CN105857309A

CN105857309A - Automotive adaptive cruise control method taking multiple targets into consideration

Info

Publication number: CN105857309A
Application number: CN201610351859.6A
Authority: CN
Inventors: 曲婷; 王秋; 麻颖俊; 陈虹
Original assignee: Jilin University
Current assignee: Jilin University
Priority date: 2016-05-25
Filing date: 2016-05-25
Publication date: 2016-08-17
Anticipated expiration: 2036-05-25
Also published as: CN105857309B

Abstract

The invention discloses a vehicle adaptive cruise control method considering multi-objectives, which adopts a layered control strategy: the upper-layer control determines the desired longitudinal acceleration according to the current state of the target vehicle and the controlled vehicle, and the lower-layer control adopts a reverse push method Realizing the tracking of the desired longitudinal acceleration includes the following steps: establishing the mutual longitudinal kinematics model of the two vehicles; designing a model predictive controller to obtain the desired distance between the two vehicles according to the constant headway strategy, and using the model predictive control algorithm to determine the expected tracking distance. The desired longitudinal acceleration required by the inter-vehicle distance; the vehicle control conditions are divided into driving conditions and braking conditions, and the vehicle inverse longitudinal dynamics model is established according to the vehicle driving equation for the two conditions; according to the vehicle inverse longitudinal dynamics model , the expected throttle opening is obtained according to the expected acceleration under the driving condition, and the expected brake pedal opening is obtained according to the expected acceleration under the braking condition.

Description

A Vehicle Adaptive Cruise Control Method Considering Multiple Objectives

技术领域technical field

本发明涉及一种车辆自适应巡航控制方法，具体涉及一种考虑多目标的车辆自适应巡航控制方法。The invention relates to a vehicle adaptive cruise control method, in particular to a vehicle adaptive cruise control method considering multiple targets.

背景技术Background technique

自适应巡航控制(ACC)系统是在传统的巡航控制系统的基础上结合安全车距保持系统演化而来。通过位于车身前部的雷达传感器检测到在雷达的可视范围内是否存在前车，当道路前方无车辆时，ACC车辆会按照事先设定的速度行驶，一旦车载传感器检测到前方有车辆时，ACC系统通过调整本车车速，使之与前车保证一个安全的跟车间距。该系统设计的目的旨在减少因驾驶员的错误操作引发的交通事故，提高行驶安全性、乘坐舒适性等。The adaptive cruise control (ACC) system is evolved from the traditional cruise control system combined with the safety distance keeping system. The radar sensor located at the front of the vehicle body detects whether there is a vehicle in front within the visible range of the radar. When there is no vehicle in front of the road, the ACC vehicle will drive at a preset speed. Once the vehicle sensor detects that there is a vehicle ahead, The ACC system adjusts the speed of the vehicle to ensure a safe following distance from the vehicle in front. The purpose of the system design is to reduce traffic accidents caused by driver's wrong operation, improve driving safety, ride comfort, etc.

目前ACC系统在设计时主要考虑安全性和跟车性两大目标，然而在实际设计的过程中还有几点仍需考虑。首先，据2008年美国National Highway Traffic Safety Administration(NHTSA)对汽车ACC系统的调查报告指出，舒适性是驾驶员最关心的性能之一，因为舒适度得不到有效保证将直接导致乘客拒绝使用ACC系统。可见，在进行ACC系统的设计过程中舒适性是不得不考虑的性能之一。其次，随着环境压力的日益增大，能源问题成为人们关心的热点之一。因此，ACC系统是否具有较高的燃油经济性也决定了其能否在道路上推广的一个关键因素。At present, the design of ACC system mainly considers the two goals of safety and car following, but there are still some points to be considered in the actual design process. First of all, according to the 2008 US National Highway Traffic Safety Administration (NHTSA) investigation report on automobile ACC systems, comfort is one of the performances that drivers are most concerned about, because the lack of effective guarantee of comfort will directly lead to passengers refusing to use ACC system. It can be seen that comfort is one of the performances that have to be considered in the design process of the ACC system. Secondly, with the increasing environmental pressure, the energy issue has become one of the hot spots that people care about. Therefore, whether the ACC system has high fuel economy also determines a key factor whether it can be popularized on the road.

本发明采用的模型预测控制(MPC)方法具有算法设计简单，鲁棒性强，并且能够处理优化问题中的多个控制目标和多约束的特点。简单来讲模型预测控制(MPC)是一种优化算法，通过滚动寻优以及反馈校正的思想实现对期望输入的跟踪控制。在每个采样时刻根据系统当前可测状态，利用模型预测系统未来输出，通过求解包含目标函数和系统约束在内的优化问题，得到优化序列，为了减小外部干扰和模型失配的影响，将优化序列的第一个元素作用到系统，便完成了一步控制输入。在下一采样时刻重复上述过程。The model predictive control (MPC) method adopted in the present invention has the characteristics of simple algorithm design, strong robustness, and the ability to deal with multiple control objectives and multiple constraints in the optimization problem. Simply speaking, Model Predictive Control (MPC) is an optimization algorithm that realizes tracking control of desired input through the idea of rolling optimization and feedback correction. According to the current measurable state of the system at each sampling time, the model is used to predict the future output of the system, and the optimization sequence is obtained by solving the optimization problem including the objective function and system constraints. In order to reduce the influence of external interference and model mismatch, the The first element of the optimization sequence applied to the system completes the one-step control input. Repeat the above process at the next sampling moment.

发明内容Contents of the invention

本发明提供了一种考虑多目标的车辆自适应巡航控制方法，采用分层的控制策略：上层控制根据目标车辆以及本车当前的状态，综合考虑车辆行驶过程中的多个目标决策出期望的纵向加速度，下层控制通过逆推的方法实现对期望纵向加速度的跟踪。The present invention provides a vehicle self-adaptive cruise control method considering multi-objectives, adopting a layered control strategy: the upper-level control determines the desired cruise control based on the target vehicle and the current state of the vehicle, comprehensively considering multiple targets during the vehicle's driving process. Longitudinal acceleration, the lower-level control implements the tracking of the desired longitudinal acceleration through the method of inversion.

本发明是通过以下技术方案实现的：The present invention is achieved through the following technical solutions:

一种考虑多目标的车辆自适应巡航控制方法，采用分层控制策略：上层控制根据目标车辆以及被控车辆当前的状态，决策出期望的纵向加速度；下层控制通过逆推的方法实现对期望纵向加速度的跟踪；该方法包括以下步骤：A multi-objective vehicle adaptive cruise control method adopts a hierarchical control strategy: the upper layer control determines the desired longitudinal acceleration according to the current state of the target vehicle and the controlled vehicle; Tracking of acceleration; the method comprises the following steps:

步骤一、建立两车相互纵向运动学模型：根据被控车辆与目标车辆之间的运动学关系，建立两车相互纵向运动学模型，同时将前车加速度信息作为扰动信号；Step 1. Establish the mutual longitudinal kinematics model of the two vehicles: according to the kinematic relationship between the controlled vehicle and the target vehicle, establish the mutual longitudinal kinematics model of the two vehicles, and simultaneously use the acceleration information of the preceding vehicle as a disturbance signal;

步骤二、上位控制器的设计：基于步骤一建立的两车相互纵向运动学模型，设计模型预测控制器，根据恒定车头时距策略获得期望的两车间距，根据车辆的实时状态，利用模型预测控制算法决策出跟踪该期望车间距所需要的期望纵向加速度；Step 2. Design of the upper controller: Based on the mutual longitudinal kinematics model of the two vehicles established in step 1, design a model predictive controller, obtain the desired distance between the two vehicles according to the constant headway strategy, and use the model to predict The control algorithm determines the desired longitudinal acceleration required to track the desired inter-vehicle distance;

步骤三、建立车辆逆纵向动力学模型：将车辆控制工况分为驱动工况和制动工况，对两种工况分别根据车辆行驶方程建立车辆逆纵向动力学模型，车辆逆纵向动力学模型用于将所述上位控制器计算出的期望加速度的指令通过车辆逆纵向动力学模型转变为期望的节气门开度或期望的制动踏板开度；Step 3. Establish vehicle inverse longitudinal dynamics model: divide the vehicle control condition into driving condition and braking condition, and establish vehicle inverse longitudinal dynamics model according to vehicle driving equation respectively for the two conditions, and vehicle inverse longitudinal dynamics The model is used to transform the command of the expected acceleration calculated by the host controller into an expected throttle opening or an expected brake pedal opening through the vehicle inverse longitudinal dynamics model;

步骤四、下位控制器的设计：根据车辆逆纵向动力学模型，在驱动工况下按照期望加速度求得期望的节气门开度，在制动工况下按照期望的加速度求得期望的制动踏板开度；将获得的控制信号输出给被控车辆，完成对期望车间距的跟踪控制。Step 4. The design of the lower controller: According to the inverse longitudinal dynamics model of the vehicle, the expected throttle opening is obtained according to the expected acceleration under the driving condition, and the expected braking is obtained according to the expected acceleration under the braking condition. Pedal opening; output the obtained control signal to the controlled vehicle to complete the tracking control of the desired inter-vehicle distance.

本发明的有益效果为：The beneficial effects of the present invention are:

1.本发明采用的分层结构的设计思想上下层功能集中且控制目标明确，模块间只传递必要的有限信号且互不影响，利于对系统的调试并在一定程度上能提高系统的鲁棒性及可靠性。1. The design idea of the layered structure adopted by the present invention is that the functions of the upper and lower layers are concentrated and the control objectives are clear. Only necessary limited signals are transmitted between the modules and do not affect each other, which is beneficial to the debugging of the system and can improve the robustness of the system to a certain extent. performance and reliability.

2.本发明在建立两车相互纵向动力学模型的过程中，充分考虑前车加速度的影响，将该信号作为扰动，同时该模型不涉及具体车辆动力学及其参数的使用，适用于实验主车以外的其他车辆，有利于控制算法的移植。2. In the process of establishing the mutual longitudinal dynamics model of the two vehicles, the present invention fully considers the influence of the acceleration of the vehicle in front, and regards the signal as a disturbance. At the same time, the model does not involve the use of specific vehicle dynamics and its parameters, and is applicable to the experimental subject. Vehicles other than vehicles are conducive to the transplantation of control algorithms.

3.本发明充分考虑了在跟踪期望的车间距的过程中，主车需要满足的多个行驶目标，包括安全性、跟车性、舒适性以及燃油经济性等。3. The present invention fully considers multiple driving objectives that the host vehicle needs to meet in the process of tracking the desired inter-vehicle distance, including safety, following performance, comfort and fuel economy.

附图说明Description of drawings

图1为自适应巡航跟踪控制系统框图；Fig. 1 is a block diagram of an adaptive cruise tracking control system;

图2为两车相互纵向运动学模型示意图；Figure 2 is a schematic diagram of the mutual longitudinal kinematics model of two vehicles;

图3为发动机转矩特性map示意图；Fig. 3 is a schematic diagram of an engine torque characteristic map;

图4为加速控制两车间距示意图；Figure 4 is a schematic diagram of the distance between two vehicles for acceleration control;

图5为加速控制两车速度示意图；Fig. 5 is a schematic diagram of speed control of two vehicles;

图6为加速控制控制量变化示意图；Fig. 6 is a schematic diagram of the variation of the acceleration control control quantity;

图7为减速控制两车间距示意图；Fig. 7 is a schematic diagram of the distance between two vehicles for deceleration control;

图8为减速控制两车速度示意图；Fig. 8 is a schematic diagram of speed reduction control of two vehicles;

图9为减速控制控制量变化示意图。Fig. 9 is a schematic diagram of the variation of the deceleration control control amount.

具体实施方式detailed description

以下结合附图详细介绍本发明的技术方案：Describe technical scheme of the present invention in detail below in conjunction with accompanying drawing:

本发明提供了一种考虑多目标的车辆自适应巡航控制方法，该方法包括以下几个步骤：The invention provides a vehicle adaptive cruise control method considering multi-objectives, the method comprises the following steps:

步骤一、建立两车相互纵向运动学模型，如图2所示。Step 1: Establish the mutual longitudinal kinematics model of the two vehicles, as shown in Figure 2.

根据前后车在行驶过程中满足的运动学关系，可以获得下面的方程：According to the kinematic relationship satisfied by the front and rear vehicles during driving, the following equation can be obtained:

$\{\begin{matrix} v v ((k k + + 11)) = = v v ((k k)) + + {a a}_{f f} ((k k)) {T T}_{s the s} \\ {v v}_{r r e e f f} ((k k + + 11)) = = {v v}_{r r e e f f} ((k k)) + + {a a}_{l l} ((k k)) {T T}_{s the s} - - {a a}_{f f} ((k k)) {T T}_{s the s} \\ Δ Δ x x ((k k + + 11)) = = Δ Δ x x ((k k)) + + {v v}_{r r e e f f} ((k k)) {T T}_{s the s} + + \frac{11}{22} (({a a}_{l l} ((k k)) - - {a a}_{f f} ((k k)))) {T T}_{s the s}^{22} \end{matrix} - - - - - - ((11))$

其中，v(k)代表k时刻本车的纵向行驶速度，单位m/s；a_l(k)、a_f(k)分别是前后两车k时刻的加速度信息，单位m/s²；v_ref(k)代表k时刻两车的相对速度，单位m/s，满足v_ref(k)＝v_l(k)-v(k)，v_l(k)是前车k时刻的纵向速度，单位m/s；Δx(k)是k时刻两车间距,单位m；T_s是系统的采样周期，单位s。Wherein, v(k) represents the longitudinal running speed of the car at the k moment, unit m/s; a _l (k), a _f (k) are the acceleration information of the front and rear two cars at k moment respectively, unit m/s ² ; v _ref (k) represents the relative speed of the two vehicles at time k, the unit is m/s, satisfying v _ref (k)=v _l (k)-v(k), v _l (k) is the longitudinal speed of the preceding vehicle at time k, The unit is m/s; Δx(k) is the distance between two vehicles at time k, the unit is m; T _s is the sampling period of the system, the unit is s.

选取状态矢量x(k)＝[Δx(k),v_ref(k),v(k)]^T，将被控车辆加速度作为系统的控制输入，即u(k)＝a_f(k)，一般情况对于被控车辆的纵向加速度可以利用车辆的加速度传感器很方便的获得，但是由于车车通信尚未实现，因此当前时刻想要获得前车的加速度还存在较大的难度。基于以上考虑，认为前车(目标车辆)加速度是ACC系统的扰动，即w(k)＝a_l(k)，由于控制的最终目标是使两车实际间距趋近于间距策略计算出的期望跟车间距，因此，系统的输出选择两车实际间距。这样就可以将上述方程描述成如下所示的状态空间表达式的形式：Select the state vector x(k)=[Δx(k),v _ref (k),v(k)] ^T , take the acceleration of the controlled vehicle as the control input of the system, that is, u(k)=a _f (k), In general, the longitudinal acceleration of the controlled vehicle can be easily obtained by using the vehicle's acceleration sensor. However, since the vehicle-to-vehicle communication has not yet been realized, it is still difficult to obtain the acceleration of the vehicle in front at the current moment. Based on the above considerations, it is considered that the acceleration of the vehicle in front (target vehicle) is the disturbance of the ACC system, that is, w(k)= _al (k), since the ultimate goal of control is to make the actual distance between the two vehicles approach the expectation calculated by the distance strategy The following distance, therefore, the output of the system selects the actual distance between the two vehicles. This allows the above equation to be described in the form of a state-space expression as follows:

${{\begin{matrix} x x ((k k + + 11)) = = A A x x ((k k)) + + B B u u ((k k)) + + G G w w ((k k)) \\ y the y ((k k)) = = C C x x ((k k)) \end{matrix} - - - - - - ((22))$

其中，in,

C＝[1 0 0] C=[1 0 0]

步骤二、上位控制器的设计：基于步骤一建立的两车相互纵向运动学模型，设计模型预测控制器，根据目前广泛采用的恒定车头时距策略获得期望的两车间距，根据车辆的实时状态，利用模型预测控制算法决策出跟踪该期望车间距所需要的期望的纵向加速度。该设计过程具体步骤如下：Step 2. Design of the upper controller: Based on the mutual longitudinal kinematics model of the two vehicles established in step 1, design a model predictive controller, obtain the expected distance between the two vehicles according to the currently widely used constant headway strategy, and obtain the desired distance between the two vehicles according to the real-time state of the vehicle , using the model predictive control algorithm to determine the desired longitudinal acceleration required to track the desired inter-vehicle distance. The specific steps of the design process are as follows:

1)优化问题的形成1) Formation of the optimization problem

ACC系统的主要目标有以下四点：安全性、跟踪性能、舒适性和燃油经济性。然而这几点是相互矛盾的。若要满足经济性要求，则希望车辆在行驶过程中尽可能平稳，即不存在加速度急剧变化的情况，这势必会影响跟踪性能。相反，如果在设计控制器的过程中仅考虑跟踪性能，这样不可避免的存在不必要的加速和紧急制动情况的发生，这不仅影响燃油经济性，在一定程度上，如果驾驶员不能很好的适应自适应巡航控制系统，则会产生所谓的信任危机，从而带来的后果就是驾驶员频繁的进行主动干预，这不仅与自适应巡航控制系统的设计初衷相违背，还会带来额外的精神负担。综上所述，在进行控制系统的设计过程中，仅仅考虑其中的任何一项是不合理的，必须在同一个框架下同时兼顾多个目标。为了量化提出的ACC系统的性能指标，我们重新分析上述目标。The main goals of the ACC system are the following four points: safety, tracking performance, comfort and fuel economy. However, these points are contradictory. To meet the economic requirements, it is hoped that the vehicle is as stable as possible during driving, that is, there is no sharp change in acceleration, which will inevitably affect the tracking performance. On the contrary, if only the tracking performance is considered in the process of designing the controller, there will inevitably be unnecessary acceleration and emergency braking, which will not only affect the fuel economy, but to a certain extent, if the driver cannot Adapting to the adaptive cruise control system will produce a so-called crisis of trust, which will result in frequent active intervention by the driver, which not only violates the original design intention of the adaptive cruise control system, but also brings additional Mental burden. To sum up, in the design process of the control system, it is unreasonable to only consider any one of them, and it is necessary to take into account multiple goals under the same framework. To quantify the performance metrics of the proposed ACC system, we reanalyze the above objectives.

首先，无论采取何种算法，安全性是系统在行驶过程中时时刻刻都要满足的首要目标。也就是说为了满足安全性需求，在任何时刻两车间距都要大于一个安全的车间距，如下面约束方程(3)所示。First of all, no matter what algorithm is adopted, safety is the primary goal that the system must meet at all times during driving. That is to say, in order to meet the safety requirements, the distance between two vehicles must be greater than a safe distance between vehicles at any time, as shown in the following constraint equation (3).

约束1：Δx(k)≥d_c (3)Constraint 1: Δx(k)≥d _c (3)

其中，d_c代表安全的两车间距。Among them, _dc represents the safe distance between two cars.

其次，对于跟踪性能，驾驶员期望稳态时实际两车间距跟踪上期望的两车间距。Secondly, for tracking performance, the driver expects the actual distance between two vehicles to track the expected distance between two vehicles in steady state.

目标1:Δx(k)→Δx_des当k→∞ (4)Goal 1: Δx(k)→Δx _des when k→∞ (4)

其中，Δx_des代表期望的两车间距。Among them, Δx _des represents the expected distance between two vehicles.

最后，对于乘坐舒适性和燃油经济性的要求，在汽车行驶过程中，体现乘坐舒适性的指标主要是车辆的纵向加速度这个参数，加速度的绝对值越小乘坐舒适性就越高，同时平滑的动态响应曲线也有利于燃油经济性的提高。Finally, for the requirements of ride comfort and fuel economy, during the driving process of the car, the index that reflects the ride comfort is mainly the parameter of the longitudinal acceleration of the vehicle. The smaller the absolute value of the acceleration, the higher the ride comfort. At the same time, the smooth The dynamic response curve also benefits fuel economy.

约束2：a_fmin≤a_f(k)≤a_fmax (5)Constraint 2: a _fmin ≤ a _f (k) ≤ a _fmax (5)

此外，考虑到车辆自身能力的限制，车辆行驶过程中还需满足如下的速度约束：In addition, considering the limitations of the vehicle's own capabilities, the following speed constraints must be met during the driving process of the vehicle:

约束3：v_min≤v(k)≤v_max (6)Constraint 3: v _min ≤ v(k) ≤ v _max (6)

综上所述，在MPC的框架下考虑多目标的车辆ACC系统的控制可以总结成如下的优化问题：In summary, the control of vehicle ACC system considering multi-objective under the framework of MPC can be summarized as the following optimization problem:

问题一：Question one:

$\underset{u u ((k k))}{m m i i n no} J J ((y the y ((k k)),, u u ((k k)),, m m,, p p)) - - - - - - ((77))$

满足两车相互纵向运动学：Satisfy the mutual longitudinal kinematics of two vehicles:

$\{\begin{matrix} v v ((k k + + 11)) = = v v ((k k)) + + {a a}_{f f} ((k k)) {T T}_{s the s} \\ {v v}_{r r e e f f} ((k k + + 11)) = = {v v}_{r r e e f f} ((k k)) + + {a a}_{l l} ((k k)) {T T}_{s the s} - - {a a}_{f f} ((k k)) {T T}_{s the s} \\ Δ Δ x x ((k k + + 11)) = = Δ Δ x x ((k k)) + + {v v}_{r r e e f f} ((k k)) {T T}_{s the s} + + \frac{11}{22} (({a a}_{l l} ((k k)) - - {a a}_{f f} ((k k)))) {T T}_{s the s}^{22} \end{matrix}$

同时满足不等式约束：while satisfying the inequality constraints:

$\{\begin{matrix} Δ Δ x x ((k k)) &GreaterEqual; &Greater Equal; {d d}_{c c} \\ {a a}_{f f m m i i n no} \leq \leq {a a}_{f f} ((k k)) \leq \leq {a a}_{f f m m a a x x} \\ {v v}_{min min} \leq \leq v v ((k k)) \leq \leq {v v}_{m m a a x x} \end{matrix}$

其中，in,

$\begin{matrix} J J ((y the y ((k k)),, u u ((k k)),, m m,, p p)),, \\ = = {Σ Σ}_{i i = = 11}^{p p} {|| || {Γ Γ}_{y the y,, i i} (({y the y}_{c c} ((k k + + i i | | k k)) - - r r ((k k + + i i)))) || ||}^{22} + + {Σ Σ}_{i i = = 11}^{m m} {|| || {Γ Γ}_{u u,, i i} ((k k + + i i - - 11)) || ||}^{22} \end{matrix}$

式中，p是系统的预测时域，m是控制时域且m≤p。In the formula, p is the prediction time domain of the system, m is the control time domain and m≤p.

2)优化问题的求解2) Solving the optimization problem

假设所有的状态都是可以测量得到的，为了推导预测方程，还需做如下假设：Assuming that all states are measurable, in order to derive the prediction equation, the following assumptions need to be made:

(1)控制时域之外，控制量不变，即u(k+i)＝u(k+m-1),i＝m,m+1,...p-1.(1) Outside the control time domain, the control quantity remains unchanged, that is, u(k+i)=u(k+m-1), i=m, m+1,...p-1.

(2)干扰在k时刻之后保持不变，即w(k+i)＝w(k),i＝1,2,…p-1.为了便于控制器的求解，首先推导预测方程的表达形式，推导过程如下：(2) The disturbance remains unchanged after time k, that is, w(k+i)=w(k), i=1, 2,...p-1. In order to facilitate the solution of the controller, the expression form of the prediction equation is derived first , the derivation process is as follows:

x(k+1|k)＝Ax(k)+Bu(k)+Gw(k)x(k+1|k)=Ax(k)+Bu(k)+Gw(k)

x(k+2|k)＝Ax(k+1|k)+Bu(k+1)+Gw(k+1)x(k+2|k)＝Ax(k+1|k)+Bu(k+1)+Gw(k+1)

＝A²x(k)+ABu(k)+Bu(k+1)+(AG+G)w(k)＝A ² x(k)+ABu(k)+Bu(k+1)+(AG+G)w(k)

x(k+3|k)＝Ax(k+2|k)+Bu(k+2)+Gw(k+2)x(k+3|k)＝Ax(k+2|k)+Bu(k+2)+Gw(k+2)

＝A³x(k)+A²Bu(k)+ABu(k+1)+Bu(k+2)+(A²G+AG+G)w(k)=A ³ x(k)+A ² Bu(k)+ABu(k+1)+Bu(k+2)+(A ² G+AG+G)w(k)

类推可以得到：Analogy can get:

x(k+m|k)＝Ax(k+m-1|k)+Bu(k+m-1)+Gw(k+m-1)x(k+m|k)＝Ax(k+m-1|k)+Bu(k+m-1)+Gw(k+m-1)

＝A^mx(k)+A^m-1Bu(k)+A^m-2Bu(k+1)+…+ABu(k+m-2)+Bu(k+m-1)＝A ^m x(k)+A ^m-1 Bu(k)+A ^m-2 Bu(k+1)+...+ABu(k+m-2)+Bu(k+m-1)

+(A^m-1G+A^m-2G+…+AG+G)w(k)+(A ^m-1 G+A ^m-2 G+…+AG+G)w(k)

x(k+p|k)＝Ax(k+p-1|k)+Bu(k+p-1)+Gw(k+p-1)x(k+p|k)=Ax(k+p-1|k)+Bu(k+p-1)+Gw(k+p-1)

＝A^px(k)+A^p-1Bu(k)+A^p-2Bu(k+1)+…+A^p-mBu(k+m-1)+＝A ^p x(k)+A ^p-1 Bu(k)+A ^p-2 Bu(k+1)+...+A ^pm Bu(k+m-1)+

A^p-m-1Bu(k+m-1)+…+ABu(k+m-1)+Bu(k+m-1)+A ^pm-1 Bu(k+m-1)+…+ABu(k+m-1)+Bu(k+m-1)+

(A^p-1G+A^p-2G+…+AG+G)w(k)(A ^p-1 G+A ^p-2 G+…+AG+G)w(k)

由于：because:

y(k)＝Cx(k)y(k)=Cx(k)

所以：so:

y(k+1|k)＝Cx(k+1|k)y(k+1|k)=Cx(k+1|k)

＝CAx(k)+CBu(k)=CAx(k)+CBu(k)

y(k+2|k)＝CA²x(k)+CABu(k)+CBu(k+1)+(CAG+CG)w(k)y(k+2|k)=CA ² x(k)+CABu(k)+CBu(k+1)+(CAG+CG)w(k)

类推可以得到：Analogy can get:

y(k+m|k)＝CA^mx(k)+CA^m-1Bu(k)+CA^m-2Bu(k+1)+…+CABu(k+m-2)+y(k+m|k)＝CA ^m x(k)+CA ^m-1 Bu(k)+CA ^m-2 Bu(k+1)+…+CABu(k+m-2)+

CBu(k+m-1)+(CA^m-1G+CA^m-2G+…+CAG+CG)w(k)CBu(k+m-1)+(CA ^m-1 G+CA ^m-2 G+…+CAG+CG)w(k)

y(k+p|k)＝CA^px(k)+CA^p-1Bu(k)+CA^p-2Bu(k+1)+…+CA^p-mBu(k+m-1)y(k+p|k)＝CA ^p x(k)+CA ^p-1 Bu(k)+CA ^p-2 Bu(k+1)+…+CA ^pm Bu(k+m-1)

+CA^p-m-1Bu(k+m-1)+…+CABu(k+m-1)+CBu(k+m-1)+CA ^pm-1 Bu(k+m-1)+…+CABu(k+m-1)+CBu(k+m-1)

+(CA^p-1G+CA^p-2G+…+CAG+CG)w(k)+(CA ^p-1 G+CA ^p-2 G+…+CAG+CG)w(k)

定义p步预测输出向量和m步输入向量如下：Define the p-step prediction output vector and the m-step input vector as follows:

$\begin{matrix} {Y Y}_{p p} ((k k + + 11 | | k k)) \overset{d d e e f f}{= =} [\begin{matrix} y the y ((k k + + 11 | | k k)) \\ y the y ((k k + + 22 | | k k)) \\ . . \\ . . \\ . . \\ y the y ((k k + + p p | | k k)) \end{matrix}] & U u ((k k)) \overset{d d e e f f}{= =} [\begin{matrix} u u ((k k)) \\ u u ((k k + + 11)) \\ . . \\ . . \\ . . \\ u u ((k k + + m m - - 11)) \end{matrix}] & W W ((k k)) = = [\begin{matrix} w w ((k k | | k k)) \\ w w ((k k | | k k)) \\ . . \\ . . \\ . . \\ w w ((k k | | k k)) \end{matrix}] \end{matrix}$

可以得到预测方程的表达式如下：The expression of the prediction equation can be obtained as follows:

Y_p(k+1|k)＝S_xx(k)+S_wW(k)+S_uU(k) (8)Y _p (k+1|k)＝S _x x(k)+S _w W(k)+S _u U(k) (8)

其中，in,

根据CTH间距策略模块，期望的两车间距应该和本车速度满足如下的关系：According to the CTH distance strategy module, the expected distance between two vehicles should satisfy the following relationship with the speed of the vehicle:

r(k+i)＝t_h·v(k+i)+r₀ (9)r(k+i)=t _h v(k+i)+r ₀ (9)

式中，t_h代表车间时距，r₀是与安全性有关的一个常数。In the formula, t _h represents the headway time distance, and r ₀ is a constant related to safety.

定义由于r(k+i)与输入u(k)有关，这样把系统的第三个状态v(k)定义为系统的输出v_b，则definition Since r(k+i) is related to the input u(k), the third state v(k) of the system is defined as the output v _b of the system, then

v_b(k+1)＝v_b(k)+T_su(k) (10)v _b (k+1)=v _b (k)+T _s u(k) (10)

将上述输出写成矩阵的形式Write the above output in the form of a matrix

V_b(k+1|k)＝V_xx(k)+V_uU(k) (11)V _b (k+1|k)＝V _x x(k)+V _u U(k) (11)

其中，in,

定义则R(k+1)＝t_h[V_xx(k)+V_uU(k)]+R₀，将上述表达形式带入目标函数(7)，并定义E_p(k+1|k)＝(S_x-t_hV_x)x(k)+S_wW(k)-R₀，重新整理该目标函数便可获得如下的形式:definition Then R(k+1)=t _h [V _x x(k)+V _u U(k)]+R ₀ , bring the above expression into the objective function (7), and define E _p (k+1| k)＝(S _x -t _h V _x )x(k)+S _w W(k)-R ₀ , rearrange the objective function to obtain the following form:

$\begin{matrix} J J = = {|| || {Γ Γ}_{y the y} (({E E.}_{p p} ((k k + + 11 | | k k)) + + (({S S}_{u u} - - {t t}_{h h} {V V}_{u u})) U u ((k k)))) || ||}^{22} + + {|| || {Γ Γ}_{u u} U u ((k k)) || ||}^{22} \\ = = U u {((k k))}^{T T} [[{(({S S}_{u u} - - {t t}_{h h} {V V}_{u u}))}^{T T} {Γ Γ}_{y the y}^{T T} {Γ Γ}_{y the y} (({S S}_{u u} - - {t t}_{h h} {V V}_{u u})) + + {Γ Γ}_{u u}^{T T} {Γ Γ}_{u u}]] U u ((k k)) \\ + + 22 {E E.}_{p p} {((k k + + 11 | | k k))}^{T T} {Γ Γ}_{y the y}^{T T} {Γ Γ}_{y the y} (({S S}_{u u} - - {t t}_{h h} {V V}_{h h})) U u ((k k)) \\ + + {E E.}_{p p} {((k k + + 11 | | k k))}^{T T} {Γ Γ}_{y the y}^{T T} {Γ Γ}_{y the y} {E E.}_{p p} ((k k + + 11 | | k k)) \end{matrix} - - - - - - ((1212))$

由于E_p(k+1|k)^TΓ_y ^TΓ_yE_p(k+1|k)与优化变量无关，这样将目标函数(12)写成如下的形式：Since E _p (k+1|k) ^T Γ _y ^T Γ _y E _p (k+1|k) has nothing to do with the optimization variables, the objective function (12) can be written as follows:

J＝U(k)^THU(k)+G(k+1|k)^TU(k) (13)J＝U(k) ^T HU(k)+G(k+1|k) ^T U(k) (13)

其中，in,

H＝(S_u-t_hV_u)^TΓ_y ^TΓ_y(S_u-t_hV_u)+Γ_u ^TΓ_u H＝(S _u -t _h V _u ) ^T Γ _y ^T Γ _y (S _u -t _h V _u )+Γ _u ^T Γ _u

G(k+1|k)^T＝2E_p(k+1|k)Γ_y ^TΓ_y(S_u-t_hV_u)G(k+1|k) ^T ＝2E _p (k+1|k)Γ _y ^T Γ _y (S _u -t _h V _u )

为了便于控制器的求解需要将优化问题中的约束转换成C_uz≥b的形式。In order to facilitate the solution of the controller, the constraints in the optimization problem need to be transformed into the form of C _u z≥b.

对于安全性约束方程(3)可以转换成系统的输出约束的形式：For the security constraint equation (3) can be transformed into the output constraint form of the system:

$Δ Δ x x ((k k)) &GreaterEqual; &Greater Equal; {d d}_{c c} &DoubleRightArrow; &DoubleRightArrow; {S S}_{u u} U u ((k k)) &GreaterEqual; &Greater Equal; {D D.}_{c c} - - {S S}_{x x} x x ((k k)) - - {S S}_{w w} W W ((k k)) - - - - - - ((1414))$

其中S_u,S_x,S_w表达式和上述相同，D_c＝[d_c d_c … d_c]^T。The expressions of _Su , S _x , and S _w are the same as above, and D _c =[d _c d _c ... d _c ] ^T .

对于控制约束(5)可以转换成如下的形式：For control constraints (5) can be transformed into the following form:

${a a}_{f f min min} \leq \leq {a a}_{f f} ((k k)) \leq \leq {a a}_{f f max max} &DoubleRightArrow; &DoubleRightArrow; [\begin{matrix} - - {I I}_{m m * * m m} \\ {I I}_{m m * * m m} \end{matrix}] U u ((k k)) &GreaterEqual; &Greater Equal; [\begin{matrix} - - {U u}_{max max} \\ {U u}_{min min} \end{matrix}] - - - - - - ((1515))$

其中，U_max＝[a_fmax a_fmax … a_fmax]^T,U_min＝[a_fmin a_fmin … a_fmin]^T。Wherein, U _max =[a _fmax a _fmax ... a _fmax ] ^T , U _min =[a _fmin a _fmin ... a _fmin ] ^T .

对于状态约束(6)前面提到定义本车速度作为一个约束输出，并推导输出的预测方程，这样便可以将上述约束写成如下的表达形式：For the state constraint (6), it was mentioned earlier that the speed of the vehicle is defined as a constraint output, and the output prediction equation is derived, so that the above constraint can be written as the following expression:

$\begin{matrix} - - {V V}_{u u} U u ((k k)) &GreaterEqual; &Greater Equal; {V V}_{x x} x x ((k k)) - - {V V}_{max max} \\ {V V}_{u u} U u ((k k)) &GreaterEqual; &Greater Equal; {V V}_{min min} - - {V V}_{x x} x x ((k k)) \end{matrix} - - - - - - ((1616))$

其中，V_x,V_u的表达式如前所述，Among them, the expressions of V _x and V _u are as mentioned above,

V_max＝[v_max v_max … v_max]^T,V_min＝[v_min v_min … v_min]^T。V _max = [v _max v _max ... v _max ] ^T , V _min = [v _min v _min ... v _min ] ^T .

至此，便将系统的约束全部转换完毕。这样优化问题一最终可以转化成问题二：So far, all the constraints of the system have been transformed. In this way, optimization problem 1 can finally be transformed into problem 2:

问题二： Question two:

其中，in,

$\begin{matrix} {C C}_{u u} = = [\begin{matrix} - - {I I}_{m m * * m m} \\ {I I}_{m m * * m m} \\ {S S}_{u u} \\ {V V}_{u u} \\ - - {V V}_{u u} \end{matrix}] & b b ((k k + + 11 | | k k)) = = [\begin{matrix} - - {U u}_{max max} \\ {U u}_{min min} \\ {D D.}_{c c} - - {S S}_{x x} x x ((k k)) - - {S S}_{w w} W W ((k k)) \\ {V V}_{min min} - - {V V}_{x x} x x ((k k)) \\ {V V}_{x x} x x ((k k)) - - {V V}_{max max} \end{matrix}] \end{matrix}$

调用MATLAB中求解器quadprog便可完成上位控制器的求解，获得期望的纵向加速度。Calling the solver quadprog in MATLAB can complete the solution of the host controller and obtain the desired longitudinal acceleration.

步骤三、建立车辆逆纵向动力学模型：本文研究的自主车辆都是基于高保真的仿真软件veDYNA中的自动换挡车辆，也就是说在车辆行驶的过程中无需考虑档位的影响。那么影响自主车辆纵向行驶的因素主要是节气门开度和制动踏板开度两个因素。根据车辆的运行过程可知，当给定一个节气门开度输入后，发动机将产生相应的输出扭矩，该扭矩经过液力变矩器传送给车辆的变速器，最终通过轴承系统作用在车轮上，产生相应的驱动力矩。制动工况同样如此，当给定一个制动压力输入后，由液压制动系统产生的力矩直接作用到车轮上，迫使车辆减速行驶。根据上述分析，由上位控制器计算出的期望加速度指令须通过车辆逆纵向动力学模型转变为期望的节气门开度和制动踏板的位置，然后将该控制信号作用到被控车辆，以控制车辆的加速、减速和匀速运动，实现自适应巡航系统的功能。所以需要分为加速和减速两种工况建立逆纵向动力学模型：Step 3: Establish vehicle inverse longitudinal dynamics model: The autonomous vehicles studied in this paper are all automatic gear-shifting vehicles based on the high-fidelity simulation software veDYNA, which means that there is no need to consider the influence of gears during the driving process of the vehicle. Then the main factors affecting the longitudinal driving of the autonomous vehicle are the throttle opening and the brake pedal opening. According to the running process of the vehicle, when a throttle opening is given, the engine will generate a corresponding output torque, which is transmitted to the vehicle's transmission through the torque converter, and finally acts on the wheels through the bearing system to generate corresponding drive torque. The same is true for braking conditions. When a brake pressure input is given, the torque generated by the hydraulic braking system acts directly on the wheels, forcing the vehicle to slow down. According to the above analysis, the expected acceleration command calculated by the upper controller must be transformed into the expected throttle opening and brake pedal position through the vehicle inverse longitudinal dynamics model, and then the control signal is applied to the controlled vehicle to control Acceleration, deceleration and uniform motion of the vehicle realize the function of the adaptive cruise system. Therefore, it is necessary to establish an inverse longitudinal dynamics model in two conditions: acceleration and deceleration:

A.加速控制(驱动工况)A. Acceleration control (driving condition)

经逻辑切换后，如果切换为加速控制，则须按照期望加速度的要求，经过计算得到期望发动机转矩，再通过发动机逆向模型查得期望的节气门开度。首先根据牛顿第二定律建立汽车行驶方程式：After logical switching, if switching to acceleration control, the expected engine torque must be obtained through calculation according to the requirements of the expected acceleration, and then the expected throttle opening can be found through the engine reverse model. First, establish the vehicle driving equation according to Newton's second law:

$δ δ m m a a = = \frac{{i i}_{g g} {i i}_{00} {η η}_{T T}}{{r r}_{e e f f f f}} {T T}_{e e} - - m m g g f f - - \frac{11}{22} {C C}_{d d} {Aρv Aρv}^{22} - - m m g g s the s i i n no θ θ - - - - - - ((1818))$

根据上式可以得到发动机的输出扭矩：According to the above formula, the output torque of the engine can be obtained:

${T T}_{e e} = = \frac{((m m g g f f + + \frac{11}{22} {C C}_{d d} {Aρv Aρv}^{22} + + m m g g s the s i i n no θ θ + + δ δ m m a a)) {r r}_{e e f f f f}}{{i i}_{g g} {i i}_{00} {η η}_{T T}} - - - - - - ((1919))$

式中各符号的含义如下：The meanings of the symbols in the formula are as follows:

T_e是发动机期望扭矩，i_g是变速器的传动比，i₀表示主减速传动比，η_T表示传动系的机械效率，r_eff是车轮的有效半径，m是整车质量，f是滚动阻力系数，C_d是空气阻力系数，A是迎风面积，ρ为空气密度，v是车辆纵向行驶速度，θ代表道路坡度，δ是汽车旋转质量换算系数，a是车辆的纵向加速度，g是重力加速度。T _e is the expected torque of the engine, i _g is the gear ratio of the transmission, i ₀ is the final reduction gear ratio, η _T is the mechanical efficiency of the drive train, r _eff is the effective radius of the wheel, m is the mass of the vehicle, and f is the rolling resistance Coefficient, C _d is the air resistance coefficient, A is the windward area, ρ is the air density, v is the longitudinal speed of the vehicle, θ is the road slope, δ is the conversion factor of the car rotating mass, a is the longitudinal acceleration of the vehicle, g is the acceleration of gravity .

利用veDYNA车辆模型中发动机转矩特性map示意图，反查表就可以得到该扭矩下对应的节气门开度的大小，如图3所示。根据T_e和发动机转速ω_e，利用发动机节气门开度特性曲线图，可以求得期望的节气门开度α_des为Using the schematic diagram of the engine torque characteristic map in the veDYNA vehicle model, the throttle opening corresponding to the torque can be obtained by looking up the table, as shown in Figure 3. According to T _e and engine speed ω _e , using the engine throttle opening characteristic curve, the desired throttle opening α _des can be obtained as

α_des＝f(T_e,ω_e) (20)α _des =f(T _e ,ω _e ) (20)

B.制动控制(制动工况)B. Braking control (braking conditions)

经过逻辑切换之后，如切换为制动控制，须按照期望加速度，求得期望制动力矩，继而通过制动器逆向模型求得期望的制动踏板开度，将β_des通过执行器施加于被控车辆进行制动控制。After logical switching, if switching to brake control, the desired braking torque must be obtained according to the desired acceleration, and then the desired brake pedal opening is obtained through the brake inverse model, and β _des is applied to the controlled vehicle through the actuator Perform brake control.

制动行驶时车辆的行驶方程如下：The driving equation of the vehicle when braking is as follows:

$δ δ m m a a = = {F f}_{b b} + + m m g g f f + + \frac{11}{22} {C C}_{d d} {Aρv Aρv}^{22} + + m m g g s the s i i n no θ θ - - - - - - ((21 twenty one))$

根据上式可以得到发动机制动力矩表达式：According to the above formula, the engine braking torque expression can be obtained:

${T T}_{b b} = = ((δ δ m m a a - - m m g g f f - - \frac{11}{22} {C C}_{d d} {Aρv Aρv}^{22} - - m m g g s the s i i n no θ θ)) {r r}_{e e f f f f} - - - - - - ((22 twenty two))$

此处认为车辆的四个轮子是相同的，也就是说整车的制动力矩由四个轮子平均分配，这样就可以每个轮子的制动力矩由于veDYNA中每一个车轮上的制动力矩的计算公式满足下面的方程：Here, the four wheels of the vehicle are considered to be the same, that is to say, the braking torque of the whole vehicle is equally distributed by the four wheels, so that the braking torque of each wheel can be Since the calculation formula of the braking torque on each wheel in veDYNA satisfies the following equation:

M_b＝2(P_b·A_b·r_b·μ_b) (23)M _b ＝2(P _b ·A _b ·r _b ·μ _b ) (23)

式中，In the formula,

P_b代表每个轮子上的制动压力，单位：PaP _b represents the brake pressure on each wheel, unit: Pa

μ_b代表刹车片和刹车盘之间的摩擦系数μ _b represents the friction coefficient between the brake pad and the brake disc

A_b代表摩擦片与制动盘的接触面积，单位：m² A _b represents the contact area between the friction plate and the brake disc, unit: ^m2

r_b代表制动半径，单位：mr _b represents the braking radius, unit: m

将上述参数带入就可以得到每个轮子的制动压力与制动力矩的关系，Bring the above parameters into the relationship between the braking pressure and braking torque of each wheel,

M_b＝0.1323×10^-3·P_b (24)M _b =0.1323×10 ^-3 ·P _b (24)

获得期望的制动压力P_b后，将其转换成期望的制动踏板开度就完成了制动工况下的减速控制。veDYNA车辆模型中制动力矩与制动踏板的开度关系满足下面的方程：After the desired brake pressure P _b is obtained, converting it into the desired brake pedal opening completes the deceleration control under braking conditions. The relationship between the braking torque and the opening of the brake pedal in the veDYNA vehicle model satisfies the following equation:

${β β}_{d d e e s the s} = = \frac{{P P}_{b b}}{{P P}_{b b m m a a x x}} \times \times 100100 % % - - - - - - ((2525))$

式中，P_bmax代表最大制动压力，取值是2×10⁷Pa。In the formula, P _bmax represents the maximum brake pressure, and its value is 2×10 ⁷ Pa.

步骤四、下位控制器的设计：下位控制器根据上位控制器求解出的期望加速度，首先经过逻辑判断模块决策出为了跟踪这个期望加速度的要求采取驱动模块还是制动模块，此处我们采取最简单的基于阈值的切换方法，认为当加速度大于零的时候采用驱动控制，加速度小于零的时候采取制动控制。如需驱动控制，根据公式(19)获得期望的驱动力矩，根据实时反馈的发动机转速信息，和方程式(20)就可以获得相应的节气门开度，将这个控制信号作用给被控车辆，完成驱动工况下的跟踪控制。同理，如需制动控制，首先根据公式(22)、(23)获得期望的驱动力矩，再根据方程式(24)、(25)就可以获得相应的制动踏板的开度，将这个控制信号作用给被控车辆，完成制动工况下的跟踪控制。Step 4. The design of the lower-level controller: The lower-level controller uses the expected acceleration obtained by the upper-level controller. First, the logical judgment module decides whether to use the driving module or the braking module to track the expected acceleration. Here we take the simplest The threshold-based switching method considers that the driving control is adopted when the acceleration is greater than zero, and the braking control is adopted when the acceleration is less than zero. If driving control is required, the desired driving torque can be obtained according to formula (19), and the corresponding throttle opening can be obtained according to the real-time feedback engine speed information and formula (20), and this control signal is applied to the controlled vehicle to complete Tracking control under driving conditions. Similarly, if brake control is required, first obtain the desired driving torque according to the formulas (22) and (23), and then obtain the corresponding brake pedal opening according to the formulas (24) and (25). The signal acts on the controlled vehicle to complete the tracking control under braking conditions.

下面给出本发明所述的考虑多目标的车辆自适应巡航控制方法的离线仿真验证。The off-line simulation verification of the vehicle adaptive cruise control method considering multi-objectives described in the present invention is given below.

为验证本发明提出的基于多目标的车辆自适应巡航控制方法的有效性，选取巡航过程中两种典型工况进行验证，下面给出具体的实验结果与分析。In order to verify the effectiveness of the multi-objective-based vehicle adaptive cruise control method proposed by the present invention, two typical working conditions in the cruise process are selected for verification. The specific experimental results and analysis are given below.

(1)加速控制实验结果(1) Acceleration control experiment results

实验中设定前20s由veDYNA的虚拟驾驶员操作车辆，使车辆加速到120km/h，观测到前方100m处前车以100km/h的速度行驶，经过计算期望的两车间距是40.33m,而实际两车间距是100m，控制器作用下车辆行驶过程中的几个状态如图4、图5、图6所示。从结果中可以看出，控制器作用的初始时刻，实际两车间距大于期望的两车间距，ACC系统首先控制本车加速，以缩短两车之间的间距，使两车间距趋近于理想安全距离，当两车间距缩短到一定程度时，ACC系统控制本车较均匀地减速，使ACC车辆的速度接近于前行车辆的速度，同时，使两车之间的间距逐步缩小到系统设定的两车间的理想安全距离。在这个过程中，两车间距始终大于安全的车间距同时车辆加速度的变化也处于合理的范围。In the experiment, it was set that the virtual driver of veDYNA operated the vehicle for the first 20 seconds to accelerate the vehicle to 120km/h. It was observed that the vehicle in front was driving at a speed of 100km/h 100m ahead. After calculation, the expected distance between the two vehicles was 40.33m, while The actual distance between the two vehicles is 100m, and several states of the vehicle during the driving process under the action of the controller are shown in Figure 4, Figure 5, and Figure 6. It can be seen from the results that at the initial moment when the controller acts, the actual distance between the two vehicles is greater than the expected distance between the two vehicles, and the ACC system first controls the acceleration of the vehicle to shorten the distance between the two vehicles and make the distance between the two vehicles approach the ideal Safety distance, when the distance between the two vehicles is shortened to a certain extent, the ACC system controls the vehicle to decelerate more evenly, so that the speed of the ACC vehicle is close to the speed of the vehicle in front, and at the same time, the distance between the two vehicles is gradually reduced to the system setting. The ideal safe distance between the two workshops. In this process, the distance between two vehicles is always greater than the safe distance between vehicles, and the change of vehicle acceleration is also within a reasonable range.

(2)减速控制实验结果(2) Experimental results of deceleration control

实验中设定前20s由veDYNA的虚拟驾驶员操作车辆，使车辆加速到120km/h，观测到前方35m处前车以100km/h的速度行驶，经过计算期望的两车间距是40.33m,而实际两车间距是35m,控制器作用下车辆行驶过程中的几个状态如图7、图8、图9所示。从图中可以看出在t＝20s时，两车初始间距小于安全间距，两车之间的跟随行驶具有一定不安全性，ACC系统直接控制本车进行一定强度的减速，提高两车跟随行驶的安全性，当主车速度减到一定程度时，稍小于前车的速度，则ACC系统控制车辆进行适当的加速，使ACC车辆的速度趋近于前车的速度，同时使两车之间的间距趋近于理想安全距离。In the experiment, it was set that the virtual driver of veDYNA operated the vehicle for the first 20 seconds to accelerate the vehicle to 120km/h. It was observed that the vehicle in front was driving at a speed of 100km/h 35m ahead. After calculation, the expected distance between the two vehicles was 40.33m, while The actual distance between the two vehicles is 35m, and several states of the vehicle during the driving process under the action of the controller are shown in Figure 7, Figure 8, and Figure 9. It can be seen from the figure that when t=20s, the initial distance between the two vehicles is smaller than the safe distance, and the following driving between the two vehicles is unsafe. When the speed of the main vehicle decreases to a certain level and is slightly lower than the speed of the vehicle in front, the ACC system controls the vehicle to accelerate appropriately, so that the speed of the ACC vehicle approaches the speed of the vehicle in front, and at the same time makes the distance between the two vehicles The spacing tends to be close to the ideal safe distance.

Claims

1. A vehicle adaptive cruise control method considering multiple targets is characterized in that a hierarchical control strategy is adopted: the upper-layer control decides the expected longitudinal acceleration according to the current states of the target vehicle and the controlled vehicle; the lower layer control realizes the tracking of the expected longitudinal acceleration by a reverse thrust method; the method comprises the following steps:

step one, establishing a mutual longitudinal kinematics model of two vehicles: establishing a longitudinal kinematic model of the two vehicles according to the kinematic relationship between the controlled vehicle and the target vehicle, and simultaneously taking the acceleration information of the front vehicle as a disturbance signal;

step two, designing an upper controller: designing a model prediction controller based on the mutual longitudinal kinematics model of the two vehicles established in the step one, obtaining an expected distance between the two vehicles according to a constant head time interval strategy, and deciding an expected longitudinal acceleration required for tracking the expected distance between the two vehicles by using a model prediction control algorithm according to the real-time state of the vehicles;

step three, establishing a vehicle inverse longitudinal dynamics model: dividing the vehicle control working condition into a driving working condition and a braking working condition, and respectively establishing a vehicle inverse longitudinal dynamic model for the two working conditions according to a vehicle running equation, wherein the vehicle inverse longitudinal dynamic model is used for converting an expected acceleration instruction calculated by the upper controller into an expected throttle opening or an expected brake pedal opening through the vehicle inverse longitudinal dynamic model;

step four, designing a lower controller: according to the vehicle inverse longitudinal dynamics model, obtaining an expected throttle opening according to expected acceleration under a driving working condition, and obtaining an expected brake pedal opening according to the expected acceleration under a braking working condition; and outputting the obtained control signal to the controlled vehicle to complete the tracking control of the expected inter-vehicle distance.

2. The multi-objective-considered vehicle adaptive cruise control method according to claim 1, wherein the vehicle-to-vehicle longitudinal kinematic model established in the step one is as follows:

\{\begin{matrix} x (k + 1) = A x (k) + B u (k) + G w (k) \\ y (k) = C x (k) \end{matrix}

wherein,

\begin{matrix} A = [\begin{matrix} 1 & T_{s} & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}] & B = [\begin{matrix} - \frac{1}{2} {T_{s}}^{2} \\ - T_{s} \\ T_{s} \end{matrix}] & G = [\begin{matrix} \frac{1}{2} {T_{s}}^{2} \\ T_{s} \\ 0 \end{matrix}] & C = [\begin{matrix} 1 & 0 & 0 \end{matrix}] \end{matrix}

u(k)＝a_f(k)，w(k)＝a_l(k)，a_l(k)、a_f(k) acceleration information of two front and rear vehicles at the time k respectively, and the unit m/s²；x(k)＝[Δx(k),v_ref(k),v(k)]^T，v_ref(k) Representing the relative speed of two vehicles at the time k, and satisfying v in the unit of m/s_ref(k)＝v_l(k)-v(k)，v_l(k) Is the longitudinal speed of the leading vehicle at time k,the unit m/s; Δ x (k) is the distance between two vehicles at time k, in m; t is_sIs the sampling period of the system, in units of s.

3. The multi-objective-considered vehicle adaptive cruise control method according to claim 1, wherein the design process of the step two upper controller specifically comprises the following steps:

1) and (3) an optimization problem is proposed:

\underset{u (k)}{m i n} J (y (k), u (k), m, p)

wherein,

\begin{matrix} J (y (k), u (k), m, p) \\ = Σ_{i = 1}^{p} | | Γ_{y, i} (y_{c} (k + i | k) - r (k + i)) | |^{2} + Σ_{i = 1}^{m} | | Γ_{u, i} u (k + i - 1) | |^{2} \end{matrix}

p is a prediction time domain of the system, m is a control time domain and m is less than or equal to p;

the mutual longitudinal kinematics of the two vehicles is satisfied:

\{\begin{matrix} v (k + 1) = v (k) + a_{f} (k) T_{s} \\ v_{r e f} (k + 1) = v_{r e f} (k) + a_{l} (k) T_{s} - a_{f} (k) T_{s} \\ Δ x (k + 1) = Δ x (k) + v_{r e f} (k) T_{s} + \frac{1}{2} (a_{l} (k) - a_{f} (k)) T_{s}^{2} \end{matrix}

and simultaneously satisfies inequality constraints:

\{\begin{matrix} Δ x (k) &GreaterEqual; d_{c} \\ a_{f m i n} \leq a_{f} (k) \leq a_{f m a x} \\ v_{\min} \leq v (k) \leq v_{\max} \end{matrix}

a_l(k)、a_f(k) acceleration information of two front and rear vehicles at the time k respectively, and the unit m/s²；x(k)＝[Δx(k),v_ref(k),v(k)]^T，v_ref(k) Representing the relative speed of two vehicles at the time k, and satisfying v in the unit of m/s_ref(k)＝v_l(k)-v(k)，v_l(k) Is the longitudinal speed of the preceding vehicle at the moment k, in m/s; Δ x (k) is the distance between two vehicles at time k, in m; t is_sIs the sampling period of the system, in units of s;

2) solving an optimization problem: converting the optimization problem proposed in the step 1) into:

\underset{U (k)}{m i n} U {(k)}^{T} H U (k) + G {(k + 1 | k)}^{T} U (k)

s.t. C_uU(k)≥b(k+1|k)

wherein,

H＝(S_u-t_hV_u)^T _y ^T _y(S_u-t_hV_u)+_u ^T _u

G(k+1|k)^T＝2E_p(k+1|k)_y ^T _y(S_u-t_hV_u)

\begin{matrix} C_{u} = [\begin{matrix} - I_{m * m} \\ I_{m * m} \\ S_{u} \\ V_{u} \\ - V_{u} \end{matrix}] & b (k + 1 | k) = [\begin{matrix} - U_{\max} \\ U_{\min} \\ D_{c} - S_{x} x (k) - S_{w} W (k) \\ V_{\min} - V_{x} x (k) \\ V_{x} x (k) - V_{\max} \end{matrix}] \end{matrix}

and calling a solver quadprog in the MATLAB to complete the solution of the upper controller and obtain the expected longitudinal acceleration.

4. The multi-objective-considered vehicle adaptive cruise control method according to claim 1, wherein the step three of establishing the vehicle inverse longitudinal dynamics model specifically comprises:

1) vehicle inverse longitudinal dynamics model of driving conditions:

the running equation of the vehicle is established according to Newton's second law:

δ m a = \frac{i_{g} i_{0} η_{T}}{r_{e f f}} T_{e} - m g f - \frac{1}{2} C_{d} {Aρv}^{2} - m g s i n θ

the output torque of the engine can be obtained according to the above equation:

T_{e} = \frac{(m g f + \frac{1}{2} C_{d} {Aρv}^{2} + m g s i n θ + δ m a) r_{e f f}}{i_{g} i_{0} η_{T}}

in the formula, T_eIs the desired torque of the engine, i_gIs the transmission ratio of the transmission, i₀Representing the final gear ratio, η_TRepresenting the mechanical efficiency of the drive train, r_effIs the effective radius of the wheel, m is the vehicle mass, f is the rolling resistance coefficient, C_dIs an air resistance coefficient, A is the windward area, ρ is the air density, v is the longitudinal running speed of the vehicle, θ represents the road gradient, is the conversion coefficient of the rotating mass of the vehicle, a is the longitudinal acceleration of the vehicle, and g is the acceleration of gravity;

utilizing an engine torque characteristic map schematic diagram in a veDYNA vehicle model, reversely checking a table to obtain the corresponding throttle opening under the torque, and obtaining the corresponding throttle opening according to T_eAnd engine speed omega_eThe desired throttle opening α is obtained from the engine throttle opening characteristic map_desComprises the following steps:

α_des＝f(T_e,ω_e)

2) vehicle inverse longitudinal dynamics model of braking regime:

the running equation of the vehicle in braking running is as follows:

δ m a = F_{b} + m g f + \frac{1}{2} C_{d} {Aρv}^{2} + m g s i n θ

an engine braking torque expression can be obtained from the above equation:

T_{b} = (δ m a - m g f - \frac{1}{2} C_{d} {Aρv}^{2} - m g \sin θ) r_{e f f}

braking torque of each wheel

The calculation formula of the braking torque on each wheel satisfies the following equation:

M_b＝2(P_b·A_b·r_b·μ_b)

in the formula,

P_brepresents the brake pressure on each wheel, in units: pa; mu.s_bRepresenting the friction coefficient between the brake block and the brake disc; a. the_bRepresents the contact area of the friction plate and the brake disc, and the unit is: m is²；r_bRepresentative braking radius, unit: m;

the above parameters are substituted to obtain the relationship between the braking pressure and the braking torque of each wheel:

M_b＝0.1323×10^-3·P_b

obtaining a desired brake pressure P_bAnd then, the control is converted into the expected brake pedal opening degree, namely, the deceleration control under the braking condition is finished.