of the fusion method is around 97%, and that the fusion method performs better stability and robustness compared with each single method. [ABSTRACT FROM AUTHOR]

This article proposes a nonlinear observer for estimating a powertrain transmitted torque of vehicles equipped with dual-clutch transmissions. A new dynamical model of vehicle driveline is presented. It introduces a single characteristic state based on the dynamic friction model to scale the clutch torque capacity, which is available from the actuator position-to-torque map. Based on this model, the generated torque on the clutch disk can be effectively estimated in real time, and the sensitivity of the estimated value caused by high gain feedback can be reduced in the observer. Also, the engine torque uncertainty is estimated from the integrated driveline model. The Lyapunov-based analysis is presented to prove the convergence of the proposed observer. The effectiveness of the proposed method is shown by experimental validations on a test vehicle that allows for real measurements of the input shaft torque of transmission. [ABSTRACT FROM AUTHOR]

This paper presents a generic analytical framework tailored for surrogate safety measures (SSMs) that is versatile across various highway geometries, capable of encompassing vehicle dynamics of differing dimensionality and fidelity, and suitable for dynamic, real-world environments. The framework incorporates a generic vehicle movement model, accommodating a spectrum of scenarios with varying degrees of complexity and dimensionality, facilitating the estimation of future vehicle trajectory evolution. It establishes a generic mathematical criterion to denote potential collisions, characterized by the spatial overlap between a vehicle and any other entity. A collision risk is present if the collision criterion is met at any non-negative estimated future time point, with the minimum threshold representing the remaining time to collision. The framework's proficiency spans from conventional one-dimensional (1D) SSMs to extended multi-dimensional, high-fidelity SSMs. Its validity is corroborated through simulation experiments that assess the precision of the framework when linearization is performed on the vehicle movement model. The outcomes showcase remarkable accuracy in estimating vehicle trajectory evolution and the time remaining before potential collisions occur, comparing to high-accuracy numerical integration solutions. The necessity of higher-dimensional and higher-fidelity SSMs is highlighted through a comparison of conventional 1D SSMs and extended three-dimensional (3D) SSMs. The results showed that using 1D SSMs over 3D SSMs could be off by 300% for Time-to-Collision (TTC) values larger than 1.5 s and about 20% for TTC values below 1.5 s. In other words, conventional 1D SSMs can yield highly inaccurate and unreliable results when assessing collision proximity and substantially misjudge the count of conflicts with predefined threshold (e.g., below 1.5s). Furthermore, the framework's practical application is demonstrated through a case study that actively evaluates all potential conflicts, underscoring its effectiveness in dynamic, real-world traffic situations. • A generic and adaptable analytical framework for SSMs. • A generic mathematical criterion for characterizing potential collisions. • High-dimensional and high-fidelity SSMs. [ABSTRACT FROM AUTHOR]

Due to the uncertainty of vehicle model parameters, modeling errors and external disturbances, the performance of path tracking control system is poor, especially under high velocity and large curvature extreme conditions. To address this issue, this paper presents a novel gain-scheduled robust control strategy based on linear parameter varying system with model predictive control (MPC) and H∞. Firstly, fully considering the influence of the time-varying characteristics of vehicle velocity and tire cornering stiffness on the path tracking system model, a novel linear parameter varying system model is built for path tracking control of autonomous vehicle. Then, a path tracking robust controller is designed based on gain-scheduled approach, and the linear matrix inequality (LMI) is applied to solve optimization problem, in which MPC and H∞ robust control theory are applied to the controller design process. Finally, the simulation experiments have verified that the proposed novel robust control strategy can improve the path tracking accuracy and ensure the vehicle lateral and roll stability, especially under high velocity and large curvature extreme conditions. Meanwhile, the proposed robust controller shows superiority to suppress the parameters uncertainty, modeling error and external disturbance. [ABSTRACT FROM AUTHOR]

In this paper, a linear time-varying model predictive controller (LTV-MPC) is proposed for automated vehicle path-following applications. In the field of path following, the application of nonlinear MPCs is becoming more common; however, the major disadvantage of this algorithm is the high computational cost. During this research, the authors propose two methods to reduce the nonlinear terms: one is a novel method to define the path-following problem by transforming the path according to the actual state of the vehicle, while the other one is the application of a successive linearization technique to generate the state–space representation of the vehicle used for state prediction by the MPC. Furthermore, the dynamic effect of the steering system is examined as well by modeling the steering dynamics with a first-order lag. Using the proposed method, the necessary segment of the predefined path is transformed, the linearized model of the vehicle is calculated, and the optimal steering control vector is calculated for a finite horizon at every timestep. The longitudinal dynamics of the vehicle are controlled separately from the lateral dynamics by a PI cruise controller. The performance of the controller is evaluated and the effect of the steering model is examined as well. [ABSTRACT FROM AUTHOR]

In order to identify the road friction coefficient of the left and right sides of the vehicle more accurately, this paper presents an estimation framework based on a novel tyre model and modified square-root cubature Kalman filter (SCKF). To begin with, a novel tyre model is proposed by adaptively calculating the longitudinal and lateral stiffness and the effective friction coefficient. The tyre forces calculated by this model are more accurate than those calculated by the Brush model. Then, to avoid the influence of abnormal measurement noise on the estimation effect, we develop an improved SCKF (ISCKF) algorithm based on the maximum correntropy criterion. The algorithm can update the measurement noise covariance adaptively. Furthermore, a real-time estimation scheme of road friction coefficient is designed by combining the vehicle dynamics model with the proposed novel tyre model and ISCKF algorithm. Finally, the performance of the presented method is verified by the co-simulation of CarSim and MATLAB/Simulink. The results show that the designed estimation scheme not only has excellent robustness in the case of abnormal measurement noise interference but also has good adaptability to the uncertainty of road friction coefficients distribution. [ABSTRACT FROM AUTHOR]

Axles with leaf spring suspension systems are still a popular choice in many commercial vehicles. However, leaf springs are not in perfect conformity to standard multibody vehicle models because they combine guidance and suspension in one single element. Combining standard multibody vehicle models with sophisticated finite element leaf spring models results in rather complex and computing time-consuming solutions. Purely kinematic models, defined by lookup tables or the design kinematics approach, cover only some but not all features of the leaf spring suspension. As shown here, the five-link model, which incorporates a quasi-static solution of the leaf spring compliance, provides a very practical model. It is comparatively lean and provides results of sufficient accuracy in the whole application range. [ABSTRACT FROM AUTHOR]

The aim of this work is to introduce a new concept for a hydraulic semi-active yaw damper (SAYD) for the improvement of the stability of a high-speed rail vehicle. This concept represents a further elaboration of Secondary Yaw Control but envisages the use of semi-active hydraulic dampers instead of full-active electromechanical dampers, simplifying the design of the system and facilitating the design of a safe and fault tolerant device. Two control algorithms are proposed for the semi-active damper: maximum power point tracking and skyhook with Karnopp approximation. A multi-physics model of the SAYD is introduced and used in co-simulation with a multi-body model of a high-speed vehicle. Using these models, numerical simulations are performed to assess the behaviour of the semi-active damper in terms of improving the running stability of the rail vehicle at very high speed, showing that the use of the SAYD in combination with any of the two control strategies considered allows to improve substantially the stability of the vehicle. The results of experimental investigations performed in the project will be reported in a companion paper. [ABSTRACT FROM AUTHOR]

This article deals with the control chassis dynamics of a light electric vehicle. In the frame of Global Chassis Control, it proposes a hierarchical control approach focuses on compensating the chassis dynamics against driver disturbances. It is based on a supervisory structure consists of two main levels, a global controller for regulating chassis variables and a local controller to each suspension system. Both controllers are designed using a fractional-order robust controller, namely CRONE controller, to provide an optimized solution for the performance-robustness tradeoff. The main objective is to improve ride comfort for passengers while respecting road holding and handling criteria. In contrast to other studies, random road disturbances are considered to investigate the limits of the proposed approach. Analysis in frequency and time domain has been done to evaluate the performance and robustness of the designed controller. Simulation results based on a full nonlinear 14 degree of freedom vehicle model show that the proposed strategy can effectively improve the ride quality in the field of interest where a significant performance in driver disturbance rejection is reported. [ABSTRACT FROM AUTHOR]

This article proposes a novel gain-scheduling control method to improve vehicle lateral stability based on a variable-parameter-dependent approach. A time-varying velocity-dependent model to describe the vehicle lateral dynamic characteristics is constructed under cornering stiffness uncertainties and controller saturation. A novel Lyapunov function with variable-parameter-dependent Lyapunov matrix is established to develop the conditions. Using the proposed Lyapunov function, a general condition of the variable-parameter-dependent saturated robust yaw moment controller is provided in terms of time-varying parameter-dependent matrix inequalities. In order to obtain a tractable solution, a condition is further developed with finite linear matrix inequalities. Moreover, an optimal distribution method is adopted to generate the desired yaw moment based on torque allocation. These torques are computed by optimizing the distribution errors and tire workloads. Simulations results under both J-turn and double-lane changing scenarios are used to illustrate the merits of the proposed method. The control synthesis approach is also applicable to other applications involving time-varying parameters. [ABSTRACT FROM AUTHOR]

This article focuses on the 3-D guidance strategy for a reusable launch vehicle (RLV) during terminal area energy management (TAEM) phase. Based on sliding-mode and shrinking-horizon techniques, the proposed scheme consists of trajectory generation and correction mechanisms, which can enhance the guidance precision and robustness against disturbances. The RLV guidance model, in the form of a set of highly nonlinear differential equations in the time domain, is recast as an altitude-domain model. By this means, the main characteristics of TAEM gliding motion are extracted. The altitude-domain model is thereby used for trajectory generation. A sliding surface and a guidance law are proposed. Hybrid TAEM constraints can be fully satisfied when the proposed guidance law drives the altitude-domain vehicle model to the designated altitude. Using the proposed guidance law as the input of the altitude-domain model, a constrained TAEM trajectory is generated, leading to TAEM guidance commands simultaneously. The commands are utilized to drive the time-domain model to the terminal target. In an attempt to compensate for model uncertainties and initial deviations, the guidance commands are modified periodically by the shrinking-horizon correction mechanism according to current states. Simulations on different scenarios are provided to demonstrate the performance of the proposed guidance strategy. [ABSTRACT FROM AUTHOR]

Longitudinal velocity, lateral velocity, and front wheel steering angle are crucial states for vehicle active safety features. However, direct measurement of these variables requires expensive measurement instruments and can be easily affected by vehicle nonlinear dynamics, outliers and noise pollution. Moreover, unknown inputs bring great challenges to their accurate estimation. Therefore, this paper develops a novel robust unscented M-estimation-based filter (RUMF) for vehicle state estimation with unknown driver steering torque. The nonlinear system model is constructed based on the vehicle dynamics model. Unscented transformation (UT) and statistical linearization are implemented to transform the nonlinear process and measurement function into a linear-like regression form with data redundancy to achieve outlier suppression. Then, an M-estimation-based iterated algorithm is designed to address process uncertainty and innovation and observation outliers for robust vehicle state estimation. The iteratively reweighted least-squares (IRLS) method based on the M-estimation methodology is utilized for unknown input estimation. Simulations and experimental results compared with extended Kalman filter (EKF) and particle filter (PF) have verified the effectiveness and robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Automated driving functions are expected to increase both the safety and ride comfort of future vehicles. Ensuring their functional safety and optimizing their performance requires thorough testing. Costs and duration of tests can be reduced if more tests can be performed numerically in a feasible simulation framework. This simulation setup must include all subsystems of the autonomous vehicle, which significantly interact with the system under test. In this paper, a modular model chain is presented, which is developed for testing systems with an impact on vehicle motion. It includes trajectory planning, motion control, and a model of the vehicle dynamics in a closed loop. Each subsystem can easily be exchanged to adapt the model chain with respect to the simulation objectives. As a use case, the testing of an active suspension control system is discussed. It is designed directly for use in autonomous cars and uses inputs from the vehicle motion planning subsystem for planning the suspension actuator motion. Using the presented closed-loop model chain, the effect of different actuator control strategies on ride comfort is compared, such as curve tilting. Furthermore, the impact of the active suspension system on lateral vehicle motion is shown. [ABSTRACT FROM AUTHOR]

Large variations load-to-curb weight ratios are linked to significant changes in parameters critical to control design for vehicle stability control system. Unique and highly customised vehicles, such as the lightweight solar car in this paper, are more susceptible to the impact of such variations when developing control methods. The purpose of this study is to study the influence of variation in loading conditions, the effect of ignoring changes in inertial parameters, and develop and compare a number of alternative vehicle stability control methods that can be applied to rear-wheel driven vehicles via in-wheel motors. In this paper a Sliding Mode Control (SMC) both nominal and when including uncertainty, Dynamic Curvature Control (DCC) and a Proportional–Integral Control (PI) strategies are compared to the baseline open-loop control case. Each controller is implemented through co-simulation via MATLAB® Simulink® and Siemens Amesim™ using a 15-DOF non-linear vehicle model. The results show that SMC achieves the best performance, whilst DCC tends to overshoot target conditions prior to settling, indicating that SMC is the preferred control strategy. It is also demonstrated that by ignoring the change in the inertial parameters in simulation environments can produce an incorrect translation of the control performance. [ABSTRACT FROM AUTHOR]

In the context of automated and connected vehicle technology, this paper proposes an environment-on-board predictive braking control system, regulating the vehicle velocity to a desired value, in order to enhance path-following performance and vehicle stability when a vehicle is driven on a path where the road friction coefficient changes suddenly on a curve. In this study, we assume that the vehicle enters a wet road from a dry road and moves on to a dry road, and that the forward road surface friction condition can be estimated. In such driving situation, the objective of the vehicle dynamics control system is to improve path-following performance and vehicle stability of automated vehicle, even under abnormal road conditions. To achieve this objective, the predictive braking control is designed to track a safe velocity which is determined based on a simplified linear two-degree-of-freedom bicycle and a 2nd order look-ahead driver model. The effectiveness of this control system is verified using a nonlinear four-degree-of-freedom four-wheel model under various conditions, with varying road friction coefficients and curvatures. Finally, the effectiveness is evaluated using a full vehicle model of the IPG CarMaker, which is similar to an actual vehicle. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to propose a complete and powerful methodology that allows the optimization of the passive suspension system of vehicles, which simultaneously takes comfort and safety into account and provides a set of optimal solutions through a Pareto-optimal front, in a low computational time. Design/methodology/approach: Unlike papers that consider simple vehicle models (quarter vehicle model or half car model) and/or simplified road profiles (harmonic excitation, for example) and/or perform a single-objective optimization and/or execute the dynamic analysis in the time domain, this paper presents an effective and fast methodology for the multi-objective optimization of the suspension system of a full-car model (including the driver seat) traveling on an irregular road profile, whose dynamic response is determined in the frequency domain, considerably reducing computational time. Findings: The results showed that there was a reduction of 28% in the driver seat vertical acceleration weighted root mean square (RMS) value of the proposed model, which is directly related to comfort, and, simultaneously, an improvement or constancy concerning safety, with low computational cost. Hence, the proposed methodology can be indicated as a successful tool for the optimal design of the suspension systems, considering, simultaneously, comfort and safety. Originality/value: Despite the extensive literature on optimizing vehicle passive suspension systems, papers combining multi-objective optimization presenting a Pareto-optimal front as a set of optimal results, a full-vehicle model (including the driver seat), an irregular road profile and the determination of the dynamic response in the frequency domain are not found. [ABSTRACT FROM AUTHOR]

A novel longitudinal, lateral, and vertical integrated stability control system is proposed for distributed electric vehicle in this paper. The integrated stability control system is based on model predictive control and takes advantage of its multi-objective optimization feature to takes manipulability, stability and comfort requirements into consideration at the same time, and realize the optimal longitudinal $/$ lateral $/$ vertical forces distribution with constraints overall considered. The advantage of the proposed integrated control system is that it can solve the control objective conflict of the cooperative motion control subsystems and the interference of the actuators compared to distributed control system. Finally, the simulation and comparison analysis are given in several different driving conditions under Carsim and Matlab $/$ Simulink environment. Results show that an improvement of over 80 $\%$ in the pitch angle and roll angle is realized compared to the simple control strategy. [ABSTRACT FROM AUTHOR]

This paper presents a novel estimation and identification approach for lateral vehicle dynamics. The algorithm leverages on a Linear Fraction Transform (LFT) reformulation of vehicle and tyre models, allowing for a simple and computationally efficient inclusion of complex and nonlinear dynamic models, like, for example, two-wheels, four-wheels or single-track as vehicle model, and Pacejka, brush or Fiala as tyre model. As a result, this technique can be easily adopted in the development of an online identification system, able to run on a standard embedded device, implementing a flexible identification procedure that can handle different driving conditions, up to the limits of handling, different vehicle modelling approaches, and different input measurements. Experimental results demonstrate the effectiveness of the proposal, either in a persistent excitation and in a non-persistent excitation scenario. [ABSTRACT FROM AUTHOR]

This research presents a data-driven Neural Network (NN)-based Virtual Sensor (VS) that estimates vehicles' Unsprung Mass (UM) vertical velocity in real-time. UM vertical velocity is an input parameter used to control a vehicle's semi-active suspension. The extensive simulation-based dataset covering 95 scenarios was created and used to obtain training, validation and testing data for Deep Neural Network (DNN). The simulations have been performed with an experimentally validated full vehicle model using software for advanced vehicle dynamics simulation. VS was developed and tested, taking into account the Root Mean Square (RMS) of Sprung Mass (SM) acceleration as a comfort metric. The RMS was calculated for two cases: using actual UM velocity and estimations from the VS as input to the suspension controller. The comparison shows that RMS change is less than the difference threshold that vehicle occupants could perceive. The achieved result indicates the great potential of using the proposed VS in place of the physical sensor in vehicles. [ABSTRACT FROM AUTHOR]

The parking environment for drivers is now increasingly complex, and parking has become a driving phenomenon with high incidence of accidents. To solve the problem, a method of path planning for autonomous parking was proposed based on improved β-spline theory. The vehicle kinematical model was established, and considering the vehicle kinematics and electric power steering(EPS) performance requirements in parking environment, the path collision avoidance constraints and the vehicle steering wheel angle and angular velocity constraints were established. The simulation model was built by Matlab/Simulink. According to the actual parking scenario, three autonomous parallel parking conditions were designed, and the path planning was simulated. The results show that the proposed algorithm can realize autonomous parking for different sizes of parking lot, and the planned path curvature is continuous with slowly changed curvature. The vehicle kinematics and EPS performance requirements can be met with high parking efficiency. [ABSTRACT FROM AUTHOR]

Path planning is a critical part for improving the driving safety and driver comfort of autonomous vehicles (AVs), especially in complex maneuvering conditions. In addition, different drivers have different preferences for AVs, thus, how to provide personalized trajectories for different drivers is a vital issue for AVs. The collision-free path planning problem in conditions with large road curvatures is investigated in this paper, with the consideration of environmental safety constraints, drivers’ comfort, vehicle actuator constraints, etc. Firstly, a Driver-Vehicle-Road (DVR) system is established based on the combination of the kinematic vehicle model and the two-point visual preview driver model, such that the driver's individual handling characteristics can be considered in the controller. The kinematic vehicle model is modified to have the similar understeering characteristics with those of the nonlinear full car models, and then the proposed DVR system can satisfy different groups of drivers and cars. Secondly, for environmental constraints, a new artificial potential field (APF) method is proposed, which can form a banana-shaped 3-D dangerous imaginary mountain and a lane boundary cliff suitable for arbitrary curvature roads to generate a collision-free evasive path. Finally, the Linear-Time-Varying (LTV) model predictive control (MPC) method is adopted to design the path planner. The CarSim-Simulink joint simulation illustrates that with the proposed planner, the host vehicle is capable of avoiding obstacles with a safer and more comfortable maneuver on large curvature roads. And the proposed path planner can provide individually safe trajectories for different drivers with good maneuverability. [ABSTRACT FROM AUTHOR]

This article suggests a model-based controller for an all-wheel drive (AWD) vehicle using a novel vehicle dynamics model. Recently, an active type of AWD system that automatically controls the clutch engagement force of the transfer case has become popular. However, its performance has been limited by its rule-based controller, which necessitates the development of a model-based controller. Although the bicycle model has been most widely adopted for upper level controller of vehicle control systems, it is not appropriate for AWD controllers because the model does not have a direct relationship between the states and control inputs. In this sense, this study adopted a tire force-based full car model for the AWD controller. The clutch engagement force limit, which varies depending on the current engagement state, was calculated systematically by considering changeable dynamic behavior that is inherent in AWD vehicle and was used as a valid value for input limit in linear quadratic regulator (LQR) control algorithm. For the real-time application of the designed controller, only data obtained from the controller area network (CAN) of production vehicles were used. Then, the performance of the proposed controller was validated through vehicle experiments that included scenarios of both longitudinal and lateral movements. [ABSTRACT FROM AUTHOR]

Study of vehicle dynamics aggregates possibilities to enhance performance, safety and reliability, such as the integration of control systems, usually requiring knowledge on vehicle's states and parameters. However, some critical values are difficult to measure or are not disclosed. For this reason, dynamics and stability analysis of six-wheeled vehicles are compromised, and available information on this matter is limited. In this context, this paper proposes the estimation of the cornering stiffness of a 6x6 vehicle by an inverse problem approach applying the Levenberg–Marquardt (LM) method. The algorithm required data from field experiments and from simulations of a vehicle model during a double-lane change manoeuvre developed using S i m u l i n k ® / M A T L A B ® . Experimental and theoretical values for the vehicle yaw rate were combined through LM method for cornering stiffness estimation. The excellent agreement between measured and simulated yaw rate indicates that the proposed model and the estimated parameters properly represent the vehicle dynamics response. [ABSTRACT FROM AUTHOR]

In this work, a novel single-level adaptive trajectory planner and tracking controller is developed for off-road autonomous vehicles operating on deformable terrains. Trajectory planning and tracking algorithms often rely on a simplified vehicle model to predict future vehicle states based upon control inputs, hence requiring accurate modeling and parameterization. On off-road deformable terrains this is a challenging task due to unknown terrain parameters and the complex interactions at tire-terrain interfaces, which pose issues in continuous differentiability, operating conditions, and computational time. To address these difficulties, in this paper, a neural network deformable terrain terramechanics model and its implementation within a terrain adaptive model predictive control algorithm is presented to improve vehicle safety and performance through more accurate prediction of the plant response. It is shown in simulations that the neural network is able to predict the lateral tire forces accurately and efficiently compared to the Soil Contact Model as a state-of-the-art model and is able to yield accurate bicycle model predictions. It is demonstrated that the implementation of the neural network within model predictive control can outperform both a baseline Pacejka-based and a rapidly exploring random tree controller by improving performance and allowing for more severe maneuvers to be completed that otherwise lead to failure when terrain deformations are not explicitly taken into account. The improved performance achieved through estimating terrain parameters online in an adaptive controller is highlighted against the nonadaptive realization. Finally, it is shown the algorithm is conducive to real-time implementation. [ABSTRACT FROM AUTHOR]

Energy storage devices such as batteries and supercapacitors are arousing a growing interest in many areas of industrial applications since they allow improving the dynamic response and efficiency. In this sense, the availability of electric models of batteries and supercapacitors is necessary for the correct sizing, control, and energy management of power systems. In order to identify the parameters of the equivalent electric model, the identification current profile is often a pulse of charge or discharge. Subsequently, these models are validated with a current verification profile. However, the verification profile compared to the identification profile is more dynamic in amplitude and frequency, producing validation errors due to the identification signal's limited bandwidth. This paper proposes a novel Pulse – Pseudo Random Binary Sequence (Pulse – PRBS) identification current profile, with similar spectral characteristics to the verification profile, in order to improve the modeling accuracy. The parameters of a Lithium-ion battery and a supercapacitor are obtained with this new identification current profile and the Optimization Toolbox of Matlab, using the electrical models in Simulink or Simscape. Finally, the models are validated with the Urban Driving Cycle ECE-15 and the Hybrid Pulse Power Characterization (HPPC) for electric vehicle applications. [ABSTRACT FROM AUTHOR]

In vehicle trajectory prediction, the difficulty in modeling the interaction relationship between vehicles lies in constructing the interaction structure between the vehicles in the traffic scene. Majority of existing models only focus on the interaction between the historical trajectory of the vehicle and the surrounding vehicles in the spatial domain, and do not pay attention to the interaction between the vehicle and the non-Euclidean correlation structure (graph structure) that exists in the environment. In order to overcome the deficiencies in the existing models, this paper proposes the Environment-Attention Network model (EA-Net) to obtain the full interactive information between the vehicle and its driving environment. In the proposed model, a new type of parallel structure consisting of Graph Attention network (GAT) and Convolutional social pooling containing Squeeze-and-Extraction mechanism (SE-CS), is constructed as the environmental feature extraction module and embedded in LSTM encoder-decoder. This structure solves the limitation of the dimension and structure influence when constructing the interaction model between the vehicle and the surrounding environment, making the extracted feature information comprehensive and effective. The prediction accuracy of the model with the RMSE loss function is tested on two public datasets– NGSIM and highD, and compared with several state-of-the-art trajectory prediction algorithm models. The results show that the prediction accuracy of the proposed Environment-Attention Network in the two datasets is more than 20% higher than that of the single structure model, which indicates that the proposed model proposed has superior performance and better adaptability to different traffic environments compared with the existing models. [ABSTRACT FROM AUTHOR]

Motion planning by considering it as an optimal problem is an effective and widely applicable method. Its comprehensive performance greatly depends on the vehicle dynamics model, which is highly coupled and nonlinear, especially under the dynamical scenarios and causes much more consumption of computation resources for the numerical optimization. To increase the real time performance of the motion planner designed by nonlinear model predictive control (NMPC), a unified and simplified vehicle dynamics model (SDM) is presented to make a balance between the accuracy and complexity for dynamical driving scenarios. Based on the statistical analysis results of naturalistic driving conditions, a unified nonlinear vehicle dynamics model is set up, which considers the tyre cornering characteristic and is also applicable to conditions with large turning angle. After the validation of this coupled dynamics model (CDM) by comparisons with other widely used models under a variety of conditions, the coupling effect is analyzed according to the transfer functions, which are obtained by linearizing CDM at equilibrium points. Furthermore, SDM is derived by ignoring the weak part of the coupling effect. The accuracy of SDM is validated by several comparative studies with other models and it is further applied to design a motion planner by NMPC to validate its contribution on the performance improvement under dynamical driving conditions. [ABSTRACT FROM AUTHOR]

Autonomous vehicles are the future of automotive engineering and understanding how this systems work is critical. In these vehicles, controller models are usually needed to generate signals that would normally be imposed by the driver e.g., steering angles, acceleration inputs and braking commands. Intuitively, each control method utilized has its peculiarities and presents different behaviours. In such situation, this paper aims to develop an error comparison between a car displacement and its reference path due the use of two different predictive driver controllers: The proportionalintegrative and the MacAdam model. For this purpose, a 14 degrees of freedom vehicle model is used with the aid of MATLAB/Simulink, whereas simulations were made using the double-lane change manoeuvre, a commonly used manoeuvre to analyse the vehicle dynamics performance. At the end of this paper, lateral acceleration, displacement and steering wheel angle analysis led the conclusion that the vehicle behaviour is smoother with the use of the proportionalintegrative control regardless of longitudinal velocity. Nevertheless, the trajectory error is smaller for MacAdam model than PI controller is and therefore it is easier to follow the reference path with this one, although in aggressive maneuverers it can cause more discomfort and increase the risk of rolling when compared to the PI controller in a vehicle with the same body stiffness. [ABSTRACT FROM AUTHOR]