Kinematic and dynamic analysis of the McPherson suspension with a planar quarter-car model

McPherson suspension modelling poses a challenging problem due to its nonlinear asymmetric behaviour. The paper proposes a planar quarter-car analytical model that not only considers vertical motion of the sprung mass (chassis) but also: (i) rotation and translation for the unsprung mass (wheel assembly), (ii) wheel mass and its inertia moment about the longitudinal axis, and (iii) tyre damping and lateral deflection. This kinematic–dynamic model offers a solution to two important shortcomings of the conventional quarter-car model: it accounts for geometry and for tyre modelling. The paper offers a systematic development of the planar model as well as the complete set of mathematical equations. This analytical model can be suitable for fast computation in hardware-in-the-loop applications. Furthermore, a reproducible Simulink implementation is given. The model has been compared with a realistic Adams/View simulation to analyse dynamic behaviour for the jounce and rebound motion of the wheel and two relevant kinematic parameters: camber angle and track width variation.     

A study on model fidelity for model predictive control-based obstacle avoidance in high-speed autonomous ground vehicles

This paper investigates the level of model fidelity needed in order for a model predictive control (MPC)-based obstacle avoidance algorithm to be able to safely and quickly avoid obstacles even when the vehicle is close to its dynamic limits. The context of this work is large autonomous ground vehicles that manoeuvre at high speed within unknown, unstructured, flat environments and have significant vehicle dynamics-related constraints. Five different representations of vehicle dynamics models are considered: four variations of the two degrees-of-freedom (DoF) representation as lower fidelity models and a fourteen DoF representation with combined-slip Magic Formula tyre model as a higher fidelity model. It is concluded that the two DoF representation that accounts for tyre nonlinearities and longitudinal load transfer is necessary for the MPC-based obstacle avoidance algorithm in order to operate the vehicle at its limits within an environment that includes large obstacles. For less challenging environments, however, the two DoF representation with linear tyre model and constant axle loads is sufficient.     

Fidelity of using scaled vehicles for chassis dynamic studies

There are many situations where physical testing of a vehicle or vehicle controller is necessary, yet use of a full-size vehicle is not practical. Some situations include implementation testing of novel actuation strategies, analysing the behaviour of chassis feedback control under system faults, or near-unstable situations such as limit handling under driver-assist feedback control. Historically, many have advocated the use of scale vehicles as surrogates for larger vehicles. This article presents analysis and experimental testing that examines the fidelity of using scaled vehicles for vehicle chassis dynamics and control studies. In support of this effort, this work introduces an experimental system called the Pennsylvania State University Rolling Roadway Simulator (the PURRS). In the PURRS, a custom-built scale-sized vehicle is freely driven on a moving roadway surface. While others have used scale-vehicle rolling roadway simulators in the past, this work is the first to attempt to directly match the planar dynamic performance of the scale-sized vehicle to a specific full-sized vehicle by careful design of the scale vehicle. This article explains details of this effort including vehicle dynamic modelling, detailed measurement of model parameters, conditions for dynamic similitude, validation of the resulting experimental vehicle in the time, frequency, and dimensionless domains. The results of the dynamic comparisons between scale- and full-sized vehicles clearly illustrate operational regimes where agreement is quite good, and other regimes where agreement is quite poor. Both are useful to understand the applicability of scale-vehicle results to full-size vehicle analysis.     

A nonlinear model predictive control formulation for obstacle avoidance in high-speed autonomous ground vehicles in unstructured environments

This paper presents a nonlinear model predictive control (MPC) formulation for obstacle avoidance in high-speed, large-size autono-mous ground vehicles (AGVs) with high centre of gravity (CoG) that operate in unstructured environments, such as military vehicles. The term ‘unstructured’ in this context denotes that there are no lanes or traffic rules to follow. Existing MPC formulations for passenger vehicles in structured environments do not readily apply to this context. Thus, a new nonlinear MPC formulation is developed to navigate an AGV from its initial position to a target position at high-speed safely. First, a new cost function formulation is used that aims to find the shortest path to the target position, since no reference trajectory exists in unstructured environments. Second, a region partitioning approach is used in conjunction with a multi-phase optimal control formulation to accommodate the complicated forms the obstacle-free region can assume due to the presence of multiple obstacles in the prediction horizon in an unstructured environment. Third, the no-wheel-lift-off condition, which is the major dynamical safety concern for high-speed, high-CoG AGVs, is ensured by limiting the steering angle within a range obtained offline using a 14 degrees-of-freedom vehicle dynamics model. Thus, a safe, high-speed navigation is enabled in an unstructured environment. Simulations of an AGV approaching multiple obstacles are provided to demonstrate the effectiveness of the algorithm.     

A New Method for Accurately Estimating the Weight of Moving Vehicles Using Piezoelectric Sensors and Adaptive-footprint Tire Model

Summary This paper presents new methods for estimating the axle weight of a moving vehicle, using two piezoelectric sensors and adaptive-footprint tire model. It is more difficult to weigh vehicles in motion accurately than to weigh standing vehicles. The difficulties in weighing moving vehicles result from sensor limitations as well as dynamic loading effects induced by vehicle/pavement interactions. For example, two identical vehicles with the same weight will generate sensor signals that differ in the shape and the peak value, depending the tire pressure, vehicle speed, road roughness, and sensor characteristics. This paper develops a method that is much less sensitive to these variable factors in determining the axle weight of a moving vehicle. In the developed method, first the piezoelectric sensor signal is reconstructed using the inverse dynamics of a high-pass filter representing the piezoelectric sensor. Then, the reconstructed signal, is normalized, using the nominal road/tire contact length obtained using an adaptive-footprint tire model, and then integrated. Experiments are performed with 3 vehicles of known weight ranging from 1,400 kg to 28,040 kg. The developed method is compared to two other algorithms. Results show that the developed method is most consistent and accurate.     

An analytical formula of driver RMS acceleration response for quarter-car considering cushion effects

In this paper, a 3-DOF (degree-of-freedom) model of quarter-car coupled with driver and cushion is used to derive an analytical formula, which can describe the driver RMS (root-mean-square) acceleration response with cars under random excitation generated by road irregularities. The study starts with the 3-DOF model. Based on the vehicle random vibration theory, using the residue theorem, the analytical formula of driver RMS acceleration considering cushion effects is obtained. Then, the driver RMS acceleration values calculated from the measured data and from the analytical formulae of the 3-DOF and the classical 2-DOF model are compared. The results show the analytical formula for the 3-DOF model provides a more reasonable approximation of the real response of the test car. Having obtained the analytical formula, the effects of vehicle parameters on driver RMS acceleration are studied. Finally, to provide critical foundations for the selection of the cushion damping, the optimal damping ratio of driver-cushion system is deciphered from the analytical formula. To uncover how each dynamic parameter effects the optimal damping ratio, the analysis of influencing factors is performed and some important conclusions are obtained. The derived analytical formula can be also conveniently used either during preliminary design or for other special purposes.     

A novel method for identifying inertial parameters of electric vehicles based on the dual H infinity filter

ABSTRACT

Accurate identification of vehicle inertial parameters is essential to the design of vehicle dynamics control systems. In this paper, a novel vehicle inertial parameter identification method based on the dual H infinity filter (DHIF) for electric vehicles (EVs) is proposed. The filter algorithm employs a nonlinear longitudinal vehicle model with three vehicle states. A hierarchical framework is engaged by the DHIF to estimate the vehicle states and inertial parameters concurrently. In order to minimise the disturbance of unknown noise, the vehicle states are estimated by using the linear H infinity filter (LHIF), while the nonlinear H infinity filter (NHIF) utilises the observed states to identify the vehicle inertial parameters. Finally, the proposed estimation method is verified and compared through the dSPACE based hardware-in-the-loop (HIL) simulation experiments. The results indicate that the DHIF-based estimation method is effective to identify the vehicle inertial parameters with high precision, remarkable robustness, and quick convergence.     

Semi-active suspension systems for railway vehicles using magnetorheological dampers. Part II: simulation and analysis

In this paper, the semi-active suspension system for railway vehicles based on the controlled (MR) fluid dampers is investigated, and compared with the passive on and passive off suspension systems. The lateral, yaw, and roll accelerations of the car body, trucks, and wheelsets of a full-scale railway vehicle integrated with four MR dampers in the secondary suspension systems, which are in the closed and open loops respectively, are simulated under the random and periodical track irregularities using the established governing equations of the railway vehicle and the modelled track irregularities in Part I of this paper. The simulation results indicate that (1) the semi-active controlled MR damper-based suspension system for railway vehicles is effective and beneficial as compared with the passive on and passive off modes, and (2) while the car body accelerations of the railway vehicle integrated with semi-active controlled MR dampers can be significantly reduced relative to the passive on and passive off ones, the accelerations of the trucks and wheelsets could be increased to some extent. However, the increase in the accelerations of the trucks and wheelsets is insignificant.     

A method for estimation of vehicle inertial parameters

In this paper, a new method is presented for estimating the current sprung mass inertial parameters of a vehicle, such as the mass, pitch and roll mass moments of inertia, and lateral and longitudinal centre of gravity locations. The method measures the sprung mass response when the vehicle is driven over an unknown and unmeasured random road profile. From these measurements, the equivalent free-decay responses are extracted and modal analysis techniques used to estimate the sprung mass natural frequencies, damping ratios and mode shapes. This information is combined with a simplified vehicle estimation model, least squares analysis and known equivalent stiffness parameters to estimate the vehicles’ inertial parameters. The results obtained from several simulation examples show that estimates of the inertial parameters generally have small relative errors.     

Construction of a stochastic model of track geometry irregularities and validation through experimental measurements of dynamic loading

This paper describes the construction of a stochastic model of urban railway track geometry irregularities, based on experimental data. The considered irregularities are track gauge, superelevation, horizontal and vertical curvatures. They are modelled as random fields whose statistical properties are extracted from a large set of on-track measurements of the geometry of an urban railway network. About 300–1000 terms are used in the Karhunen–Loève/Polynomial Chaos expansions to represent the random fields with appropriate accuracy. The construction of the random fields is then validated by comparing on-track measurements of the contact forces and numerical dynamics simulations for different operational conditions (train velocity and car load) and horizontal layouts (alignment, curve). The dynamics simulations are performed both with and without randomly generated geometrical irregularities for the track. The power spectrum densities obtained from the dynamics simulations with the model of geometrical irregularities compare extremely well with those obtained from the experimental contact forces. Without irregularities, the spectrum is 10–50?dB too low.     

A driver-adaptive stability control strategy for sport utility vehicles

Conventional vehicle stability control (VSC) systems are designed for average drivers. For a driver with a good driving skill, the VSC systems may be redundant; for a driver with a poor driving skill, the VSC intervention may be inadequate. To increase safety of sport utility vehicles (SUVs), this paper proposes a novel driver-adaptive VSC (DAVSC) strategy based on scaling the target yaw rate commanded by the driver. The DAVSC system is adaptive to drivers’ driving skills. More control effort would be exerted for drivers with poor driving skills, and vice versa. A sliding mode control (SMC)-based differential braking (DB) controller is designed using a three degrees of freedom (DOF) yaw-plane model. An eight DOF nonlinear yaw-roll model is used to simulate the SUV dynamics. Two driver models, namely longitudinal and lateral, are used to ‘drive’ the virtual SUV. By integrating the virtual SUV, the DB controller, and the driver models, the performance of the DAVSC system is investigated. The simulations demonstrate the effectiveness of the DAVSC strategy.     

A nonlinear model for top fuel dragster dynamic performance assessment

The top fuel dragster is the fastest and quickest vehicle in drag racing. This vehicle is capable of travelling a quarter mile in less than 4.5 s, reaching a final speed in excess of 330 miles per hour. The average power delivered by its engine exceeds 7000 Hp. To analyse and eventually increase the performance of a top fuel dragster, a dynamic model of the vehicle is developed. Longitudinal, vertical, and pitching chassis motions are considered, as well as drive-train dynamics. The aerodynamics of the vehicle, the engine characteristics, and the force due to the combustion gases are incorporated into the model. Further, a simplified model of the traction characteristics of the rear tyres is developed where the traction is calculated as a function of the slip ratio and the velocity. The resulting nonlinear, coupled differential equations of motion are solved using a fourth-order Runge–Kutta numerical integration scheme. Several simulation runs are made to investigate the effects of the aerodynamics and of the engine's initial torque in the performance of the vehicle. The results of the computational simulations are scrutinised by comparisons with data from actual dragster races. Ultimately, the proposed dynamic model of the dragster can be used to improve the aerodynamics, the engine and clutch set-ups of the vehicle, and possibly facilitate the redesign of the dragster.     

A semi-empirical dynamic tire model for combined-slip forces

This article presents a semi-empirical combined-slip tire model including transient behavior. It is assumed that the transient behavior is a result from the dynamic deformation of the tire carcass and that the interaction between the lateral and longitudinal slip, and forces can be explained by the deformation of the rubber treads. The deformation of the tire carcass makes the tread slip deviate from the wheel-rim motion in a way that may be described by differential equations. A method based on brush-model tire mechanics is used to construct the combined-slip forces as nonlinear scalings of corresponding pure-slip forces.     

A stochastic analysis of highway capacity: Empirical evidence and implications

This paper presents a stochastic characterization of highway capacity and explores its implications on ramp metering control at the corridor level. The stochastic variation of highway capacity is captured through a Space–Time Autoregressive Integrated Moving Average (STARIMA) model. It is identified following a Seasonal STARIMA model (0, 0, 2₃) × (0, 1, 0)₂, which indicates that the capacities of adjacent locations are spatially–temporally correlated. Hourly capacity patterns further verify the stochastic nature of highway capacity. The goal of this paper is to study (1) how to take advantage of the extra information, such as capacity variation, and (2) what benefits can be gained from stochastic capacity modeling. The implication of stochastic capacity is investigated through a ramp metering case study. A mean–standard deviation formulation of capacity is proposed to achieve the trade-off between traffic operation efficiency and robustness. Following that, a modified stochastic capacity-constraint ZONE ramp metering scheme embedded cell transmission model algorithm is introduced. The numerical experiment suggests that considering capacity variation information would alleviate the spillback effect and improve throughput. Monte Carlo simulation further supports this argument. This study helps verify and characterize the stochastic nature of capacity, validates the benefits of using capacity variation information, and thus enhances the necessity of implementing stochastic capacity in traffic operation.     

A novel global sensitivity analysis on the observation accuracy of the coupled vehicle model

ABSTRACT

This paper proposes a novel 2-step global sensitivity analysis algorithm to provide an in-depth sensitivity analysis of the vehicle parameters on the system responses. A 9 degree-of-freedom nonlinear vertical–lateral coupled vehicle model is developed, and 12 parameters along with 7 system responses are selected for the sensitivity analysis. In order to reduce the computational effort, the proposed 2-step algorithm calculates the elementary effects and selects 7 influential parameters from these 12, and then uses the Sobol' method to obtain the global sensitivity indexes of these influential parameters. An unscented Kalman filter is finally designed to show the effect and importance of the selected sensitive parameters on the observation accuracy. Simulations with different vehicle types, velocities and tyre models have verified that the proposed algorithm can accurately describe the relationship between the vehicle parameters and system responses, which is of directive significance to improve vehicle controller and observer performances.     

Vehicle dynamic estimation with road bank angle consideration for rollover detection: theoretical and experimental studies

This article describes a method of vehicle dynamics estimation for impending rollover detection. This method is evaluated via a professional vehicle dynamics software and then through experimental results using a real test vehicle equipped with an inertial measurement unit. The vehicle dynamic states are estimated in the presence of the road bank angle (as a disturbance in the vehicle model) using a robust observer. The estimated roll angle and roll rate are used to compute the rollover index which is based on the prediction of the lateral load transfer. In order to anticipate the rollover detection, a new method is proposed in order to compute the time-to-rollover using the load transfer ratio. The used nonlinear model is deduced from the vehicle lateral dynamics and is represented by a Takagi–Sugeno (TS) fuzzy model. This representation is used in order to take into account the nonlinearities of lateral cornering forces. The proposed TS observer is designed with unmeasurable premise variables in order to consider the non-availability of the slip angles measurement. Simulation results show that the proposed observer and rollover detection method exhibit good efficiency.     

A polynomial chaos approach to the analysis of vehicle dynamics under uncertainty

The ability of ground vehicles to quickly and accurately analyse their dynamic response to a given input is critical to their safety and efficient autonomous operation. In field conditions, significant uncertainty is associated with terrain and/or vehicle parameter estimates, and this uncertainty must be considered in the analysis of vehicle motion dynamics. Here, polynomial chaos approaches that explicitly consider parametric uncertainty during modelling of vehicle dynamics are presented. They are shown to be computationally more efficient than the standard Monte Carlo scheme, and experimental results compared with the simulation results performed on ANVEL (a vehicle simulator) indicate that the method can be utilised for efficient and accurate prediction of vehicle motion in realistic scenarios.     

带有随机需求的车辆路径选择问题算法研究

为带有随机需求的车辆路径问题（VRPSD）提供一个具有通用性的算法,将一个VRPSD问题转化成带有运力限制的车辆路径问题（CVRP）的有限集,通过解CVRP问题来解决VRPSD问题。为提高解的可靠性引入了安全库存的概念,并运用了蒙特卡罗仿真方法,得到了在不同安全库存水平下每条路径的可靠性。用实例检验所述方法的可靠性和通用性。     

A theoretical justification of the sine with dwell manoeuvre

The sine with dwell (SWD) manoeuvre has received much attention within the context of vehicle stability testing. This manoeuvre is used in a test developed by the NHTSA, designed to certificate electronic stability control systems in light vehicles. The test is used in legislations as well as in consumer tests all over the globe. The SWD manoeuvre was designed using test vehicles on a test track and experimentally validated. The paper at hand uses optimal control theory to theoretically justify the use of the SWD manoeuvre to produce a severe lateral motion and over-steering based on steering input. It is shown that a manoeuvre similar to the SWD manoeuvre can be obtained from an optimal control problem using simple vehicle dynamics models. The optimal control method is further used to analyse the manoeuvre's robustness with respect to vehicle dimensions and tyre properties. It is shown that the manoeuvre is robust in dimensions, which theoretically motivates its application for various sizes of vehicles.     

Rear wheel torque vectoring model predictive control with velocity regulation for electric vehicles

In this paper we propose a constrained optimal control architecture for combined velocity, yaw and sideslip regulation for stabilisation of the vehicle near the limit of lateral acceleration using the rear axle electric torque vectoring configuration of an electric vehicle. A nonlinear vehicle and tyre model are used to find reference steady-state cornering conditions and design two model predictive control (MPC) strategies of different levels of fidelity: one that uses a linearised version of the full vehicle model with the rear wheels' torques as the input, and another one that neglects the wheel dynamics and uses the rear wheels' slips as the input instead. After analysing the relative trade-offs between performance and computational effort, we compare the two MPC strategies against each other and against an unconstrained optimal control strategy in Simulink and Carsim environment.