Real-time capable vehicle–trailer coupling by algorithms for differential-algebraic equations

The real-time simulation of vehicle trains requires an accurate and numerically feasible representation of the vehicle–trailer coupling. Although the equations of motion for the chassis instances can be reduced to systems of ordinary differential equations, additional constraints on the relative motion of vehicle and trailer are introduced when considering the hitch. In this article, we present a strategy for the simulation of vehicle–trailer combinations, where the algebraic constraints of the coupling are treated explicitly. Although this approach allows exact modeling of the respective joint geometry and realistic calculation of the coupling forces, a suitable numerical algorithm is required in order to solve the resulting differential-algebraic system of index 3 in real-time. The implementation in a commercial vehicle dynamics program is discussed and real-time simulation results are shown, which prove its feasibility for different coupling joints and demanding driving maneuvers.     

用于汽车动力学实时仿真的悬架建模方法的研究

针对汽车动力学实时仿真的要求提出一种新的悬架建模方法—复合约束隔离解耦建模方法。将悬架系统视为连接车身和车轮之间的无质量复合约束,基于这个概念建立的悬架系统模型,由于实现有质量刚体的相互隔离及代数方程与微分方程的解耦,提高了模型求解效率。应用该方法建立的悬架模型,由于是面向结构的模型,因而可较为准确地描述悬架动态特性,同时由于求解效率的提高又能够满足仿真实时性的要求。     

基于微分几何的四轮独立驱动车辆运动解耦控制研究

针对车辆在纵向运动和横摆运动时的强耦合关系给车辆动力学控制带来的困难，以四轮独立电驱动车辆作为研究对象，基于微分几何理论设计了车辆系统运动解耦控制方法，将非线性强耦合的四轮驱动车辆动力学系统解耦为纵向和横向两个相对独立运动控制子系统，并设计了鲁棒控制器，以提高抵抗车辆行驶时不确定外力如侧风的干扰能力。基于 Trucksim 软件建立四轮驱动车辆模型，并针对车辆解耦控制策略和抗干扰策略进行了仿真测试。结果表明，相比于无解耦控制的车辆，采用微分几何解耦控制的四轮独立驱动车辆纵向速度偏差降低了 82.1%，横摆角速度偏差降低了80.7%，且微风干扰下的抗干扰能力明显改善，车辆稳定性显著提升。为验证该运动解耦控制策略在实时系统中的控制效果，还进行了硬件在环试验，结果表明，硬件在环试验的结果与仿真结果一致。     

Tractor-Semitrailer Dynamics: Design of the Fifth Wheel*

The nonlinear equations of motion are derived for a tractor-semitrailer truck where both the itractor and the semitrailer yaw, pitch, roll, and translate. Special emphasis is placed on the constraints imposed by the fifth wheel on the vehicle motion. In particular, the effects of two proposed fifth wheel design changes on the jackknifing behavior of a vehicle in a turning, braking maneuver are studied. The results demonstrate that the tendency of the vehicle to jackknife can be reduced with a geometric modification of the fifth wheel.     

Tractor-Semitrailer Dynamics: Design of the Fifth Wheel∗

SUMMARY

The nonlinear equations of motion are derived for a tractor-semitrailer truck where both the itractor and the semitrailer yaw, pitch, roll, and translate. Special emphasis is placed on the constraints imposed by the fifth wheel on the vehicle motion. In particular, the effects of two proposed fifth wheel design changes on the jackknifing behavior of a vehicle in a turning, braking maneuver are studied. The results demonstrate that the tendency of the vehicle to jackknife can be reduced with a geometric modification of the fifth wheel.     

面向交通枢纽的车辆三维真实感实时仿真

为分析和解决城市交通拥挤问题并提高城市道路利用率提供可行的途径,提出了一种面向交通枢纽的车辆运行仿真方法,通过场景、道路与车辆的三维动态建模,实现交通枢纽交通状况的实时真实感仿真.首先,提出了基于道路关键点连接网络模型表示交通枢纽的通行道路.其次,基于粒子系统实现车辆的动态运行实时仿真,并采用基于空间剖分的车辆碰撞检测方法对车辆运动控制算法进行了优化.最终,通过对路段的动态观测和反馈机制实现车辆行驶路线的规划和调度.实验结果表明,本文提出的方法可以生动直观地呈现实际路面的交通状况,并且能以较为流畅的帧速率实现交通场景的动态仿真.     

基于二次规划的智能车辆动态换道轨迹规划研究

为实现智能车辆的自主换道操作并满足安全性、舒适性和实时性等约束条件,提出一种针对动态交通环境的换道轨迹规划模型。该模型由道路平面曲线表征模块、路径生成模块以及速度曲线生成模块组成。首先,在道路平面曲线表征模块中,模型基于实时获取的周边道路信息,利用切比雪夫多项式插值法回归拟合出连续可导的道路平面曲线函数,用以保证模型在各种道路平面线形上的普适性。然后,在路径生成模块中,根据换道车辆初始时刻的运动状态,建立一系列多项式方程,并利用牛顿迭代法求解方程未知参数,以此生成连接初始位置和目标位置的换道路径,用以保证换道轨迹的平滑性。最后,在速度曲线生成模块中,以满足防碰撞约束、跟驰加速度约束以及车辆运动状态约束为目标,构建二次规划模型,生成沿着换道路径的车辆速度曲线,用以保证换道轨迹的安全性和舒适性。此外,考虑到周边动态的交通环境,车辆系统在每个时间步内会循环调用提出的模型实时更新换道轨迹,直至车辆到达目标位置。仿真试验结果表明：应用提出的换道轨迹规划模型,车辆能够有效避免与周边动态车辆发生碰撞,成功完成换道;基于二次规划框架,模型优化求解时间明显缩短,满足轨迹规划的实时性和有效性要求。     

Longitudinal Tire Dynamics

This article begins with a brief review of the traditional concept of lateral relaxation length. The review illustrates that this concept yields a useful approximation which can be used with semi-empirical tire models which assume lateral forces are a function of steady-state slip angles. The article then presents an analogous derivation for longitudinal slip. Like its lateral counterpart, the derivation yields an approximation for transient longitudinal slip which can be used with tire models which assume longitudinal forces are a function of steady-state longitudinal slip. It is shown that, like the relaxation-length-based lateral slip angle, this formulation for longitudinal slip yields the ability to compute shear forces at the tire/road interface for either high or low speed applications, a necessary feature of simulations which support human in the loop driving simulation. Like traditional kinematically-based longitudinal slip, the transient formulation presented here is coupled with the wheel spin equation, and it shares the characteristic that it is very stiff compared to the equations of vehicle motion. This characteristic is a challenge impeding the real-time calculations required for driving simulation. The paper shows that local linearization of the wheel spin equations coupled with analytical solutions of the transient longitudinal slip formulation provide the basis for both insight into the longitudinal dynamics of the tire and for integrating the model in real-time.     

车辆系统垂向与横向耦合的侧倾状态估计

为有效解决复杂行驶工况下车辆耦合侧倾运动状态无法精确获取,进而对车辆系统操纵稳定性与乘坐舒适性兼顾优化无法提供准确输入的难题,本文中设计了基于车辆垂向与横向耦合动力学的双非线性状态观测器算法,以实现复杂行驶工况下车辆耦合侧倾运动状态的实时准确估计。首先,建立了路面激励模型与整车系统垂向与横向耦合动力学模型;接着,利用无迹卡尔曼滤波方法(UKF)与非线性模糊观测(T-S)理论,设计了非线性状态观测算法,以在不同路面激励工况下对车辆系统簧载质量与侧倾状态进行联合估计;最后,运用CarSim■动力学软件,对比分析了在标准A级与C级路面上进行J-turn试验工况下,采用联合状态观测器(UKF&T-S)实时估计车辆侧倾角与侧倾率的观测精度。结果表明,本文所设计的UKF&T-S观测器可有效估计车辆侧倾状态,且与CarSim■仿真数据相比识别状态标准偏差不超过10%。     

步行车辆运动弹性动力学分析

步行车辆在快速运动中,既有大刚体运动又有小弹性位移,且还有不连续的边界约束条件,是一个很复杂的动力学问题。本文用有限元方法建立了该系统的动力学模型,采用分段的直接积分法求解其弹性动力响应。     

基于凯恩方法的汽车悬架实时仿真模型

提出了一种用于汽车动力学实时仿真的悬架建模方法。将悬架系统模型建成为连接车身和车轮的无质量复合铰,并基于凯恩方法推导了悬架复合铰的运动方程。在满足动力学实时仿真要求的同时不降低悬架系统的运动学精度。利用该方法建立了某轿车面向结构的麦弗逊式前悬架模型,并集成到由符号计算软件产生的该轿车的多体动力学模型中。仿真与实车道路试验结果的对比表明该悬架模型具有较高的仿真精度。     

Longitudinal Tire Dynamics

SUMMARY

This article begins with a brief review of the traditional concept of lateral relaxation length. The review illustrates that this concept yields a useful approximation which can be used with semi-empirical tire models which assume lateral forces are a function of steady-state slip angles. The article then presents an analogous derivation for longitudinal slip. Like its lateral counterpart, the derivation yields an approximation for transient longitudinal slip which can be used with tire models which assume longitudinal forces are a function of steady-state longitudinal slip. It is shown that, like the relaxation-length-based lateral slip angle, this formulation for longitudinal slip yields the ability to compute shear forces at the tire/road interface for either high or low speed applications, a necessary feature of simulations which support human in the loop driving simulation. Like traditional kinematically-based longitudinal slip, the transient formulation presented here is coupled with the wheel spin equation, and it shares the characteristic that it is very stiff compared to the equations of vehicle motion. This characteristic is a challenge impeding the real-time calculations required for driving simulation. The paper shows that local linearization of the wheel spin equations coupled with analytical solutions of the transient longitudinal slip formulation provide the basis for both insight into the longitudinal dynamics of the tire and for integrating the model in real-time.     

Automatic generation of the non-holonomic equations of motion for vehicle stability analysis

The mathematical analysis of vehicle stability has been utilised as an important tool in the design, development, and evaluation of vehicle architectures and stability controls. This paper presents a novel method for automatic generation of the linearised equations of motion for mechanical systems that is well suited to vehicle stability analysis. Unlike conventional methods for generating linearised equations of motion in standard linear second order form, the proposed method allows for the analysis of systems with non-holonomic constraints. In the proposed method, the algebraic constraint equations are eliminated after linearisation and reduction to first order. The described method has been successfully applied to an assortment of classic dynamic problems of varying complexity including the classic rolling coin, the planar truck–trailer, and the bicycle, as well as in more recent problems such as a rotor–stator and a benchmark road vehicle with suspension. This method has also been applied in the design and analysis of a novel three-wheeled narrow tilting vehicle with zero roll-stiffness. An application for determining passively stable configurations using the proposed method together with a genetic search algorithm is detailed. The proposed method and software implementation has been shown to be robust and provides invaluable conceptual insight into the stability of vehicles and mechanical systems.     

无人驾驶车辆解耦混合运动规划方法研究

高速公路无人驾驶车辆运动规划要充分考虑车辆的动力学特性和道路环境构成的复杂约束,优先确保车辆的无碰撞行驶轨迹,同时算法实时性比常速情况下要求更高,要充分考虑计算的复杂性。提出一种可生成横纵向最优解逼近群的解耦增强混合运动规划方法,引入Frent坐标系将运动规划问题进行横纵向解耦,在横向偏移规划中融合数值优化和多项式规划算法,在纵向速度规划中融合围绕速度和围绕避障规划算法,解耦规划完成后使用代价函数和碰撞检测方法对生成的轨迹群进行评估和选择。搭建Apollo-LGsvl无人驾驶联合仿真测试平台,对所提出的运动规划方法进行仿真验证。结果表明,提出的横纵向解耦增强混合运动规划算法在高速公路各工况中所生成的运动轨迹能够有效避免车辆发生碰撞,其横向偏移和纵向速度均能满足二阶平滑,最大横向加速度、最大纵向加速度、最大纵向jerk等满足动力学约束。该方法有效减少了最优解逼近群内的轨迹数量,使轨迹评估阶段计算复杂度降低了46%,证明提出的方法具备一定的应用价值。     

Influence of wheel–rail contact modelling on vehicle dynamic simulation

This paper presents a comparison of four models of rolling contact used for online contact force evaluation in rail vehicle dynamics. Until now only a few wheel–rail contact models have been used for online simulation in multibody software (MBS). Many more models exist and their behaviour has been studied offline, but a comparative study of the mutual influence between the calculation of the creep forces and the simulated vehicle dynamics seems to be missing. Such a comparison would help researchers with the assessment of accuracy and calculation time. The contact methods investigated in this paper are FASTSIM, Linder, Kik–Piotrowski and Stripes. They are compared through a coupling between an MBS for the vehicle simulation and Matlab for the contact models. This way the influence of the creep force calculation on the vehicle simulation is investigated. More specifically this study focuses on the influence of the contact model on the simulation of the hunting motion and on the curving behaviour.     

The critical hitch angle for jackknife avoidance during slow backing up of vehicle–trailer systems

We set out to answer the question: At what hitch angle does it become impossible for a vehicle and trailer to continue to backing up without getting into a jackknife? Jackknifing during backing up of trailers occurs when the hitch angle increases to a point such that the vehicle and trailer fold together about the hitch point like a jackknife. If the backward motion is continued, the jackknife effect progressively worsens, until the vehicle and trailer are in physical contact with each other. Jackknifing can result in traffic disruptions and wasted time, and can potentially cause damage or personal injury. Our goal is to analytically determine the ‘critical hitch angle’ (θ_cr), the hitch angle threshold beyond which a continued reverse motion causes an inescapable jackknifing. In this paper, we provide a formal definition of θ_cr for slow backing up of vehicle–trailer systems on a level solid surface, beyond which the vehicle must stop backing up and revert to forward motion in order to escape from jackknifing. The critical hitch angle is sub-categorised into Absolute (θ_cr, a) and Directional (θ_cr, d) critical hitch angles depending on the operating constraints and vehicle steering objectives. One solution for θ_cr is posed as a numerical solution to the steady-state conditions of the dynamic equations. The effects of such hitch angle limitations are demonstrated through simulation. Also, a warning system making use of the θ_cr is proposed. Such warning systems can assist drivers in avoiding jackknifing while backing up a vehicle–trailer system.     

基于hp自适应伪谱法的智能汽车紧急变道轨迹规划与优化

为了提高智能汽车紧急变道轨迹规划的实时性和适应性，将紧急变道过程分为初始阶段和跟踪阶段，初始阶段的轨迹由优秀驾驶人紧急变道模型产生，跟踪阶段的轨迹采用Sigmoid函数规划出紧急避让路径。首先通过聚类分析处理优秀驾驶人转向操作的实车试验数据，拟合得出紧急变道过程中的方向盘转角随时间的关系（即驾驶人紧急变道模型），作为智能汽车在紧急变道初始阶段不同速度下车辆控制的输入量。然后通过建立与求解约束方程，满足避撞约束、侧向位移约束以及最大侧向加速度约束，得出Sigmoid函数表达式，作为智能汽车在紧急变道过程跟踪阶段的参考路径。最后利用hp自适应伪谱法加入切换点的物理量约束，逼近全局正交多项式的状态量和控制量，自动调整和处理2个阶段的切换点位置和衔接问题，以最小变道距离为目标对跟踪阶段的变道轨迹进行优化。运用PreScan与MATLAB对4种不同工况下的紧急变道轨迹规划进行联合仿真。结果表明：提出的轨迹规划与优化方法在满足各项约束的情况下成功避开障碍物，同时缩短了需要优化的轨迹，优化时间都小于0.9 s，并且与基于多项式函数轨迹规划方法相比，该方法能够以距障碍物较远的距离避开障碍物，在不同的车辆速度、道路曲率和障碍物宽度的复杂工况下具有更好的适应性。     

Spatial Dynamics of Multibody Tracked Vehicles Part II: Contact Forces and Simulation Results

In this part of the paper, three dimensional computational capabilities, that includes significant details, are developed for the nonlinear dynamic analysis of large scale spatial tracked vehicles. Three dimensional nonlinear contact force models that describe the interaction between the track links and the vehicle components such as the rollers, sprockets, and idlers as well as the interaction between the track links and the ground are developed and used to define the generalized contact forces associated with the vehicle generalized coordinates. Tangential friction and contact forces are developed in order to maintain the stability of the track motion and avoid the slippage of the track or its rotation as a rigid body. Body and surface coordinate systems are introduced in order to define the spatial contact conditions. The nonlinear equations of motion of the tracked vehicle are solved using the velocity transformation procedure developed in the first part of this paper. This procedure is used in order to obtain a minimum set of differential equations, and avoid the use of the iterative Newton-Raphson algorithm. A computer simulation of a tracked vehicle that consists of one hundred and six bodies and has one hundred and sixteen degrees of freedom is presented in order to demonstrate the use of the formulations presented in this study.     

Accessible pre-design calculation tool to support the definition of EV components

The new freedoms in design that electric powertrains offer lead to a wide variety of configurations to consider when developing an electric vehicle (EV) from scratch. Furthermore, the strong relation of the battery size with vehicle weight, range and performances leads to a set of interrelated dependencies that can result in many design loops to fulfil the vehicle targets, market constraints and regulations simultaneously. The paper presents a pre-design tool to assist the electric vehicle development process by representing the different constraints and the possible feasible solutions in a single plot with the need of a small amount of inputs accesible to assess at pre-design phase. As a result, the tool depicts a set of feasible vehicle configurations that could fulfil the targets easing the interaction and loops among different expertise areas. To better assist selection, it also provides a sensitivity analysis of the performances to selected inputs and the user can introduce a cost function depending on vehicle weight and battery size. The tool is based on the vehicle longitudinal dynamics equations and equations that model the market and regulations constraints. It is aimed at providing an overview of the main specifications for component selection avoiding detailed vehicle modelling in the early pre-design phase at which the vehicle characteristics and even powertrain architecture are unknown. Finally, the tool results quality is evaluated by further developing one of its solutions for passenger car in four different vehicle configurations with the simulation software vemSim and AVL Cruise. The results of the simulations are compared to the solution of the pre-design tool to evaluate the level of fidelity and the deviations in the final result that can appear depending on the final architecture, components characteristics and control strategy.     

A 9-DOF Tractor-Semitrailer Dynamic Handling Model for Advanced Chassis Control Studies

Summary This paper describes a flexible and modular 9-degrees-of-freedom nonlinear dynamic handling model for a tractor-semitrailer combination vehicle. The equations of motion are derived from the fundamental equations of dynamics in Euler’s formulation, with the use of general computer-algebra software. The primary aim of the model is simulation of handling scenarios with active yaw control, using unilateral braking. However, it may also prove useful in other areas of tractor-semitrailer handling analysis or hardware-in-the-loop simulations. The model is formulated as a state-space model that may be implemented in standard simulation environments. A Simulink implementation is presented, and simulation results are compared with experiments to validate the model.