Article

A combined use of phase plane and handling diagram method to study the influence of tyre and vehicle characteristics on stability

Article

A combined use of phase plane and handling diagram method to study the influence of tyre and vehicle characteristics on stability

If you want to read the PDF, try requesting it from the authors.

Abstract

This paper deals with in curve vehicle lateral behaviour and is aimed to find out which vehicle physical characteristics affect significantly its stability. Two different analytical methods, one numerical (phase plane) and the other graphical (handling diagram) are discussed. The numerical model refers to the complete quadricycle, while the graphical one refers to a bicycle model. Both models take into account lateral load transfers and nonlinear Pacejka tyre road interactions. The influence of centre of mass longitudinal position, tyre cornering stiffness and front/rear roll stiffness ratio on vehicle stability are analyzed. The presented results are in good agreement with theoretical expectations about the above parameters influence, and show how some physical characteristics behave as saddle node bifurcation parameters.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... Flavio Farroni [20] proposed an improved model, a quadricycle planar model, characterized by two states referring to in-plane vehicle body motions (lateral and yaw motions). The model implements a nonlinear tire model for lateral behavior and two different analytical methods, the phase plane and the handling diagram, are applied to better analyze the in-curve vehicle lateral stability. ...
... As the extensive bibliography reveals [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], the simplified models neglect these elements or the highly nonlinear dependence of the tires with combined slip (longitudinal/lateral), temperature, or internal pressure. A local linear model can be accurate enough to analyze the behavior of the vehicle in the vicinity of the equilibrium point and at low lateral acceleration, but it is not suitable if the distance between the different equilibrium points is large or the lateral accelerations are medium or high [21]. ...
... A complex multibody model has more than two state variables but, for many systems, its stability can be analyzed using only two state variables of one body. This is the case of ground vehicles where the phase portrait describes vehicle sideslip angle (β V ) and vehicle yaw rate (ω V z ) or vehicle body side slip angle (β V ) and its changing rate (β V ) in a planar diagram [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. ...
Article
Full-text available
A new methodology for constructing stability maps (phase-plane analysis) is presented and validated for application to complex multibody vehicle models implemented in Multibody Dynamics simulation software (Adams®). Traditional methodologies are developed to be applied to explicit mathematical models. Given the complexity of some special multibody systems, particularly in vehicle dynamics, simplifications are needed to apply this stability analysis technique. The main limitation when using simplified models is the need to neglect components which could have a significant influence on the dynamic behavior of the system and therefore on its stability. In the proposed methodology it is not necessary to have access to explicit mathematical models of multibody systems. Thus, the stability map of a vehicle model can be constructed by considering highly nonlinear dynamic elements, such as tires and silent-blocks components, modeled using the nonlinear finite element technique.
... Vertical forces acting on each wheel are defined as follows [40,41]: ...
... The slip dynamic . λ from Equation (14) is substituted into (41), and it becomes: ...
Article
Full-text available
Estimation and control of wheel slip is a critical consideration in preventing loss of traction, minimizing power consumptions, and reducing soil disturbance. An approach to wheel slip estimation and control, which is robust to sensor noises and modeling imperfection, has been investigated in this study. The proposed method uses a simplified form of wheels longitudinal dynamic and the measurement of wheel and vehicle speeds to estimate and control the optimum slip. The longitudinal wheel forces were estimated using a robust sliding mode observer. A straightforward and simple interpolation method, which involves the use of Burckhardt tire model, instantaneous values of wheel slip, and the estimate of longitudinal force, was used to determine the optimum slip ratio that guarantees maximum friction coefficient between the wheel and the road surface. An integral sliding mode control strategy was also developed to force the wheel slip to track the desired optimum value. The algorithm was tested in Matlab/Simulink environment and later implemented on an autonomous electric vehicle test platform developed by the Nanjing agricultural university. Results from simulation and field tests on surfaces with different friction coefficients (μ) have proved that the algorithm can detect an abrupt change in terrain friction coefficient; it can also estimate and track the optimum slip. More so, the result has shown that the algorithm is robust to bounded variations on the weight on the wheels and rolling resistance. During simulation and field test, the system reduced the slip from non-optimal values of about 0.8 to optimal values of less than 0.2. The algorithm achieved a reduction in slip ratio by reducing the torque delivery to the wheel, which invariably leads to a reduction in wheel velocity.
... In [23], the sideslip angle-sideslip angle rate phase plane portrait analysis contributes to design a weight factor for coordinating the coupled effects of differential drive assist steering and vehicle motion. Only the vehicle velocity and tire-road friction are adopted to define the stability regions, while the influence of the front wheel steering angle is neglected thus limiting the accuracy of stability assessment [24]. Similarly, based on phase plane portrait analysis, Ref. [25] proposes a supervisory strategy for stability, handling, and energy efficiency, including a LQR controller and a rule-based torque allocation. ...
... Its main idea is to accurately determine the stable bounds offline, that is adopted in online supervising vehicle states for trading off each target via the controller. A widely used approach is the two-lines method [23][24][25], which defines the stable region by two lines crossing the saddle points in the sideslip angle-sideslip angle rate phase plane portrait. However, it still includes the unstable region that corresponds to the vehicle lateral acceleration out of the limits and is unable to accurately decide the stable bounds. ...
Article
Full-text available
A supervisory control strategy, including dynamic control supervisor, handling-stability controller, energy efficiency controller, and coordinated torque allocator, is proposed for distributed drive electric vehicles to coordinate vehicle handling, lateral stability, and energy economy performance. In the dynamic control supervisor, firstly phase plane analysis is implemented to accurately define the vehicle stability boundary so that the look-up table of bounds can be established for online application. Subsequently, based on the feedback drive conditions and vehicle states, the identified boundary is dynamically quantified by the designed varying weight factor (VWF) in real time. In the handling-stability controller, a unified yaw rate reference of VWF is developed to simultaneously guarantee vehicle manoeuvrability and lateral stabilization. Then, a novel integral triple-steps method is proposed to calculate the proper direct yaw moment for the desired vehicle motion. In the energy efficiency controller, inter-axle torque distribution map is optimized for optimal vehicle energy economy. In the coordinated torque allocator, a torque increment allocation problem is formulated and optimized to realize the desired forces, meanwhile based on VWF to minimize energy consumption and tire workload usage. The validations of proposed strategy are conducted under various manoeuvres, yielding comprehensive improvements in terms of vehicle handling, lateral stability, and energy performance.
... In recent years, with the development of tyre mechanics and nonlinear dynamics theory, the fact that the vehicle dynamics bifurcation mechanism due to nonlinear characteristics of the tyre lateral force has been basically confirmed [1][2][3]. The 2DOF vehicle model assumes that the longitudinal velocity is constant and does not consider the effect of tyre longitudinal force on the system stability [4]. ...
... = sin ( arctan ( − ( − arctan ))) , (2) where , , , and are coefficients. is the longitudinal or lateral tyre force, and is the longitudinal slip or sideslip angle. ...
Article
Full-text available
The typical method of vehicle steering bifurcation analysis is based on the nonlinear autonomous vehicle model deriving from the classic two degrees of freedom (2DOF) linear vehicle model. This method usually neglects the driving effect on steering bifurcation characteristics. However, in the steering and driving combined conditions, the tyre under different driving conditions can provide different lateral force. The steering bifurcation mechanism without the driving effect is not able to fully reveal the vehicle steering and driving bifurcation characteristics. Aiming at the aforementioned problem, this paper analyzed the vehicle steering and driving bifurcation characteristics with the consideration of driving effect. Based on the 5DOF vehicle system dynamics model with the consideration of driving effect, the 7DOF autonomous system model was established. The vehicle steering and driving bifurcation dynamic characteristics were analyzed with different driving mode and driving torque. Taking the front-wheel-drive system as an example, the dynamic evolution process of steering and driving bifurcation was analyzed by phase space, system state variables, power spectral density, and Lyapunov index. The numerical recognition results of chaos were also provided. The research results show that the driving mode and driving torque have the obvious effect on steering and driving bifurcation characteristics.
... A ( )-( ) phase-plane analysis (where is time) is carried out with a vehicle simulation model including nonlinear tire behavior and the effect of the load transfers induced by the lateral acceleration. Several combinations of and ̇ are imposed as initial conditions for the vehicle simulator, which outputs the evolution of the model states in the time domain [23]. Then these can be represented in the ̇ -plane, to identify the initial conditions from which the system response converges to an equilibrium. ...
Conference Paper
Full-text available
Many torque-vectoring controllers are based on the concurrent control of yaw rate and sideslip angle through complex multi-variable control structures. In general, the target is to continuously track a reference yaw rate, and constrain the sideslip angle to remain within thresholds that are critical for vehicle stability. To achieve this objective, this paper presents a single input single output (SISO) formulation, which varies the reference yaw rate to constrain sideslip angle. The performance of the controller is successfully validated through simulations and experimental tests on an electric vehicle prototype with four drivetrains.
... The bb -& phase plane analysis is more effective at representing the vehicle nonlinear stability characteristic than the conventional state plane method with the state variable β and the yaw velocity γ [21]. In this paper, we used a diamond shape to represent the stable area [22]. ...
Article
Full-text available
With the rapid development of intelligent transportation system, the research on vehicle stability can be a theoretical basis for realizing autonomous driving technology. Previous stability control strategies have not taken into account the tire force saturation factor, the slip rate and the robustness of the control system sufficient. According to the characteristic that the torque of each wheel can be distributed independently, a torque distribution algorithm under emergency conditions is proposed. The proposed torque distribution algorithm is constructed using three hierarchical controllers. The upper controller attempts to judge whether the vehicle is in stable state using the phase plane method. Also, it judges whether the wheels are slipping. The middle controller aims to calculate the demands for the desired traction force and yaw moment, whereas the lower controller is designed to translate those virtual signals into actual actuator commands. When designing the middle controller, a sliding mode control method is utilized to guarantee system stability and robustness by taking into account various factors, including lateral wind and sensor noise. For the lower controller, the control allocation optimization method is utilized to determine an appropriate control input for each in-wheel motor by considering the road conditions, adhesion utilization and maximum output torque of the motor. Numerical simulation studies are conducted to evaluate the performance of the torque distribution algorithm. Comparison results indicate that the proposed algorithm presents better performance to distribute the appropriate torque for each wheel and ensure the stability of the vehicle under emergency conditions.
... It is necessary to consider that system (1) should not be used for transitory analysis and the achieved results allow only qualitative considerations. In the three figures the blue lines refer to very stable conditions: in the time histories of the seven states and in the 3D plot of the car states, no oscillating behaviors can be seen (the equilibrium point appears to be a "node") [17], [18]. ...
Article
Full-text available
Nowadays, the automotive field takes care of human safety in the everyday driving. In this sense, the vehicle dynamics control systems and ADAS (Advanced Driver Assistance System) play a crucial role for both active and passive safety. In terms of handling, the critical issues for the everyday driver are during braking or steering maneuvers: the main idea of this paper is to investigate the possibility to recognize some critical behaviors leading to vehicle instability, using only the wheel sensors signals, already available as mandatory in actual passenger car (in particular for ABS). In order to do this, a seven degrees of freedom model of a vehicle that runs in a curve with constant longitudinal speed is formulated. With no particular reference to the power unit (IC motor or electrical motors), three different traction schemes configurations are considered. The numerical solutions of the model are analyzed to evaluate their stability, the associated modal shapes and the modal participation factors. A systematic analysis allows recognizing some vehicle behaviors that may constitute instability precursors useful to develop a suitable control logic. Results provided by both a standard vehicle dynamics simulation software and a "on-road" test are presented and discussed to verify the actual feasibility of the proposed precursors employment.
... Further studies characterised the transient vehicle response, first by using the single-track model, and then with the progressive introduction of more advanced simulators, e.g. including non-linear tire force characteristics and suspension elasto-kinematics [4][5][6][7][8]. ...
Article
The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied by analyzing the understeer coefficient in quasi-steady-state maneuvers. In this paper, experimental tests are performed on an electric vehicle with four independent motors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. The study presents a procedure to compute the longitudinal and lateral tire forces, which is based on a first estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the understeer coefficient, and allow to infer a relationship between the understeer coefficient and the yaw moment analysis. The handling characteristics vary with speed and front-to-rear wheel torque distribution. An apparently surprising result arises at low speed: the RWD architecture is the most understeering configuration. This is discussed by analyzing the yaw moment caused by the longitudinal forces of the front tires, which is significant for high values of lateral acceleration and steering angle.
... In stability studies of vehicle systems, this method can be used together with handling diagrams. 20,21 Sun and He 22 use this method to verify the stability of a nonlinear articulated vehicle model in single lane change maneuvers performed with open loop sinusoidal steering input. The authors compare the dynamic behavior of the proposed model with a 21 degrees of freedom (DOF) CarSim model and determine the maximum steering amplitude allowed without the occurrence of instability events. ...
Article
This article addresses the yaw stability of articulated vehicles by assessing the influence of the road-tire friction coefficient on the convergence region of a particular equilibrium condition. In addition, the boundaries of this region are compared to the boundaries of the non-jackknife and non-rollover regions to distinguish the instability phenomenon, jackknife or roll-over, responsible for this delimitation. The vehicle configuration considered in this analysis is composed by one tractor unit and one towed unit connected through an articulation point, for instance, a tractor-semitrailer combination. A nonlinear articulated bicycle model with four degrees of freedom is used together with a nonlinear lateral force tire model. To estimate the convergence region, the phase trajectory method is used. The equations of motion of the mathematical model are numerically integrated for different initial conditions in the phase plane, and the state orbits are monitored in order to verify the convergence point and the occurrence of instability events. In all cases, the longitudinal force on each tire, such as traction and braking, is not considered. The results show the existence of convergence regions delimited only by jackknife events, for low values of the friction coefficient, and only by rollover events, for high values of the friction coefficient. Moreover, the transition between these two conditions as the friction coefficient is changed is graphically presented. The main contributions of this article are the identification of the abrupt reduction of the convergence region as the value of the friction coefficient increases and the distinction of the instability events, jackknife or rollover, that define the boundaries of the convergence region.
... For the determination of the stability of the vehicle, the vehicle side slip angle and the yaw rate are generally controlled at a fixed range at home and abroad as a judgment method. 23 Based on the experience, this paper limits the vehicle side slip angle and yaw rate to a certain range. When the vehicle's side slip angle and yaw rate are within the stable boundary, the vehicle is in a stable state. ...
Article
Full-text available
To study the overall performance of the distributed drive intelligent electric vehicle (EV), a in-wheel motor drive (IWMD) vehicle is developed in this study. The configuration and 11-degrees of freedom model of IWMD EV is introduced firstly. Then, the co-simulation model of IWMD EV based on Carsim and Matlab/Simulink is established. The block design is employed for the co-simulation modelling, including the in-wheel motor model, driver model, tyre model, steering model, braking model, suspension model, aerodynamic model, and road surface model. The effectiveness and the reasonableness of the co-simulation model of IWMD EV are verified by the snake testing with on the campus road. The co-simulation model provides accuracy and reliable simulation method for the path-tracking and self-driving study of IWMD intelligent vehicle in the future.
... where the friction coefficient μ is a function of the slip λ and F Ni (N) denotes the vertical wheel reaction force applied to the wheel. According to the previous discussions in [29,30], the weight of the vehicle is transferred between the wheels during different car accelerations, hence F Ni varies at different wheels. The model force, F Ni , for the four-wheel forces can be represented as follows: ...
Article
The interaction between the tyre and the road is crucial for understanding the dynamic behaviour of a vehicle. The road–tyre friction characteristics play a key role in the design of braking, traction and stability control systems. Thus, in order to have a good performance of vehicle dynamic stability control, real-time estimation of the tyre–road friction coefficient is required. This paper presents a new development of an on-line tyre–road friction parameters estimation methodology and its implementation using both LuGre and Burckhardt tyre–road friction models. The proposed method provides the capability to observe the tyre–road friction coefficient directly using measurable signals in real-time. In the first step of our approach, the recursive least squares is employed to identify the linear parameterisation form of the Burckhardt model. The identified parameters provide, through a T–S fuzzy system, the initial values for the LuGre model. Then, a new LuGre model-based nonlinear least squares parameter estimation algorithm using the proposed static form of the LuGre to obtain the parameters of LuGre model based on recursive nonlinear optimisation of the curve fitting errors is presented. The effectiveness and performance of the algorithm are demonstrated through the real-time model simulations with different longitudinal speeds and different kinds of tyres on various road surface conditions in both Matlab/Carsim environments as well as collected data from real experiments on a commercial trailer.
... Della Rossa et al. examined bifurcations in the α f -α r plane -for a two degree-of-freedom vehicle model in [6] and a combined driver-vehicle model in [7] -using handling diagrams and phase portraits to visualise vehicle behaviour for a variety of vehicle speeds and steering angles. Farroni et al. found similar stability properties with a phase plane method using a four-wheel vehicle model and a handling diagram method using a two-wheel vehicle model [8]. ...
Article
Full-text available
Phase portraits provide control system designers strong graphical insight into nonlinear system dynamics. These plots readily display vehicle stability properties and map equilibrium point locations and movement to changing parameters and system inputs. This paper extends the usage of phase portraits in vehicle dynamics to control synthesis by illustrating the relationship between the boundaries of stable vehicle operation and the state derivative isoclines in the yaw rate–sideslip phase plane. Closed-loop phase portraits demonstrate the potential for augmenting a vehicle's open-loop dynamics through steering and braking. The paper concludes by applying phase portrait analysis to an envelope control algorithm for yaw stability and a sliding surface controller for stabilising a saddle point equilibrium in drifting.
... Since the motion of a ground vehicle is primarily determined by the friction forces transferred from roads via tyres, information about the tyre/road interaction is critical to many active vehicle safety control systems, including longitudinal control, yaw stability control and rollover prevention control systems. In particular friction formation is crucial tool for Brake Assist Systems (BAS), Electronic Stability Control (ESC-ESP) and Adaptive Cruise Control (ACC) systems that have recently become essential for active safety systems, as shown in [1][2][3][4][5][6][7][8]. For instance, in the case of adaptive cruise control, estimation of friction force enables the braking distances to be adjusted in real time. ...
Article
Driving safety can be achieved by better understanding critical situations which may require the knowledge of interaction between vehicle tyres and the road surfaces. It is thus essential to have a good estimation of the tyre/road friction forces in real-time. The paper deals with a new method for on-line estimation of tyre/road friction forces. This method provides an appropriate modelling to observe the tyre/road friction forces directly using measurable signals in realtime. In this work, we present a new mixed model-based approach using the steady state solution of the partial differential equation (PDE) form of LuGre to obtain the forces based on recursive nonlinear optimization of the curve fitting errors. Finally, real-time simulations in various conditions are provided to demonstrate the efficacy of the method. It is also compared with the well-known Pacejka tyre friction results which show the effectiveness of the proposed approach.
... The main subsystem contains all the equations describing the vehicle dynamics: the Longitudinal Balance Equation, Lateral and Yaw Vehicle Dynamics and Vertical Load Determination, taking into account load transfers by means of the handling diagram/phase plane approach described in [26] and of the influence of roll stiffness [27]. In the input/output subsystem all the model's exchange parameters with the other subsystems and in particular with the ADAS model are suitably adjusted and displayed. ...
Article
Full-text available
This paper presents some results on the development and testing of new solutions in the field of driving automation. The introduction of increasing levels of vehicle automation aimed at enhancing road safety requires a renewed approach to the research and development process and needs a multi-actor environment where the innovation can be tested. Indeed, vehicle automation spans several scientific disciplines and it is becoming exceedingly difficult and too costly for a single research innovation team to go in depth into all technologies and solutions. This is shifting the innovation process toward a multidisciplinary approach in which the only way to ensure an easy, rapid, efficient and scalable introduction of the required innovation is to adopt integrated and complex testing platforms for the simulation of automation solutions, based on a modular architecture, where independent components can be developed and then integrated and tested in a multi-actor environment. A platform for virtual testing is presented herein and employed to assess the performance of an integrated driving assistance solution based on computing appropriate surrogate measures of safety that allow for the transition between different automation logics in free-flow, car-following and emergency braking conditions.
... As shown in Figure 8 In Figure 8(a), the equilibrium point is marked with a circle, and the two saddle points are marked with asterisks. As the literature [25,28] notes, the two saddle points are the boundary points of the stable region on the abscissa. However, two limitations may exist. ...
Article
Full-text available
A multi-objective active front steering (AFS) control system considering the road adhesion constraint on vehicle stability is developed using the sliding mode control (SMC) method. First, an identification function combined with the relationship between the yaw rate and the steering angle is developed to determine whether the tyre state is linear or nonlinear. On this basis, an intervention criterion for the AFS system is proposed to improve vehicle handling and stability in emergent conditions. A sideslip angle stability domain enveloped by the upper, lower, left, and right boundaries, as well as the constraint of road adhesion coefficient, is constructed based on the phase-plane method. A dynamic weighting coefficient to coordinate the control of yaw rate and sideslip angle, and a control strategy that considers changing control objectives based on the desired yaw rate, the desired sideslip angle, and their proportional weights, are proposed for the SMC controller. Because road adhesion has a significant effect on vehicle stability and to meet the control algorithm's requirement of real-time access to vehicle states, a unscented Kalman filter-based state observer is proposed to estimate the adhesion coefficient and the required states. Finally, simulations are performed using high and low road adhesion conditions in a Matlab/Simulink environment, and the results show that the proposed AFS control system promptly intervenes according to the intervention criterion, effectively improving vehicle handling and stability.
... The TV yaw moment is directly applied as an input to the yaw moment balance equation. Several combinations of β andβ are imposed as initial conditions for the model, which is run for a high tire-road friction coefficient with constant steering wheel angle (50 • ) and vehicle speed (80 km/h) [25], [52]. This process identifies the set of initial conditions providing stable response. ...
Article
Full-text available
Electric vehicles with independently controlled drivetrains allow torque vectoring, which enhances active safety and handling qualities. This article proposes an approach for the concurrent control of yaw rate and sideslip angle based on a single-input single-output (SISO) yaw rate controller. With the SISO formulation, the reference yaw rate is first defined according to the vehicle handling requirements and is then corrected based on the actual sideslip angle. The sideslip angle contribution guarantees a prompt corrective action in critical situations such as incipient vehicle oversteer during limit cornering in low tire-road friction conditions. A design methodology in the frequency domain is discussed, including stability analysis based on the theory of switched linear systems. The performance of the control structure is assessed via: 1) phase-plane plots obtained with a nonlinear vehicle model; 2) simulations with an experimentally validated model, including multiple feedback control structures; and 3) experimental tests on an electric vehicle demonstrator along step steer maneuvers with purposely induced and controlled vehicle drift. Results show that the SISO controller allows constraining the sideslip angle within the predetermined thresholds and yields tire-road friction adaptation with all the considered feedback controllers.
... The implemented model does not only involve vehicle dynamics, but it stands for a general vehiclebehaviour model: as a matter of fact, besides the 'pure' vehicle dynamics equations, also the modelling of some other essential vehicle's components (such as engine, gearbox, braking system and others) has been performed. In order to make the vehicle dynamics model more clear and readable, it has been organized in different subsystems.The main subsystem contains all the equations describing the vehicle dynamics: Longitudinal Balance Equation, Lateral and Yaw Vehicle Dynamics and Vertical Loads Determination, taking into account load transfers by means of the handling diagram/phase plane approach described in [27] and of the influence of roll stiffness [28]. In the input/output subsystem all the model's exchange parameters with the other subsystems and in particular with ADAS model are properly adjusted and displayed. ...
Conference Paper
Full-text available
This paper presents some preliminary analyses on the development of new tools for the transport industry, able to deal with the introduction of increasing levels of vehicle automation. Driving assistance is aimed at increasing road safety, but it needs a renewed approach to the research and development process. Indeed, vehicle automation spans several scientific disciplines and it's becoming exceedingly difficult and too costly for a single research innovation team to " go deep " across all technologies and solutions. The only way to ensure an easy, fast, efficient, and scalable introduction of the required innovation is to adopt integrated and complex testing platform for the simulation of automation solutions. To this aim virtual-testing platforms should be conceived to allow different actors to work on different components, possibly at different levels of detail, any of the actors being allowed to sophisticate with a particular simulation issue (e.g. the driver behaviour in presence of Advanced Driving Assistance Systems) knowing that the other components (e.g. the vehicle dynamics) have been (or will be) simulated at the required sophistication level, possibly by another actor of the innovation process. In this paper the authors wishes to contribute to the development of these new-generation tools. Analyses will be carried out in order to identify the key opportunities and criticalities in the development of virtual testing platform for testing driving automation. From these analyses research perspectives will be identified and proposed for future developments.
... The nonlinear vehicle stability can be analyzed by the phase-plane method. 36,37 This method is an effective tool for considering vehicle system stability, and can reflect the stability of the vehicle during the under-steering or over-steering maneuvers. Furthermore, the sideslip angle and the time derivative of this angle in the phase-plane are depicted in Figure 15. ...
Article
To improve the stability of the autonomous vehicle for high speed tracking, a vehicle estimator scheme integrated into a path-tracking system has been proposed in this paper. Vehicle stability is related to road condition (low road adhesion, high road adhesion, and changing road adhesion) and vehicle state, thus a state observer has been preferred in this paper to estimate vehicle state and tire-road friction as a means of judging vehicle stabilization. For the approach to the estimation, an unscented Kalman filter (UKF) employing a three degrees-of-freedom vehicle model combined with a Magic Formula (MF) tire model was designed. As a widely used model control method, the multi-constraints model predictive control (MMPC) was proposed and that was then used to calculate the desired front steering angle for tracking the planned path. The performance of the MMPC controller, with the estimator, was evaluated by the vehicle simulation software CARSIM and Matlab/Simulink. The simulation results show that the designed MMPC controller with the estimator successfully performs path-tracking at high speed for the intelligent vehicle.
... With the development of non-linear theory and vehicle dynamics, the nature of non-linear vehicle dynamics has been basically confirmed and accepted. [1][2][3] According to the significance of the theoretical research and engineering applications, investigation of the vehicle-handling stability based on the vehicle dynamics stability region has become an important research field. ...
Article
Full-text available
Integrated control systems for vehicle-handling stability are usually based on the steering bifurcation mechanism. The best integrated control performance is obtained by coordinating different control methods. However, in vehicle steering and driving conditions, the coupling characteristics of the longitudinal forces and the lateral forces of the tyres must lead to changes in the bifurcation characteristics. The corresponding vehicle dynamics stability region has to be redetermined. The corresponding integrated control method also needs to be adjusted. Therefore, in combination with the physical significance of the dynamics equilibrium point of the vehicle system, the definition of the driving stability region of the vehicle based on the characteristics of the driving torque and the steering angle bifurcation is proposed. With the concept presented above, the five-degree-of-freedom non-linear vehicle system model for the driving stability region of the vehicle was solved. The simulation results show that, according to the driving stability region of the vehicle, the vehicle dynamics stability with different driving torque inputs and different front-wheel steering-angle inputs can be accurately estimated. The study of the driving stability region of the vehicle is beneficial for engineering applications in non-linear automotive dynamics research. In addition, it provides the theoretical basis for integrated control of the vehicle-handling stability.
... URING its real working life a tyre rolls over uneven road and the presence of irregularities generates sudden variations both in tyre position and in interaction forces direction and modulus. This aspect concerns transient performances and is usually not taken into account in vehicle dynamics modelling and simulation [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11] despite it has not a negligible influence on tyre dynamics and then on vehicle behaviour. Moreover, vehicle dynamics control systems [12], [13], [14], [15], [16], [17] are usually based on the hypothesis that the tyre is always in contact with the road and this not always verified assumption can cause their improper intervention. ...
Article
Full-text available
This paper deals with tyre enveloping behaviour on uneven road surface. To build realistic and reliable vehicle dynamics models it is of fundamental importance to study the influence of road obstacles and irregularities on forces and displacements involving a rolling tyre. After a brief review about early studies concerning this phenomenon, the tandem model with elliptical cams is introduced and described, highlighting its hypothesis and the parameters on which it is based, the most important of which are the cams profiles and the distance between them. The main aim of this paper is the executive project of a test rig aimed to carry out an experimental campaign for the identification of the parameters of the tandem cam model and for its validation. The idea is to experimentally acquire the path of the patch centre of a tyre rolling over an obstacle, to define the parameters of the curves employed for the cam profiles and the distance between them in the tandem model. It is important to highlight that these parameters are strictly connected to tyre properties and need tests to be investigated and identified. The design started from a test bench for motorcycles already available at DII’s Tyre Lab, introducing proper changes without compromising original test bench destination. © 2016, International Association of Engineers. All rights reserved.
... Since the motion of a ground vehicle is primarily determined by the friction forces transferred from roads via tyres, information about the tyre/road interaction is critical to many active vehicle safety control systems, including longitudinal control, yaw stability control and rollover prevention control systems. In particular friction formation is crucial tool for Brake Assist Systems (BAS), Electronic Stability Control (ESC-ESP) and Adaptive Cruise Control (ACC) systems that have recently become essential for active safety systems, as shown in Sharifzadeh et al. (2014a); Farroni et al. (2014bFarroni et al. ( , 2013 . For instance, in the case of adaptive cruise control, estimation of friction coefficient (µ) enables the braking distances to be adjusted in real time. ...
Article
Full-text available
Driving safety can be achieved by better understanding critical situations which may require the knowledge of interaction between vehicle tyres and the road surfaces. It is thus essential to have a good estimation of the tyre/road friction parameters in real-time. The paper deals with the trust-region based method for on-line estimation of tyre/road friction parameters. This method provides an appropriate modeling (of a vehicle and the tyre/road contact) to observe the tyre/road friction coefficients directly using measurable signals in real-time. In this work, we present a new LuGre model-based nonlinear least squares (NLLS) parameter estimation algorithm using vehicle dynamic to obtain the parameters of LuGre model based on recursive nonlinear optimization of the curve fitting errors. The proposed estimation method can also be utilized in large-scale problems with similar conditions. Very promising results have been obtained in real-time simulations for most of the driving and road situations.
... Since the motion of a ground vehicle is primarily determined by the friction forces transferred from roads via tyres, information about the tyre/road interaction is critical to many active vehicle safety control systems, including longitudinal control, yaw stability control and rollover prevention control systems. In particular friction formation is crucial tool for Brake Assist Systems (BAS), Electronic Stability Control (ESC-ESP) and Adaptive Cruise Control (ACC) systems that have recently become essential for active safety systems, as shown in Sharifzadeh et al. (2014a); Farroni et al. (2014bFarroni et al. ( , 2013 . For instance, in the case of adaptive cruise control, estimation of friction coefficient (µ) enables the braking distances to be adjusted in real time. ...
Conference Paper
Driving safety can be achieved by better understanding critical situations which may require the knowledge of interaction between vehicle tyres and the road surfaces. It is thus essential to have a good estimation of the tyre/road friction parameters in real-time. The paper deals with the trust-region based method for on-line estimation of tyre/road friction parameters. This method provides an appropriate modeling (of a vehicle and the tyre/road contact) to observe the tyre/road friction coefficients directly using measurable signals in real-time. In this work, we present a new LuGre model-based nonlinear least squares (NLLS) parameter estimation algorithm using vehicle dynamic to obtain the parameters of LuGre model based on recursive nonlinear optimization of the curve fitting errors. The proposed estimation method can also be utilized in large-scale problems with similar conditions. Very promising results have been obtained in real-time simulations for most of the driving and road situations. Link: https://ifac.papercept.net/conferences/scripts/abstract.pl?ConfID=213&Number=81
... For the determination of the stability of the vehicle, the vehicle side slip angle and the yaw rate are generally controlled at a fixed range at home and abroad as a judgment method. 23 Based on the experience, this paper limits the vehicle side slip angle and yaw rate to a certain range. When the vehicle's side slip angle and yaw rate are within the stable boundary, the vehicle is in a stable state. ...
Article
The torque distribution strategy of distributed drive electric vehicle is only aimed at safety or economy. A multi-target coordinated control method considering stability and economy is proposed to solve the problem of single torque distribution target, which consists of a coordination decision controller, a high-level motion controller, and a low-level allocation controller. The coordination decision controller based on the phase plane method determines whether to adopt a stability or economic control strategy. The high-level motion controller consists of a bicycle model with 2 degree of freedom, a speed tracking controller, a stability controller, and an economic controller to calculate the desired direct yaw moment of the four in-wheel motors. The stability controller based on the fuzzy algorithm tracks the desired vehicle side slip angle and yaw rate calculated by the bicycle model with 2 degree of freedom to control vehicle stability. The economical controller based on a multi-motor loss model optimizes the efficiency of the vehicle’s drive system. The low-level allocation controller is presented to provide optimally distributed torques for each wheel. Finally, the simulation and hardware-in-the-loop testing show that the coordinated control strategy can effectively improve the stability and economy of the distributed drive electric vehicle.
... The precision of the obtained results is highly affected by the degree of complexity of the employed model, that is by the reliability of the physical and geometrical parameters inserted in the model, like the vehicle's characteristic lengths and dimensions, its inertial features, transmission ratios, tyres' behavior parameters and so on [17]. ...
Conference Paper
Full-text available
Accurate measurement of the vehicle sideslip angle is fundamental to improve reliability of the vehicle dynamics control systems focused on stability and developed both for safety and performance optimization. Many experimental procedures to estimate the vehicle sideslip angle have been proposed in the last years, mainly based on GPS, INS and physical models. The aim of this paper is to compare different methods to estimate sideslip angle employing an instrumented vehicle, equipped with a system for data acquisition and time-synchronized storage capabilities, a stand-alone GPS, a GPS aided MEMS-based Attitude and Heading Reference System (AHRS) and specific sensors to collect data on the steering wheel angle and on the position of brake, throttle and clutch pedals. Further information is collected by capturing the available data at the OBD port of the vehicle. Data acquisitions (from all sensors) are synchronized by means of an external triggering signal. After driving sessions performed with specific manoeuvres in order to highlight the main phenomena concerned with the dynamic behaviour of the vehicle, the different estimation procedures have been applied, discussing on the advantages and the degree of reliability of each one of them.
... The literature [25][26] analyzed the influence of sideslip angle on the vehicle stability through the phase plane and gave the criteria for judging the vehicle stability. 23 1 CC   The above stability judgment criteria are obtained through simplified analysis of vehicle models or based on experience. ...
Article
Full-text available
For four-wheel independent drive intelligent vehicle, the Model Predictive Control (MPC) is adopted to design the trajectory tracking controller through active steering and four-wheel independent drive/brake. The control objective is to follow a desired trajectory while taking into account the control actuator constraints and vehicle dynamic stability constraints. To reduce the computational complexity, a linear time-varying model predictive controller is designed to linearize the nonlinear vehicle model locally at each sampling point. The co-simulation of CarSim/Simulink shows that the designed controller has high tracking accuracy on the basis of ensuring vehicle stability and strong robustness to vehicle velocity and road adhesion coefficient. The trajectory tracking accuracy based on MPC is better than that of the preview driver model (PDM).
... The tire slip control method presented in [13][14][15][16][17] is commonly used for actuator constraints but cannot present vehicle stability property. While the stability boundary method based on the phase plane adopted in [19][20][21][22][23][24] is affected by many factors (e.g., model simplification, uncertainties of vehicle parameters, and road friction coefficient error [20,27]). Inaccurate information will lead to unreliable boundaries and control action may not be taken in time, resulting in vehicle instability [28]. ...
Article
Full-text available
In order to make full use of the direct yaw control (DYC) in electric vehicles with four in-wheel motors (IWMs), this paper presents an adaptive SMC control scheme to improve the handling and stability based on a novel stability index proposed to quantitatively represent stability level. Firstly, a vehicle stability evaluation method is designed based on the front and rear tire slip angles phase plane and the quantitative stability index is derived according to the area where the states stay and the changing trend of the states. Secondly, a sliding mode controller (SMC) is designed to track the reference obtained by a two degrees of freedom (DoF) vehicle model as the desired vehicle motion. To enhance both vehicle handling and stability, the weight of the sliding surface is adaptively scheduled according to this stability index. The torque of each wheel is then distributed by solving the optimal adhesion rate consumption problem. Finally, the effectiveness of the proposed method is verified by CarSim–Simulink co-simulation. The simulation results illustrate that the proposed method can effectively improve vehicle handling and stability and has good robustness for the uncertainties of vehicle sideslip angle and road friction coefficient.
... Farroni et al. aimed to find out which physical vehicle characteristics affect the stability of incurve vehicles significantly. For their phase plan method the quadricycle vehicle model was used together with Pacejka's tire model [11]. ...
Conference Paper
In recent years the number of electronic systems dramatically increased in vehicles. In the field of autonomous braking the Electronic Stability Control (ESC) is one of the most important braking functions. Two of the biggest challenges of the development of ESC are the validity of the inputs and logic of the intervention. In this paper the initial results of a new phase plane-based approach are introduced. This approach can be the base of a wide spectrum of vehicle dynamic application but from ESC point of view it can be used for detecting critical driving maneuvers and for monitoring of inertia sensors plausibility. The main advantage of the phase-based method is that it can decrease the number of necessary vehicle dependent parameters during the detection of critical driving situations and sensor plausibility problems. In the article simulation results are presented to highlight the advantage of the proposed approach. The results show that our phase plane method can be used in the development of ESC in the future.
... Sadri and Wu [10] introduced a new method based on the Lyapunov exponent for lateral region estimation and discussed changes in the system and structural stabilities caused by changes in the vehicle parameters and driving conditions. Farroni et al. [11] analysed the effects of the centroid position, tire cornering stiffness, and front and rear roll stiffness on the lateral stability of a vehicle traveling on a curve based on the phase-plane method. ...
Article
Full-text available
This study aimed to develop a coach state estimation and prediction system to enhance driving safety. Different from existing vehicle stability estimation studies, the authors propose a hybrid method to estimate and predict the state of a coach in real time. First, the vehicle sideslip angle and yaw rate are estimated by a three‐degrees‐of‐freedom vehicle model combined with an extended Kalman filter (EKF) estimation algorithm. Then, a steering system is established that replaces the front‐wheel angle with the steering wheel input torque. Next, a seven‐degrees‐of‐freedom vehicle model analyses the effects of various driving influencing factors on the vehicle sideslip angle and the boundary of the stable region of the phase plane of the vehicle sideslip angle rate, and a boundary value parameter database is obtained. A back propagation neural network (BPNN) model is then established to obtain the boundary function parameter values under multifactor coupling conditions. Furthermore, an online prediction of the steering wheel input torque in a time series is done, and the prediction value is input to the steering system and neural network model. The effectiveness of the proposed method was evaluated via simulations based on MATLAB/Simulink and TruckSim software.
... One of the earliest investigations using phase portraits and equilibrium analysis was made by Sachs and Singh (1977); a two-state model with a cubic functions for lateral tyre forces is used, which resulted in a phase portrait showing the unstable saddle points, as well as unstable foci in the β-r plane. The unstable foci were also reported later by Farroni et al. (2013) and Nguyen et al. (2009), using 2 DOF four-wheel models. Inagaki et al. (1995) used phase portraits of a two-state four-wheel model and explained the stability of the vehicle on the dynamic equilibria. ...
Thesis
Full-text available
This study looks into the handling limit condition from a rather innovative perspective, by making use of an assumption, namely the independent wheel actuation. This assumption is recently becoming more relevant to the vehicle dynamics, as the electrified vehicles with in-wheel motors are getting a more common type of passenger vehicles. The focus of this research is on passenger vehicles moving at high-speed around the handling limit. Handling limit refers to the condition where the tyre forces reach their maximum value in a particular direction. This conditions is well-observed in the practice of drifting, as performed by highly-skilled drivers, which narrows down the focus of this work to those manoeuvres. The ultimate goal of this study is providing the analysis and guidelines on how the vehicle behaviour changes with different slips under the tyres when the vehicle starts to slide. First, a thorough planar motion analysis is performed, using a simplified vehicle model and the general behaviour of the vehicle is evaluated. An effective method for path-tracking control of the vehicle is studied and further developed. A qualitative metric to measure the amount of drifting in vehicle is suggested in a mathematical form, based on the quantitative descriptions about drifting. In the next stage, a four-wheel model with 7 degrees of freedom is introduced and validated for use in vehicle sliding analysis. To capture the nonlinear behaviour of the tyre forces, an elliptic tyre model is introduced for the combined-slip conditions. The model is then used to analyse the drifting manoeuvres. Drifting is studied in detail, in terms of dynamic equilibria and stability. The four-wheel vehicle model is used to calculate the dynamic equilibria in planar motion, numerically, by introducing an assumption on constant longitudinal tyre slips. This assumption enables studying the system effectively with three state variables. Other than the unstable drifting points that were reported by previous researchers, a new pair of drifting equilibria are identified and the difference of the two types is studied. The phase portrait approach is used to identify the type of these equilibria. The two-by-two phase portraits reveal the type of instability in the primary and the secondary drifting points and provide control suggestions to stabilise the drifting equilibria. Finally, general remarks on using the primary drifting for path-tracking during drifting are stated. Full-text available at: https://researchrepository.rmit.edu.au/discovery/delivery?vid=61RMIT_INST:ResearchRepository&repId=12268692140001341#13268692130001341
... which can be rearranged for _ b, obtaining Eq. 8. This means that the M z;TC contribution prevents b from excessively increasing/decreasing, which is an indicator of potential incipient loss of vehicle stability [41]. ...
Article
Full-text available
A key feature achievable by electric vehicles with multiple motors is torque-vectoring. Many control techniques have been developed to harness torque-vectoring in order to improve vehicle safety and energy efficiency. The majority of the existing contributions only deal with specific aspects of torque-vectoring. This paper presents an integrated approach allowing a smooth coordination among the main blocks that constitute a torque-vectoring control framework: (1) a reference generator, that defines target yaw rate and sideslip angle; (2) a high level controller, that works out the required total torque and yaw moment at the vehicle level; (3) a low level controller, that maps the required force and yaw moment into individual wheel torque demands. In this framework, the driver can select one among a number of driving modes that allow to change the vehicle cornering response and, as a second priority, maximise energy efficiency. For the first time, the selectable driving modes include an “Energy efficiency” mode that uses torque-vectoring to prioritise the maximisation of the vehicle energy efficiency, thus further increasing the vehicle driving range. Simulation results show the effectiveness of the proposed framework on an experimentally validated 14 degrees of freedom vehicle model.
... Due to high height of the center of gravity, SUVs have higher probability of instability than the other vehicles [1]. The influence of center of mass longitudinal position, tire cornering stiffness and front/rear roll stiffness ratio on the vehicle stability analyzed by Farroni et al. [2]. Hisaoka et al. [3] discussed an analysis of driver-vehicle behavior during braking in turns. ...
Article
Full-text available
In this study, the vehicle's dynamic behavior during braking and steering input is investigated by considering the quarter-car model. The case study for this research is a Sport-Utility Vehicle (SUV) with the anti-lock braking system (ABS) and nonlinear dynamic equations are considered for it along with Pacejka tire model. Regulating the wheel slip ratio in the optimal value for different conditions of the road surface (dry, wet and icy) during braking is considered as the ABS control strategy. In order to regulating the wheel slip ratio in the optimal value, an intelligent adaptive fuzzy controller that can perform online parameter estimation is considered. In this regard, the proposed controller tracks the optimal wheel slip ratio with changing the condition of the road surface from dry to wet and icy. The adaptive fuzzy controller consists of linguistic base, inference engine and defuzzifier section. The wheel slip ratio and vehicle longitudinal acceleration are selected as inputs of the controller, controller adapter and detector of the road surface condition. During braking and steering input, effective parameters of the wheel that are affected on the vehicle's dynamic behavior and its stability are investigated.
Article
In this paper, a two-stage expectation stability controller was proposed for driving stability of four wheel independent drive electric vehicles. The proposed controller has three levels. There were three steps to the stability control of the vehicle. First, the three-dimensional state portraits were drawn based on the 14DOFs vehicle model and used the s tem equation to find two-stage expectation. The surface was derived from the analysis of the tire-road adhesion divides the portraits into safe areas and unsafe areas. Second, the stability controller with sliding mode algorithm was designed. When the state parameter is in the unsafe areas, the safe boundary surface is taken as the first-stage expectation; after the system enters the safe areas, the stem is taken as the second-stage expectation. Then the fuzzy algorithm is applied to distribute the control demand of yaw moment to generate the torques of each in-wheel motor. Finally, simulation verification is performed in Simulink-CarSim co-simulation environment. The simulation results show that the designed control strategy can improve the lateral stability while the loss of longitudinal speed is within 3.25%.
Article
The classical conclusions about the vehicle stability are usually drawn from the 2-DOF vehicle model. As more and more researchers begin to explore the complex dynamic characteristics of nonlinear and high degrees of freedom vehicle plane motion system, it is of value to intuitively reveal the global dynamic characteristics by objective quantitative indicators. Moreover, a new quantitative indicator, dissipation of energy, was proposed in 2021, and it is also worth further analyzing its rationality. For the above purposes, first of all, this paper briefly introduces the difference between the 2-DOF model and the high degree of freedom (≥3) model based on previous work. Secondly, this paper objectively discusses the stability characteristics of high degrees of freedom vehicle system from different aspects (dissipation of energy, longitudinal velocity, tire sideslip angle, convergence time) for the first time. In addition, the relationship between each indicator is systematically compared with the dissipation of energy, and their advantages and disadvantages are explained. Therefore, the main contributions of this paper are as follows: (1) This paper supplements previous conclusions on the dynamic characteristics of high-DOF vehicle plane motion system and helps researchers better understand the global dynamic characteristics from different perspectives. (2) This paper supplements previous discussions on the rationality and effectiveness of dissipation of energy method, and objectively reveals the relationship between dissipation of energy and stability. (3) This paper establishes a link between qualitative and quantitative methods. The vehicle system dynamics characteristics are presented from a variety of quantitative perspectives for the first time, supplementing the relevant research in the field of dynamics quantitative indicators.
Article
Vehicle driving stability is the basis of chassis integrated control and automatic driving. In this paper, we construct an 18 degrees of freedom (DOF) unified dynamics model of vehicle chassis. The unified dynamics model includes three subsystems: steering subsystem, brake subsystem and suspension subsystem, in which the coupling relationships among the three subsystems above are considered. Combined with phase plane analysis method, choosing the sideslip angle of vehicle center of gravity (c.g.) and yaw rate as the evaluation indexes, the influences of front wheel steering angle, road adhesion coefficient, braking mode of front and rear wheels and initial speed on vehicle driving stability are analyzed. In particular, phase plane and bifurcation analysis methods are used to study the influence of uneven road on vehicle driving stability, which has not been reported yet. The main contribution of this paper is to make a comprehensive analysis of the vehicle driving stability by the 18-DOF model above. Through the comprehensive simulation analysis of the above factors by Matlab/Simulink, we can fully grasp the driving stability law of the vehicle under different working conditions. With the above analysis method, the stability of various control systems designed for vehicle chassis can be evaluated more objectively.
Article
In the research of vehicle handling stability, it is important to analyze the vehicle driving stability region based on the driving torque and the front wheel steering angle bifurcation characteristics. Therefore, further simplifying and optimizing the method of solving the vehicle driving stability region is very useful. This paper proposes a new method for solving driving stability region based on dissipation of energy for the first time. This method has clear physical significance, and has a lot of advantages comparing with the classic methods: (1) The dissipation of energy is a quantitative indicator. (2) The calculation equation is simpler, and the calculation process is more intuitive. (3) This method is easier to expand, such as solving the driving stability region for higher degrees of freedom model.
Article
This paper proposes the dissipation of the energy analysis approach for vehicle plane motion stability analysis. The vehicle uses a three-degree-of-freedom vehicle model, and a unified tire-sideslip-angle model suitable for large tire-sideslip-angle and wheel reverse rotation conditions. Two calculation methods of total dissipation of energy are proposed: the integral calculation method and the energy difference calculation method. This paper analyses the system stability of the vehicle model, using the total dissipation of the energy indicator and compares the results with the Lyapunov exponent indicator. It shows that the dissipation of the energy analysis approach has a fast calculation speed, strong interpretability and high calculation accuracy, which can intuitively and quantitatively reveal the global stability characteristics of vehicle plane motion.
Article
Full-text available
The vehicle sideslip angle is an important variable that contains information concerning the directional behaviour and stability of vehicles. As a consequence, it represents a very functional feedback for all the actual vehicle dynamics control systems. Since the measurement of the sideslip angle is expensive and unsuitable for common vehicles, its estimation is nowadays an important task. To this aim, several approaches have been adopted and the limits due to the nonlinear nature of the vehicle system are emerged. In order to overcome these limits, this paper focuses on an alternative nonlinear estimation method based on the State-Dependent-Riccati-Equation (SDRE). The technique is able to fully take into account the system nonlinearities and the measurement noise. A single track vehicle model has been employed for the synthesis of the estimator. Simulations have been conducted and comparisons with the largely used Extended Kalman Filter (EKF) are illustrated. Performance of the estimator have subsequently been verified by means of experimental data acquired with an instrumented vehicle. The results show the effectiveness of the SDRE based technique, able to give an estimated sideslip angle fully in accordance with the measured one.
Article
The dynamics of automated vehicles are studied and the existence and stability of steady state cornering maneuvers are investigated. Utilizing tools from analytical mechanics, namely the Appellian approach, vehicle models are constructed which incorporate geometrical nonlinearities and differentiate between front wheel drive (FWD) and rear wheel drive (RWD) automobiles. The dynamics of these models are studied using bifurcation analysis. Stable and unstable steady states are mapped out as a function of speed and steering angle. It is demonstrated that RWD and FWD vehicles exhibit different behavior, especially when they operate close to their handling limits. The theoretical results are verified experimentally using an automated vehicle performing safety critical maneuvers.
Article
A coordination control strategy based on stability judgment is presented for autonomous vehicles (AVs) aiming to enhance the handling and stability performance. Firstly, the stability judgment scheme is used to evaluate the real-time stability level of vehicles based on the Self-Organizing Feature Map (SOFM) neural network and K-Means algorithm. Secondly, a coordination controller of active front steering (AFS) and direct yaw moment control (DYC) is designed to track the desired vehicle motion. To enhance the handling and stability of AVs, the weights of AFS and DYC controllers are adaptively adjusted according to the vehicle stability level. Finally, the effectiveness of the proposed method is verified in co-simulation environment of CarSim and Simulink, and a rapid control prototyping test is implemented to evaluate the feasibility and robustness. The results indicate that the stability judgment scheme and coordination control strategy for AVs can not only satisfy the requirements of path tracking accuracy but also enhance the handling and stability performance.
Chapter
Vehicle safety is of a fundamental importance in the automotive industry and, with an increasing level of automation, the impact of vehicles on the global environment has to be investigated from a totality of different perspectives starting from pollution impact objectives up to the vehicle risk-prevention capabilities. For this reason, the state estimation techniques and the advanced control logics have being developed in recent years with the aim of improving the safety of the semi-automated vehicles, able to assist the driver in emergency situations minimizing the connected risks. Furthermore, the vehicle stability topic has acquired more interest since it could allow to pre-determine the vehicle stability and maneuverability regions, optimizing both the real-time computational efficiency of the control-related logics and the correct identification of the optimum vehicle operating boundaries in completely different use scenarios. Since a vehicle is a strongly nonlinear system mainly because of tyres behaviour, the methodology able to adequately determine the stability region becomes crucial. Starting from a specific literature survey, this work aims to investigate control-oriented approaches, employing the local stability criteria method, able to determine stability regions within the system phase-plane potentially adoptable in a computationally-efficient vehicle onboard logic. The techniques presented and the sensitivity analyses conducted highlight which should be the research directions in this field to remove several not-negligible but yet present assumptions in the literature.
Article
The mechanism of vehicle dynamics steering bifurcation has almost been confirmed. But the present steering bifurcation mechanism cannot explain the bifurcation phenomena caused by the driving torque. As a result, the vehicle coupled bifurcation analysis of the steering angle and driving torque has not been studied. Based on the five degrees of freedom (5DOF) vehicle system dynamics model with driving torque involved, the vehicle dynamics equilibriums under different driving torque and driving mode were searched by a hybrid method in this paper. The hybrid method combined the real-coded Genetic Algorithm with Quasi-Newton gradient method. According to the definition of static bifurcation of nonlinear systems, the equilibrium bifurcation of 5DOF vehicle system was confirmed. Then, the 5DOF vehicle system model was transformed into autonomous equation with the front wheel steering angle as intermediate variable. From the two aspects of constant steering angle amplitude and constant driving torque, the bifurcation diagrams of different driving mode were calculated. The vehicle coupled bifurcation characteristics of steering angle and driving torque were analyzed. The results show that the values of the driving torque will directly affect the bifurcation characteristics of vehicle dynamics system. The coupled feature of the front wheel steering angle and driving torque effect on vehicle bifurcation is obvious.
Article
An adaptive-prediction-horizon model prediction control-based path tracking controller for a four-wheel independent control electric vehicle is designed. Unlike traditional model prediction control with fixed prediction horizon, this paper devotes to satisfy the varied path tracking demand by adjusting online the prediction horizon of model prediction control according to its effect on vehicle dynamic characteristics. Vehicle dynamic stability quantized with the vehicle sideslip-feature phase plane is preferentially considered in the prediction horizon adjustment. For stability during switching prediction horizon and for robustness during path tracking, the numerical problem inherent in the adaptive-prediction-horizon model prediction control is analysed and solved by introducing exponentially decreasing weight. Subsequently, the desired motion for path tracking with the four-wheel independent control electric vehicle is realized with a hierarchical control structure. Simulation results finally illustrate the effectiveness of the proposed method.
Article
A new method is proposed to estimate and analyze the vehicle lateral stability region, which provides a direct and intuitive demonstration for the safety and stability control of ground vehicles. Based on a four-wheel vehicle model and a nonlinear two-dimensional (2D) analytical LuGre tire model, a local linearization method is applied to estimate the vehicle lateral stability regions by analyzing the vehicle stability at each operation point on a phase plane, which includes but not limited to the equilibrium points. As the collections of all the locally stable operation points, the estimated stability regions are conservative because both vehicle and tire stability are simultaneously considered, which are especially important for characterizing the stability features of highly/fully automated ground vehicles (AGV). The obtained lateral stability regions can be well explained by the vehicle characteristics of oversteering and understeering in the context of vehicle handling stability. The impacts of vehicle lateral load transfer, longitudinal velocity, tire-road friction coefficient, and steering angle on the estimated stability regions are presented and discussed. To validate the correctness of the estimated stability regions, a case study by matlab/simulink and CarSim® co-simulation is presented and discussed.
Article
The differential drive assist steering (DDAS) system improves the handiness of steering by torque difference between two-side wheels. However, the DDAS and the vehicle stability control (VSC) will interfere with each other due to the same actuators. This paper proposes a hierarchical coordination control approach for the DDAS and VSC. The system is divided into four layers: the parameter estimation layer, the control region division layer, the coordination decision layer, and the control allocation layer. In the control region division layer, the stable area is firstly determined on the β-β <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">·</sup> phase portrait, and the coordinated control region is obtained by applying the simulated annealing algorithm inwardly and outwardly to the boundary of the stable area. In the coordination decision layer, the direct control strategy of steering hand wheel torque is used to establish the controller of the DDAS based on the fuzzy adaptive PID algorithm. At the same time, the controller of yaw moment is established based on the sliding mode control theory. In the stable region, the DDAS works separately. The VSC works separately in the unstable region. In the coordination region, the Sigmoid function is used to adjust the weight coefficient of the DDAS dynamically. Besides, the control allocation layer includes torque distribution controller and vehicle slip ratio controller. Finally, the vehicle model is established in CarSim, the control strategy, and the wheel motor model are established in Simulink. The joint simulation results of several typical conditions show that the designed control strategy can improve the handling stability of the vehicle effectively while DDAS working even in severe driving condition.
Article
Active front steering (AFS), as an effective active technology, can enhance the handling stability of the emergency rescue vehicle. In order to deal with the shortcomings of full AFS intervention for the vehicle, the intervention criterion and control strategy of AFS system for the emergency rescue vehicle are studied deeply. Based on the phase plane theory, the double-line and yaw rate methods are combined to construct the closed polygonal stable area of the vehicle Depending on whether the vehicle status is outside the closed polygonal stable area, the AFS intervention criterion is proposed. Taking the yaw rate and the sideslip angle of the vehicle as the control targets, a sliding mode control (SMC) controller for the AFS system of the emergency rescue vehicle is designed based on the variable structure theory, and the extended Kalman filter (EKF) state observer is introduced to estimate the vehicle sideslip angle. Based on Matlab/Simulink software, the intervention criterion and control strategy of AFS system are simulated and analyzed. In addition, the self-developed fire rescue prototype vehicle is selected as the experimental vehicle, and the proposed AFS intervention criterion and control strategy is tested. The simulation and experimental results showed that the proposed AFS control strategy with the intervention criterion is reasonable and effective, and it improves the handling stability of the emergency rescue vehicle.
Article
Full-text available
In this article, a logic for vehicle dynamics control during partial braking while turning a corner is presented, which only requires knowledge of the instantaneous speed of the four wheels. For this reason, the proposed control algorithm can be adopted on all ABS equipped cars. A scheme of the simulation program for logic validation is described, which is constituted by a loop of software models of the principal vehicle subsystems which are singly illustrated. The proposed logic has been tested both in closed and open-loop maneuvers. The results are provided in the form of time histories of the principal analyzed quantities. The analysis of the results confirms the goodness of the proposed control strategy.
Conference Paper
Full-text available
In vehicle dynamics, active control is often necessary to extend the open-loop stability range in critic or hard road conditions. Active control of steering angle results in an extension of car stability and safety. In this paper, an adaptive minimal control synthesis algorithm is proposed for active steering. This method offers an efficient way of solving control problem strongly affected by parametric and modelling uncertainties, as in our case of study, where tire-force characteristics, modelled with the "magic formula", are not known a priori. The control action is synthesized starting from a bifurcation analysis of the open-loop nonlinear plant. The effectiveness of the proposed method is tested through numerical simulation of the time-trajectories and the numerical continuation of the steady-state behaviour of the closed-loop vehicle.
Article
In this new paperback edition of Tyre and Vehicle Dynamics, theory is supported by practical and experimental evidence. Pacejka provides both basic and advanced explanations of the pneumatic tyre and its impact on vehicle dynamic performance. The book shows the way in which tyre models are incorporated in vehicle models and how important tyre influence is on overall vehicle behaviour. Those working in any industry involving equipment with tyres will continue to find this book both extremely relevant and useful. * Written by a world expert in tyre dynamics * Covers both basic and advanced tyre modelling and simulation, including case studies of application examples and chapter exercises * Indispensable for any engineer working in vehicle system dynamics and for any industry involving equipment with tyres.
Article
In this paper a sliding-mode yaw moment controller and fuzzy logic wheel slip controller are proposed to enhance vehicle stability in a split-μ manoeuvre. The proposed wheel slip controller shows good performance in improving vehicle handling in a braking manoeuvre. However, when a braking manoeuvre was conducted under the split-μ condition, the yaw moment generated by the asymmetric braking forces may cause the vehicle-handling stability to deteriorate. The sliding-mode yaw moment controller was introduced to regulate the wheel slip controller to improve the vehicle-handling performance. A target slip allocation algorithm was employed to coordinate the control conflict between the anti-lock braking system and vehicle stability control. First, the proposed control system was evaluated through pure computer simulation and a hardware in-the-loop simulation system. Then an experimental test was also introduced to verify the effectiveness of the proposed control system.
Article
In this article, the problems of dynamics and stability for vehicle planar motion systems have been investigated. By introducing a so-called joint-point locus approach, equilibria of the system and their associated stability properties are given geometrically. With this method, it is discovered that the difference between the front and the rear steering angles plays a key role in vehicle system dynamics and that the topological structure of the phase portrait and the types of bifurcations are different from those published previously. In particular, the vehicle system could still be stabilized even when pushed to work in a certain severely nonlinear region, by applying extremely large steering angles. However, it is worth noticing that the attractive domain of the stable equilibrium is very narrow. These developments might prove to be important in active steering control design. Numerical experiments are carried out to illustrate the potentials of the proposed techniques.
Article
An approximate method is presented which produces a handling diagram useful for the study of steady-state turning behaviour at different values of steer angle, path radius and speed In three successive parts the steady state response of simple and more elaborate vehicle models and the stability of the resulting motion are discussed.
Article
This paper presents a semi-active differential, magneto-rheological fluid limited slip differential, which allows us to bias the torque between the driving wheels. It is based on the magneto-rheological fluid employment, by which it is possible to change, in a controlled manner, the internal friction torque and, consequently, the torque bias ratio. This device is an adaptive one and allows us to obtain an asymmetric torque distribution in order to improve vehicle handling. The device modelling and the control algorithm, realised for this activity, are described. The illustrated results highlight the advantages that are attainable regarding directional behaviour, stability, and traction.
Article
The paper gives an introductory treatment of the handling, stability and vibrating behaviour of two-axle, two-track single unit road vehicles in combined lateral and yaw directions. The treatment is divided into two chapters. The first deals with the steady-state cornering behaviour and properties of disturbed motions. The chapter starts out with a discussion of tyre force and moment generation properties. The second chapter deals with the vibrations of front wheel assemblies. An extensive discussion is given of the in-plane and out-of-plane tyre dynamic behaviour. Unstable shimmy motions and forced wheel vibrations illustrate the problem area.
This paper is to investigate the motion and stability of a four-wheel-steering (4WS) vehicle with the nonlinearity of the lateral tyre forces, and the effects of the steering mechanism are considered as well. A new nonlinear model is developed for the steady state motion of the vehicle. The stability of a typical steady state motion generated by the model is also presented with application of bifurcation method. It is demonstrated in the paper that Hopf bifurcation of the steady state motion of the 4WS vehicle is evident.
Article
The dynamic stability of a vehicle depends on various maneuvering features, such as traction, braking, and cornering. This study presents nonlinear vehicle models for estimating the stability region and simulating the dynamic behavior of a vehicle. Two types of vehicle models were found by considering the degrees of freedom and linearity. A simple model with nonlinear tire dynamics is useful for determining the stability region, while a complex model (a multi-body dynamic model in MSC.ADAMS) is appropriate for carrying out accurate simulations. Actual data for a mid-sized passenger car were used, and the models were validated by comparison with test results. Key wordsVehicle stability-Nonlinear tire dynamics-Vehicle modeling-Model validation-MSC.ADAMS
Article
This paper reports a method for the stability analysis of the steady curving of vehicles based on equations of motion that are obtained using multibody dynamics. The use of multibody dynamics techniques allows the systematic accurate analysis of vehicle dynamics in complex scenarios. However, stability analyses of vehicles are much more complicated than the use of conventional vehicle dynamics methods. The use of global coordinates and rotational parameters for the bodies involved implies the description of steady motions of the vehicle as periodic orbits rather than equilibrium points in the coordinate space. As a result, stability analyses must rely on Floquet’s theory instead of simple eigenvalue analyses of linearized equations. In practice, applying Floquet’s theory to large multibody systems involves very high computational costs. This paper reports an alternative stability analysis method based on two coordinate projections and a special eigenvalue analysis of differential algebraic equations. With this method, steady circular motions can be described in terms of equilibrium points rather than periodic motions. Stability analyses are thus made much more simple and computationally efficient. By way of example, the method was applied to a simple wheeled mechanism. The numerical results thus obtained were consistent with those of analytical and classical theories, which testifies to the accuracy of the proposed method.
Article
This paper describes the development of side slip angle-based vehicle stability control (VSC) schemes and the evaluation of the control schemes on a virtual test track. A differential braking control law based on vehicle planar motion has been designed using a three-degree-of-freedom yaw plane vehicle model. The control threshold for the VSC is designed based on the vehicle body side slip angle. Since VSC always works with the driver, the overall vehicle performance will depend not on how well the VSC works but rather on its interaction with the human driver. Vehicle behavior and interactions between the vehicle, the controller, and the human driver are investigated using a vehicle simulator on a virtual test track (VTT). The VTT consists of a real-time vehicle simulator, a visual animation engine, a visual display, and human-vehicle interfaces. The VTT has been developed and used for the evaluation of the VSC under various realistic conditions in the laboratory. In this paper, the effects of the different control threshold on the vehicle-driver-controller interaction for a novice and expert driver are compared. Test results obtained using the VTT establish the need for a variable control threshold. The VTT makes it possible to perform exhaustive design trials and evaluations in the laboratory without risk of injury before field testing and promises to significantly reduce development cost and cycle time.
Article
A control strategy is proposed for designing a steering control for automotive vehicles to protect the vehicle from spin and to realize the improved cornering performance. The saturation characteristics of rear tires are modeled by a linear function with uncertainty terms of a special structure. The nonlinearity of the saturation is included in the part of uncertainty. The linear H<sup>∞</sup> control theory is applied to the design of a front wheel steering controller which compensates the instability against the nonlinear uncertainty. The designed controller is shown to work quite well for nonlinear systems in achieving robust stability and protecting the vehicle from spin. Furthermore, the computer simulations show that the control improves cornering performance in critical motions. The motion realized by the controller resembles the one known as a counter steering which skilful drivers often use
The magic formula tyre model. Proceedings of the 1st international colloquium on tyre models for vehicle dynamics analysis
  • H B Pacejka
  • E Bakker
Pacejka HB, Bakker E. The magic formula tyre model. Proceedings of the 1st international colloquium on tyre models for vehicle dynamics analysis. Amsterdam/Lisse: Swets & Zeitlinger BV;1993.
Anewtire model with an application in vehicle dynamics studies. Proceed-ings of 4th Auto Technologies Conference
  • Hb Pacejka
  • E Bakker
  • Lidner
Pacejka HB, Bakker E, Lidner L. Anewtire model with an application in vehicle dynamics studies. Proceed-ings of 4th Auto Technologies Conference, Monte Carlo, Society of Automotive Engineers (SAE) Paper no. 890087;1989.
Lateral dynamics of road vehicles-3rd ICTS seminar on 'Advanced Vehicle Systems Dynamics'
  • Hb Pacejka
Pacejka HB. Lateral dynamics of road vehicles-3rd ICTS seminar on 'Advanced Vehicle Systems Dynamics'; Amalfi, Italy;1986.
Dinamica del veicolo. Italia: Città studi Edizioni
  • M Guiggiani
Guiggiani M. Dinamica del veicolo. Italia: Città studi Edizioni;2007.
Software-in-the-loop development and experimental testing of a semi-active magnetorheological coupling for 4WD on demand vehicles
  • R Russo
  • M Terzo
  • F Timpone
Russo R, Terzo M, Timpone F. Software-in-the-loop development and experimental testing of a semi-active magnetorheological coupling for 4WD on demand vehicles. Proc Mini Conf Veh Sys Dyn Identif Anomalies. 2008;73-82.
Proceedings of the 1st international colloquium on tyre models for vehicle dynamics analysis
  • H Pacejka
  • E Bakker