CN112238856B - An intelligent vehicle overtaking trajectory optimization method based on hybrid particle swarm algorithm - Google Patents

An intelligent vehicle overtaking trajectory optimization method based on hybrid particle swarm algorithm Download PDF

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CN112238856B
CN112238856B CN202011092410.5A CN202011092410A CN112238856B CN 112238856 B CN112238856 B CN 112238856B CN 202011092410 A CN202011092410 A CN 202011092410A CN 112238856 B CN112238856 B CN 112238856B
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trajectory
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CN112238856A (en
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任师通
魏民祥
赵炳振
杨嘉伟
季桢杰
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Nanjing University of Aeronautics and Astronautics
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W30/00—Purposes of road vehicle drive control systems not related to the control of a particular sub-unit, e.g. of systems using conjoint control of vehicle sub-units
    • B60W30/18—Propelling the vehicle
    • B60W30/18009—Propelling the vehicle related to particular drive situations
    • B60W30/18163—Lane change; Overtaking manoeuvres
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001—Details of the control system
    • B60W2050/0019—Control system elements or transfer functions
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001—Details of the control system
    • B60W2050/0019—Control system elements or transfer functions
    • B60W2050/0028—Mathematical models, e.g. for simulation
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Abstract

The invention discloses an intelligent vehicle overtaking track optimization method based on a hybrid particle swarm algorithm, which comprises a vehicle environment sensing unit (a camera and a laser radar), a vehicle sensor unit (a speed sensor, an acceleration sensor and a front wheel steering angle sensor) and a vehicle electronic control unit; the method comprises the steps of firstly judging the feasibility of overtaking through a vehicle electronic control unit, further establishing a quintic polynomial overtaking track function, secondly establishing a target function based on the driving efficiency and stability of the vehicle, and finally optimizing the target function by adopting a hybrid particle swarm optimization to obtain the optimal overtaking driving track. The intelligent vehicle overtaking track optimization method based on the hybrid particle swarm optimization can enable the vehicle to quickly and stably complete overtaking tasks; the hybrid particle swarm algorithm can efficiently and accurately optimize the target function, and compared with other algorithms, the hybrid particle swarm algorithm is strong in convergence and short in optimization time.

Description

一种基于混合粒子群算法的智能车超车轨迹优化方法An intelligent vehicle overtaking trajectory optimization method based on hybrid particle swarm algorithm

技术领域technical field

本发明涉及到智能驾驶技术领域，尤其涉及到一种基于混合粒子群算法优化智能车超车轨迹方法。The invention relates to the technical field of intelligent driving, in particular to a method for optimizing the overtaking trajectory of an intelligent vehicle based on a hybrid particle swarm algorithm.

背景技术Background technique

近几年来，智能车辆由于其在提高交通效率，减少交通事故，增强车辆的安全性方面具有的优势，成为了汽车行业的最受关注的热点之一。对于智能车辆的研究主要包括感知层、决策规划层以及控制层三大模块。超车作为汽车行驶过程中一个重要的部分，据不完全统计，每年因超车所导致的交通事故占所有交通事故的15％以上。通常情况下，驾驶员依靠自身的驾驶经验和周围环境(车速、距离)情况执行超车行为。然而，对于一些驾驶员来说，其可能对超车的可行性进行错误的判断，由此导致了意外事故的发生。超车轨迹规划作为智能车辆能否安全、高效完成超车任务的关键，因此，对于智能车辆的超车轨迹规划的研究对于提高车辆通行效率具有重要的意义。In recent years, smart vehicles have become one of the hotspots in the automotive industry due to their advantages in improving traffic efficiency, reducing traffic accidents, and enhancing vehicle safety. The research on intelligent vehicles mainly includes three modules: perception layer, decision planning layer and control layer. Overtaking is an important part of the car driving process. According to incomplete statistics, traffic accidents caused by overtaking account for more than 15% of all traffic accidents every year. Usually, drivers rely on their own driving experience and surrounding environment (vehicle speed, distance) to perform overtaking behavior. However, for some drivers, they may make a wrong judgment on the feasibility of overtaking, thus leading to accidents. Overtaking trajectory planning is the key to whether intelligent vehicles can safely and efficiently complete the overtaking task. Therefore, the research on the overtaking trajectory planning of intelligent vehicles is of great significance to improve the efficiency of vehicle traffic.

发明内容SUMMARY OF THE INVENTION

发明目的：本发明要解决的技术问题是在智能车辆在超车过程中兼顾效率、安全方面的缺陷，提出一种基于混合粒子群优化算法优化的超车轨迹规划方法。Purpose of the invention: The technical problem to be solved by the present invention is to take into account the defects of efficiency and safety in the overtaking process of intelligent vehicles, and propose an overtaking trajectory planning method based on hybrid particle swarm optimization algorithm optimization.

技术方案：Technical solutions:

一种基于混合粒子群算法的智能车超车轨迹优化方法，包括如下步骤：A method for optimizing the overtaking trajectory of an intelligent vehicle based on a hybrid particle swarm algorithm, comprising the following steps:

步骤1：信息采集，根据摄像头采集的道路信息，包括障碍物位置信息、车道限速信息，激光雷达采集的前车车辆与自车车辆信息、前车速度、加速度信息以及车辆传感器单元采集的车辆状态信息确定大地坐标系与车辆坐标系，建立超车安全距离模型；Step 1: Information collection, according to the road information collected by the camera, including the obstacle position information, lane speed limit information, the preceding vehicle and ego vehicle information collected by the lidar, the preceding vehicle speed, acceleration information, and the vehicle collected by the vehicle sensor unit. The state information determines the geodetic coordinate system and the vehicle coordinate system, and establishes the overtaking safety distance model;

步骤2：超车决策的判定，车辆电子控制单元通过判断自车与前车的实际距离Sreal与超车安全距离Sf的差值，记作a；通过摄像头检测道路信息，识别出车道限制速度vl；通过摄像头检测左侧车道是否存在障碍物，当自车与前车的实际距离满足超车安全距离，两车车速均在车道限制速度内，且左侧超车道无障碍物时，车辆电子控制单元发信号给车辆执行机构，开始超车；车辆电子控制单元将超车信号发送给车辆执行机构；Step 2: Judgment of overtaking decision, the vehicle electronic control unit judges the difference between the actual distance S real and the overtaking safe distance S f between the vehicle and the preceding vehicle, denoted as a; detects the road information through the camera, and identifies the lane limit speed v l ; Use the camera to detect whether there are obstacles in the left lane. When the actual distance between the vehicle and the vehicle in front meets the safety distance for overtaking, the speed of the two vehicles is within the lane limit speed, and the left overtaking lane is free of obstacles, the electronic control of the vehicle The unit sends a signal to the vehicle executive agency to start overtaking; the vehicle electronic control unit sends the overtaking signal to the vehicle executive agency;

步骤3：超车轨迹函数建立，建立五次多项式超车轨迹函数，确定初始时刻状态

Figure BDA0002722586030000021
与结束时刻状态
Figure BDA0002722586030000022
中各项的数值，将以上各数值代入五次多项式超车轨迹函数，可得到含有初始车速、换道纵向轨迹长度、换道所需时间三个参数变量的函数式；Step 3: Establish the overtaking trajectory function, establish the quintic polynomial overtaking trajectory function, and determine the initial time state
Figure BDA0002722586030000021
and end time state
Figure BDA0002722586030000022
By substituting the above values into the quintic polynomial overtaking trajectory function, a functional formula containing three parameter variables of initial vehicle speed, length of lane-changing longitudinal trajectory, and time required for lane-changing can be obtained;

步骤4：参数变量的优化，利用混合粒子群算法对换道纵向轨迹长度、换道所需时间两个参数变量进行参数优化，即可得到不同初始车速下的最优超车轨迹。Step 4: Optimization of parameter variables, using the hybrid particle swarm algorithm to optimize the parameters of the two parameter variables, the length of the longitudinal trajectory of the lane change and the time required for the lane change, to obtain the optimal overtaking trajectory under different initial vehicle speeds.

进一步地，所述步骤1中摄像头将采集到的道路信息、激光雷达将采集到的前车与自车相对位置以及前车速度、加速度信息传到车辆电子控制单元中，车辆传感器包括车速传感器、前轮转角传感器以及加速度传感器分别采集车辆的速度、前轮转角以及加速度，同时将得到的信息传到车辆电子控制单元中；Further, in the step 1, the camera transmits the road information collected, the relative position of the preceding vehicle and the vehicle, the speed and acceleration information of the preceding vehicle collected by the lidar to the electronic control unit of the vehicle, and the vehicle sensors include a vehicle speed sensor, The front wheel angle sensor and the acceleration sensor respectively collect the speed, front wheel angle and acceleration of the vehicle, and at the same time transmit the obtained information to the vehicle electronic control unit;

进一步地，所述步骤2的超车安全距离模型为：Further, the overtaking safety distance model of the step 2 is:

Figure BDA0002722586030000023
Figure BDA0002722586030000023

式中，vf为自车车速，vr为自车与前车相对速度，μ为道路附着系数，g为重力加速度，t1为驾驶员反应延迟时间，t2为制动器起作用时间，d为最小停车距离。In the formula, v f is the speed of the ego vehicle, v r is the relative speed of the ego vehicle and the preceding vehicle, μ is the road adhesion coefficient, g is the acceleration of gravity, t 1 is the driver’s response delay time, t 2 is the brake action time, d is the minimum parking distance.

进一步地，所属步骤3的具体实现包括首先将超车轨迹函数分为换道、超越、并道三个阶段函数，为了减小计算量，将换道阶段轨迹与并道阶段轨迹看作是相对称的，超越阶段轨迹为一条直线无需优化，因此，只对换道阶段进行优化即可得到整个超车轨迹，建立五次多项式换道轨迹函数：Further, the specific implementation of step 3 includes first dividing the overtaking trajectory function into three stage functions: lane changing, overtaking, and merging. , the trajectory of the overtaking phase is a straight line and does not need to be optimized. Therefore, the entire overtaking trajectory can be obtained only by optimizing the lane-changing phase, and a quintic polynomial lane-changing trajectory function is established:

Figure BDA0002722586030000024
Figure BDA0002722586030000024

式中,a0,a1,a2,a3,a4,a5,b0,b1,b2,b3,b4,b5表示上述多项式函数的各项系数，确定初始时刻t0状态为：

Figure BDA0002722586030000025
结束时刻tz状态为：
Figure BDA0002722586030000026
In the formula, a 0 , a 1 , a 2 , a 3 , a 4 , a 5 , b 0 , b 1 , b 2 , b 3 , b 4 , b 5 represent the coefficients of the above polynomial functions, and determine the initial time The t 0 state is:
Figure BDA0002722586030000025
The end time t z state is:
Figure BDA0002722586030000026

则多项式的各项系数可表示为：Then the coefficients of each polynomial can be expressed as:

a0＝0,a1＝v0,a2＝0,a3＝10(xz-v0tz)/tz 3,a4＝-15(xz-v0tz)/tz 4,a5＝6(xz-v0tz)/tz 5 a 0 =0,a 1 =v 0 ,a 2 =0,a 3 =10(x z -v 0 t z )/t z 3 ,a 4 =-15(x z -v 0 t z )/t z 4 ,a 5 =6(x z -v 0 t z )/t z 5

b0＝0,b1＝0,b2＝0,b3＝10yz/tz 3,b4＝-15yz/tz 4,b5＝yz/tz 5 b 0 =0,b 1 =0,b 2 =0,b 3 =10y z /t z 3 ,b 4 =-15y z /t z 4 ,b 5 =y z /t z 5

式中，v0表示自车初始时刻的纵向车速，xz表示换道纵向轨迹长度，tz表示换道所需时间，yz表示车道宽度，一般取3.75mIn the formula, v 0 represents the longitudinal speed of the vehicle at the initial moment, x z represents the length of the longitudinal trajectory of lane changing, t z represents the time required for lane changing, and y z represents the lane width, generally 3.75m

则可以求出换道曲线函数为：Then the lane changing curve function can be obtained as:

Figure BDA0002722586030000031
Figure BDA0002722586030000031

由于超车轨迹中第三阶段函数与第一阶段函数互相对称，则可得超车轨迹函数为：

Figure BDA0002722586030000032
Since the third-stage function and the first-stage function in the overtaking trajectory are symmetrical to each other, the overtaking trajectory function can be obtained as:
Figure BDA0002722586030000032

式中，t1,t2,t3分别表示超车第一阶段、第二阶段、第三阶段的结束时间。In the formula, t 1 , t 2 , and t 3 represent the end time of the first stage, the second stage and the third stage of overtaking, respectively.

进一步地，所属步骤4的具体实现包括：Further, the specific implementation of step 4 includes:

步骤4.1，种群初始化与个体编码Step 4.1, Population Initialization and Individual Encoding

在一定的搜索空间中，初始化微粒数目为n的种群，第i个粒子代表一个m维的向量

Figure BDA0002722586030000034
i＝1,2,…,n,粒子所在的位置都是方程的解，第i个粒子在搜索空间中运动的速度也是m维的向量，为
Figure BDA0002722586030000035
对种群中的粒子个体采用编码的方式，每个粒子包含换道纵向轨迹长度，换道总时间两个参数变量。In a certain search space, initialize a population of n particles, and the ith particle represents an m-dimensional vector
Figure BDA0002722586030000034
i=1,2,...,n, the position of the particle is the solution of the equation, and the velocity of the i-th particle moving in the search space is also an m-dimensional vector, which is
Figure BDA0002722586030000035
The individual particles in the population are coded, and each particle contains two parameter variables: the length of the lane-changing longitudinal trajectory and the total lane-changing time.

步骤4.2，个体适应度值计算Step 4.2, individual fitness value calculation

粒子个体的适应度值计算公式表示如下:fitness＝min(J)，The calculation formula of the fitness value of the individual particle is expressed as follows: fitness=min(J),

J表示目标函数，利用其来确定参数变量纵向轨迹长度，换道总时间，ay可由以下公式直接求二次导数获得，J represents the objective function, which is used to determine the length of the longitudinal trajectory of the parameter variables, the total time of lane changing, and a y can be obtained by directly calculating the second derivative of the following formula,

J表示目标函数，利用其来确定参数变量纵向轨迹长度，换道总时间，考虑到汽车稳定性问题，基于纵向位移，侧向加速度，横摆角速度，质心侧偏角和前轮转角建立目标函数，上述五个指标均可由五次多项式函数求得，且只包含纵向轨迹长度，换道总时间两个变量，J represents the objective function, which is used to determine the length of the longitudinal trajectory of the parameter variables and the total time of lane changing. Considering the problem of vehicle stability, the objective function is established based on the longitudinal displacement, lateral acceleration, yaw rate, center of mass slip angle and front wheel rotation angle. , the above five indicators can be obtained by the quintic polynomial function, and only include the length of the longitudinal trajectory and the total time of changing lanes.

Figure BDA0002722586030000033
Figure BDA0002722586030000033

ωr可由以下公式获得，ω r can be obtained by the following formula,

Figure BDA0002722586030000041
Figure BDA0002722586030000041

其中，vx是车辆纵向速度，R为车辆转向半径；Among them, v x is the longitudinal speed of the vehicle, and R is the turning radius of the vehicle;

β可由以下公式获得，β can be obtained by the following formula,

Figure BDA0002722586030000042
Figure BDA0002722586030000042

δ可由以下公式获得，δ can be obtained by the following formula,

Figure BDA0002722586030000043
Figure BDA0002722586030000043

其中

Figure BDA0002722586030000044
k1,k2表示前轮与后轮的侧偏刚度，a,b分别表示质心至前轴和后轴的距离，L表示轴距，m表示汽车总质量，i为汽车转向系传动比，一般取i＝17。in
Figure BDA0002722586030000044
k 1 , k 2 represent the cornering stiffness of the front and rear wheels, a, b represent the distance from the center of mass to the front and rear axles, respectively, L represents the wheelbase, m represents the total mass of the vehicle, i is the transmission ratio of the steering system of the vehicle, Generally, i=17 is taken.

由此可建立目标函数表达式：From this, the objective function expression can be established:

Figure BDA0002722586030000045
Figure BDA0002722586030000045

式中，xz表示换道纵向轨迹长度，ay表示换道任意时刻侧向加速度，ωr表示换道任意时刻横摆角速度，β表示换道任意时刻质心侧偏角，δ表示换道任意时刻前轮转角，xamax、aymax、ωrmax、βmax、δmax分别表示所有换道轨迹中所允许的最大纵向轨迹长度、最大侧向加速度、最大横摆角速度、最大质心侧偏角和最大前轮转角，ω1、ω2、ω3、ω4、ω5为权值系数，且ω1+ω2+ω3+ω4+ω5＝1；In the formula, x z represents the length of the longitudinal trajectory of the lane change, a y represents the lateral acceleration at any time of the lane change, ω r represents the yaw rate at any time of the lane change, β represents the side-slip angle of the centroid at any time of the lane change, and δ represents the arbitrary time of the lane change. Front wheel rotation angle at time, x amax , a ymax , ω rmax , β max , δ max represent the maximum longitudinal track length, maximum lateral acceleration, maximum yaw rate, maximum center of mass slip angle and Maximum front wheel rotation angle, ω 1 , ω 2 , ω 3 , ω 4 , and ω 5 are weight coefficients, and ω 1 +ω 2 +ω 3 +ω 4 +ω 5 =1;

即粒子的适应度值为目标函数的最小值，将

Figure BDA0002722586030000046
带入目标函数即可求得该粒子对应的适应度值，根据所求的适应度值来判定解的优劣；That is, the fitness value of the particle is the minimum value of the objective function, and the
Figure BDA0002722586030000046
The fitness value corresponding to the particle can be obtained by bringing in the objective function, and the pros and cons of the solution can be determined according to the obtained fitness value;

步骤4.3，寻找个体极值和群体极值Step 4.3, looking for individual extremum and group extremum

通过计算每个粒子的适应度值以及粒子所经历过的位置，则可以得到粒子的个体极值与群体极值，令第i个粒子搜索到的最优位置为

Figure BDA0002722586030000047
在全局中搜索到的最优位置为
Figure BDA0002722586030000048
将粒子当前适应度值与粒子经过最优位置
Figure BDA0002722586030000049
的适应度值比较，根据比较结果选择其作为粒子当前最优位置，同时，将粒子当前适应度值比较，根据比较结果选择其作为粒子全局最优位置，上述可由以下公式确定：By calculating the fitness value of each particle and the position experienced by the particle, the individual extreme value and the group extreme value of the particle can be obtained, and the optimal position searched by the ith particle is
Figure BDA0002722586030000047
The optimal position searched in the global is
Figure BDA0002722586030000048
Compare the particle's current fitness value with the particle's optimal position
Figure BDA0002722586030000049
Compare the fitness values of the particles, select it as the current optimal position of the particle according to the comparison result, and at the same time, compare the current fitness value of the particle, and select it as the global optimal position of the particle according to the comparison result. The above can be determined by the following formula:

Figure BDA0002722586030000051
Figure BDA0002722586030000051

其中，Xi(t+1)表示第i个粒子t+1时刻的s维向量，Pi(t)表示第i个粒子在搜索空间中的最优位置；Among them, X i (t+1) represents the s-dimensional vector of the ith particle at time t+1, and P i (t) represents the optimal position of the ith particle in the search space;

步骤4.4，更新粒子的速度和位置Step 4.4, update particle velocity and position

通过以下公式对粒子进行更新操作：The particles are updated by the following formula:

vim(t+1)＝vim(t+1)+c1r1m(t)(pim(t)-xim(t))+c2r2m(t)(pgm(t)-xgm(t))v im (t+1)=v im (t+1)+c 1 r 1m (t)(p im (t)-x im (t))+c 2 r 2m (t)(p gm (t) -x gm (t))

xim(t+1)＝xim(t)+vim(t+1)x im (t+1)=x im (t)+v im (t+1)

式中：vim(t+1)表示第i个粒子在t+1时刻的速度，xim(t)表示第i个粒子在t+1时刻的位置，i＝[1,n],s＝[1,m]学习因子c1和c2为非负常数；r1与r2为相互独立的伪随机数，服从[0,1]上的均匀分布，vim∈[-vmax,vmax],其中，vmax是由自己设定的常数；In the formula: vi im (t+1) represents the velocity of the ith particle at time t+1, x im (t) represents the position of the ith particle at time t+1, i=[1,n],s =[1,m] The learning factors c 1 and c 2 are non-negative constants; r 1 and r 2 are mutually independent pseudo-random numbers, obeying the uniform distribution on [0,1], vi im ∈[-v max , v max ], where v max is a constant set by itself;

步骤4.5，交叉操作Step 4.5, Crossover Operation

选择两个交叉位置，将个体和个体极值或个体与群体极值进行交叉，对于获得的新粒子采取保留优秀原则，只有当新粒子适应度值优于旧粒子的适应度值时才可更新；Select two intersection positions, cross the individual and the individual extreme value or the individual and the group extreme value, adopt the principle of retaining the excellence for the new particles obtained, and update only when the fitness value of the new particle is better than the fitness value of the old particle. ;

步骤4.6，变异操作Step 4.6, mutation operation

选择粒子个体内部的两个变异位置st1和st2，所选的两个位置互换，对于获得的新粒子同样采取保留优秀原则，只有当新粒子适应度值优于旧粒子的适应度值时才可更新。Select the two mutation positions st1 and st2 within the particle individual, and the two selected positions are exchanged. The principle of retaining excellence is also adopted for the new particles obtained. Only when the fitness value of the new particle is better than the fitness value of the old particle. Updatable.

确定初始状态和目标函数，考虑到汽车稳定性问题，基于纵向位移，侧向加速度，横摆角速度，质心侧偏角和前轮转角建立目标函数，通过混合粒子群算法对目标函数的换道纵向轨迹长度和换道所需时间两个参数变量进行优化，最后得到最优超车轨迹；Determine the initial state and objective function, consider the vehicle stability problem, establish an objective function based on longitudinal displacement, lateral acceleration, yaw rate, center of mass slip angle and front wheel rotation angle, and use the hybrid particle swarm algorithm to change lanes of the objective function longitudinally The two parameter variables, the trajectory length and the time required to change lanes, are optimized, and finally the optimal overtaking trajectory is obtained;

通过混合粒子群算法中的寻优特性，求得不同车速下的换道纵向轨迹长度以及换道所需时间，进而得到最优超车轨迹函数。Through the optimization feature in the hybrid particle swarm optimization algorithm, the length of the longitudinal trajectory of lane changing and the time required for lane changing at different vehicle speeds are obtained, and then the optimal overtaking trajectory function is obtained.

有益效果：Beneficial effects:

1.本发明提出的轨迹优化算法兼顾了行驶效率以及车辆稳定性、舒适性等原则，使车辆能够快速、稳定的完成超车任务；1. The trajectory optimization algorithm proposed by the present invention takes into account the principles of driving efficiency, vehicle stability and comfort, so that the vehicle can quickly and stably complete the overtaking task;

2.采用的混合粒子群算法可以高效准确的对目标函数进行优化，相比于其他算法，收敛性强且优化时间较小；2. The adopted hybrid particle swarm algorithm can optimize the objective function efficiently and accurately. Compared with other algorithms, it has strong convergence and less optimization time;

3.分别对低速、中速和高速三种行驶工况下进行分析，使得该模型可以适用更加复杂的情况。3. The three driving conditions of low speed, medium speed and high speed are analyzed separately, so that the model can be applied to more complex situations.

附图说明Description of drawings

图1是车辆超车轨迹优化逻辑框图；Fig. 1 is a logic block diagram of vehicle overtaking trajectory optimization;

图2是车辆超车行为示意图；Figure 2 is a schematic diagram of vehicle overtaking behavior;

图3是混合粒子群优化结果图；Fig. 3 is the result diagram of mixed particle swarm optimization;

图4是不同纵向车速下的最优超车轨迹图。Figure 4 shows the optimal overtaking trajectories at different longitudinal vehicle speeds.

具体实施方式Detailed ways

以下结合附图对本发明的具体实施方式进行详细的说明。The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

如图1所示，图1为该系统的逻辑框图，其特征在于包括环境感知单元、自车传感器单元、车辆电子控制单元、轨迹规划模块以及混本粒子群算法对目标函数优化求解以得到最优超车轨迹。As shown in Figure 1, Figure 1 is a logical block diagram of the system, which is characterized in that it includes an environmental perception unit, a self-vehicle sensor unit, a vehicle electronic control unit, a trajectory planning module, and a hybrid particle swarm algorithm to optimize the objective function to obtain the optimal solution. Excellent overtaking track.

步骤1：根据摄像头、激光雷达以及车辆传感器单元来采集道路信息，车辆状态信息，确定大地坐标系与车辆坐标系；Step 1: Collect road information and vehicle status information according to the camera, lidar and vehicle sensor units, and determine the geodetic coordinate system and the vehicle coordinate system;

步骤2：车辆电子控制单元对接收到的摄像头信息、激光雷达信息以及车辆各传感器信息进行处理，建立超车安全距离模型；Step 2: The vehicle electronic control unit processes the received camera information, lidar information and vehicle sensor information, and establishes an overtaking safe distance model;

步骤3：通过对信息进行处理，车辆电子控制单元将超车信号发送给车辆执行机构；Step 3: By processing the information, the vehicle electronic control unit sends the overtaking signal to the vehicle executive agency;

步骤4：建立五次多项式超车轨迹模型，通过混合粒子群算法对超车轨迹进行优化，最后得到最优超车轨迹；Step 4: Establish a quintic polynomial overtaking trajectory model, optimize the overtaking trajectory through the hybrid particle swarm algorithm, and finally obtain the optimal overtaking trajectory;

进一步的，步骤1中，通过摄像头采集车道线信息以及车道限定速度信息，将得到的信息传到车辆电子控制单元中，激光雷达采集前方车辆信息、相邻车道信息、前车与自车相对位置以及前车速度、加速度信息，并将得到的信息传到车辆电子控制单元中，汽车中的车速传感器、前轮转角传感器以及加速度传感器负责采集车辆的行驶速度、前轮转角以及加速度，同时将得到的信息传到车辆电子控制单元中；Further, in step 1, the lane line information and the lane limit speed information are collected by the camera, and the obtained information is transmitted to the vehicle electronic control unit, and the lidar collects the information of the vehicle ahead, the information of the adjacent lane, and the relative position of the vehicle in front and the own vehicle. As well as the speed and acceleration information of the preceding vehicle, and transmit the obtained information to the vehicle electronic control unit, the vehicle speed sensor, front wheel angle sensor and acceleration sensor in the car are responsible for collecting the vehicle's driving speed, front wheel angle and acceleration. The information is transmitted to the vehicle electronic control unit;

进一步的，步骤2中，车辆电子控制单元接收到的摄像头信息、激光雷达信息以及车辆各传感器信息进行处理，建立超车安全距离模型；Further, in step 2, the camera information, lidar information and information of various sensors of the vehicle received by the electronic control unit of the vehicle are processed to establish a safe distance model for overtaking;

Figure BDA0002722586030000061
Figure BDA0002722586030000061

式中，vf为自车车速，vr为自车与前车相对速度，μ为道路附着系数，g为重力加速度，t1为驾驶员反应延迟时间，t2为制动器起作用时间，d为最小停车距离。In the formula, v f is the speed of the ego vehicle, v r is the relative speed of the ego vehicle and the preceding vehicle, μ is the road adhesion coefficient, g is the acceleration of gravity, t 1 is the driver’s response delay time, t 2 is the brake action time, d is the minimum parking distance.

进一步的，步骤3中，车辆电子控制单元通过判断自车与前车的实际距离Sreal与超车安全距离Sf的差值，记作a，Further, in step 3, the vehicle electronic control unit determines the difference between the actual distance S real and the overtaking safety distance S f between the vehicle and the preceding vehicle, denoted as a,

进一步的，通过摄像头检测道路信息，识别出车道限制速度vl，Further, the road information is detected by the camera, and the lane limit speed v l is identified,

进一步的，通过摄像头检测左侧车道是否存在障碍物，Further, the camera detects whether there are obstacles in the left lane,

当自车与前车的实际距离满足超车安全距离，两车车速均在车道限制速度内，且左侧超车道无障碍物时，车辆电子控制单元发信号给车辆执行机构，开始超车；When the actual distance between the vehicle and the vehicle in front meets the overtaking safety distance, the speed of both vehicles is within the speed limit of the lane, and there is no obstacle in the left overtaking lane, the vehicle electronic control unit sends a signal to the vehicle actuator to start overtaking;

进一步的，步骤4中，如图2所示，首先由自车道的中心线进入超车道的中心线(超车第一阶段：换道阶段)，在超车道超越前车(超车第二阶段：超越阶段)后，再由超车道返回到原车道(超车第三阶段：并道阶段)。因此，超车行为可以看作两次换道行为与一次超越行为，为了减小计算量，本文将两次换道行为看作是相对称的，且超越阶段为一条直线无需优化，即只对超车第一阶段(换道阶段)换道轨迹进行一次优化，便可得到最优超车轨迹。Further, in step 4, as shown in Figure 2, the center line of the own lane first enters the center line of the overtaking lane (the first stage of overtaking: lane-changing stage), and the vehicle in front is overtaken in the overtaking lane (the second stage of overtaking: overtaking stage), and then return to the original lane from the overtaking lane (the third stage of overtaking: merge stage). Therefore, the overtaking behavior can be regarded as two lane-changing behaviors and one overtaking behavior. In order to reduce the amount of calculation, this paper regards the two lane-changing behaviors as relatively symmetrical, and the overtaking stage is a straight line without optimization, that is, only for overtaking In the first stage (lane change stage), the lane change trajectory is optimized once, and the optimal overtaking trajectory can be obtained.

进一步的，步骤4中，如图2所示，设定自车车道为大地坐标系的横坐标，纵坐标与车身垂直，自车质心初始位置设为原点，则自车车道的路径公式为y＝0，超车车道的路径公式为y＝yz，yz为一个车道的宽度，一般取(yz＝3.75m)。Further, in step 4, as shown in Figure 2, the own vehicle lane is set as the abscissa of the geodetic coordinate system, the ordinate is perpendicular to the vehicle body, and the initial position of the own vehicle's center of mass is set as the origin, then the path formula of the own vehicle lane is y. = 0, the path formula of the overtaking lane is y=y z , y z is the width of a lane, generally taken (y z =3.75m).

进一步的，步骤4中，采用五次多项式函数为换道曲线，即换道方程为：Further, in step 4, the fifth-order polynomial function is used as the lane-changing curve, that is, the lane-changing equation is:

Figure BDA0002722586030000071
Figure BDA0002722586030000071

确定初始时刻t0为：

Figure BDA0002722586030000072
结束时刻tz为：Determine the initial time t 0 as:
Figure BDA0002722586030000072
The end time t z is:

Figure BDA0002722586030000073
Figure BDA0002722586030000073

则多项式的各项系数可表示为：Then the coefficients of each polynomial can be expressed as:

Figure BDA0002722586030000074
Figure BDA0002722586030000074

则可以求出换道曲线函数为：Then the lane changing curve function can be obtained as:

Figure BDA0002722586030000081
Figure BDA0002722586030000081

综上可得超车轨迹函数为：In summary, the overtaking trajectory function can be obtained as:

Figure BDA0002722586030000082
Figure BDA0002722586030000082

式中，t1,t2,t3分别表示超车第一阶段、第二阶段、第三阶段的结束时间。In the formula, t 1 , t 2 , and t 3 represent the end time of the first stage, the second stage and the third stage of overtaking, respectively.

对于超车过程中的第一阶段，由于纵向车速v0、纵向轨迹长度xz以及换道所需总时间tz的不同，可以得到无数条换道曲线。因此需要对换道函数的参数进行优化，以得到最优换道函数曲线。For the first stage in the overtaking process, due to the differences in the longitudinal vehicle speed v 0 , the longitudinal trajectory length x z and the total time t z required for lane changing, an infinite number of lane changing curves can be obtained. Therefore, it is necessary to optimize the parameters of the lane-changing function to obtain the optimal lane-changing function curve.

进一步的，步骤4中，设定目标函数：Further, in step 4, the objective function is set:

Figure BDA0002722586030000083
Figure BDA0002722586030000083

式中，xz表示换道纵向轨迹长度，ay表示换道任意时刻侧向加速度，ωr表示换道任意时刻横摆角速度，β表示换道任意时刻质心侧偏角，δ表示换道任意时刻前轮转角，xamax、aymax、ωrmax、βmax、δmax分别表示所有换道轨迹中所允许的最大纵向轨迹长度、最大侧向加速度、最大横摆角速度、最大质心侧偏角和最大前轮转角，ω1、ω2、ω3、ω4、ω5为权值系数，且ω1+ω2+ω3+ω4+ω5＝1In the formula, x z represents the length of the longitudinal trajectory of the lane change, a y represents the lateral acceleration at any time of the lane change, ω r represents the yaw rate at any time of the lane change, β represents the side-slip angle of the centroid at any time of the lane change, and δ represents the arbitrary time of the lane change. Front wheel rotation angle at time, x amax , a ymax , ω rmax , β max , δ max represent the maximum longitudinal track length, maximum lateral acceleration, maximum yaw rate, maximum center of mass slip angle and Maximum front wheel rotation angle, ω 1 , ω 2 , ω 3 , ω 4 , and ω 5 are weight coefficients, and ω 1 +ω 2 +ω 3 +ω 4 +ω 5 =1

进一步的，上述目标函数中的ay可由以下公式直接求二次导数获得，Further, a y in the above objective function can be obtained by directly calculating the second derivative of the following formula,

Figure BDA0002722586030000084
Figure BDA0002722586030000084

进一步的，上述目标函数中的ωr可由以下公式获得，Further, ω r in the above objective function can be obtained by the following formula,

Figure BDA0002722586030000085
Figure BDA0002722586030000085

进一步的，上述目标函数中的β可由以下公式获得，Further, β in the above objective function can be obtained by the following formula,

Figure BDA0002722586030000086
Figure BDA0002722586030000086

进一步的，上述目标函数中的δ可由以下公式获得，Further, δ in the above objective function can be obtained by the following formula,

Figure BDA0002722586030000091
Figure BDA0002722586030000091

其中

Figure BDA0002722586030000092
k1,k2表示前轮与后轮的侧偏刚度，a,b分别表示质心至前轴和后轴的距离，m表示汽车总质量，i为汽车转向系传动比，一般取i＝17。in
Figure BDA0002722586030000092
k 1 , k 2 represent the cornering stiffness of the front and rear wheels, a, b represent the distance from the center of mass to the front and rear axles respectively, m represents the total mass of the vehicle, i is the transmission ratio of the steering system of the vehicle, generally i=17 .

进一步的，步骤4中，车辆在行驶过程中需要满足稳定性要求，因此设置约束条件如下：Further, in step 4, the vehicle needs to meet the stability requirements during driving, so the constraints are set as follows:

Figure BDA0002722586030000093
Figure BDA0002722586030000093

进一步的，步骤4中，通过混合粒子群算法对目标函数进行优化，提出一种遗传算法(GA)与标准粒子群算法(PSO)相结合的混合粒子群算法，摒弃了标准粒子群算法通过跟踪极值来更新粒子的位置的方法，通过加入遗传算法中的交叉和变异操作，使粒子同个体极值和群体极值的交叉以及粒子自身变异的方式来搜索最优解。Further, in step 4, the objective function is optimized by the hybrid particle swarm algorithm, and a hybrid particle swarm algorithm that combines the genetic algorithm (GA) and the standard particle swarm algorithm (PSO) is proposed, which abandons the standard particle swarm algorithm through tracking. The method of updating the position of the particle by the extreme value, by adding the crossover and mutation operations in the genetic algorithm, makes the particle cross the individual extreme value and the group extreme value and the particle itself mutates to search for the optimal solution.

进一步的，混合粒子群算法求解的具体步骤为：Further, the specific steps of the hybrid particle swarm algorithm solution are:

步骤4.1，种群初始化与个体编码Step 4.1, Population Initialization and Individual Encoding

在一定的搜索空间中，初始化微粒数目为n的种群，第i个粒子代表一个m维的向量

Figure BDA0002722586030000094
粒子所在的位置都是方程的解。第i个粒子在搜索空间中运动的速度也是m维的向量，为
Figure BDA0002722586030000095
对种群中的粒子个体采用编码的方式，每个粒子包含换道纵向轨迹长度，换道总时间两个自变量。In a certain search space, initialize a population of n particles, and the ith particle represents an m-dimensional vector
Figure BDA0002722586030000094
The positions of the particles are the solutions of the equations. The velocity of the i-th particle moving in the search space is also an m-dimensional vector, which is
Figure BDA0002722586030000095
Encoding is used for the individual particles in the population, and each particle contains two independent variables: the length of the longitudinal trajectory of the lane change and the total time of the lane change.

步骤4.2，个体适应度值计算Step 4.2, individual fitness value calculation

粒子个体的适应度值计算公式表示如下:fitness＝min(J)The formula for calculating the fitness value of an individual particle is expressed as follows: fitness=min(J)

即粒子的适应度值为目标函数的最小值。将

Figure BDA0002722586030000096
带入目标函数即可求得该粒子对应的适应度值，根据所求的适应度值来判定解的优劣。That is, the fitness value of the particle is the minimum value of the objective function. Will
Figure BDA0002722586030000096
The fitness value corresponding to the particle can be obtained by bringing in the objective function, and the quality of the solution can be determined according to the obtained fitness value.

步骤4.3，寻找个体极值和群体极值Step 4.3, looking for individual extremum and group extremum

通过计算每个粒子的适应度值以及粒子所经历过的位置，则可以得到粒子的个体极值与群体极值，令第i个粒子搜索到的最优位置为

Figure BDA0002722586030000101
在全局中搜索到的最优位置为
Figure BDA0002722586030000102
将粒子当前适应度值与粒子经过最优位置
Figure BDA0002722586030000103
的适应度值比较，根据比较结果选择其作为粒子当前最优位置。同时，将粒子当前适应度值比较，根据比较结果选择其作为粒子全局最优位置。上述可由以下公式确定：By calculating the fitness value of each particle and the position experienced by the particle, the individual extreme value and the group extreme value of the particle can be obtained, and the optimal position searched by the ith particle is
Figure BDA0002722586030000101
The optimal position searched in the global is
Figure BDA0002722586030000102
Compare the particle's current fitness value with the particle's optimal position
Figure BDA0002722586030000103
The fitness value is compared, and it is selected as the current optimal position of the particle according to the comparison result. At the same time, the current fitness value of the particle is compared, and it is selected as the global optimal position of the particle according to the comparison result. The above can be determined by the following formula:

Figure BDA0002722586030000104
Figure BDA0002722586030000104

步骤4.4，更新粒子的速度和位置Step 4.4, update particle velocity and position

通过以下公式对粒子进行更新操作：The particles are updated by the following formula:

vim(t+1)＝vim(t+1)+c1r1m(t)(pim(t)-xim(t))+c2r2m(t)(pgm(t)-xgm(t))v im (t+1)=v im (t+1)+c 1 r 1m (t)(p im (t)-x im (t))+c 2 r 2m (t)(p gm (t) -x gm (t))

xim(t+1)＝xim(t)+vim(t+1)x im (t+1)=x im (t)+v im (t+1)

式中：i＝[1,n],s＝[1,m]学习因子c1和c2为非负常数；r1与r2为相互独立的伪随机数，服从[0,1]上的均匀分布。vim∈[-vmax,vmax],其中，vmax是由自己设定的常数。In the formula: i=[1,n], s=[1,m] The learning factors c 1 and c 2 are non-negative constants; r 1 and r 2 are mutually independent pseudo-random numbers, obeying [0,1] uniform distribution. v im ∈[-v max ,v max ], where v max is a constant set by itself.

步骤4.5，交叉操作Step 4.5, Crossover Operation

选择两个交叉位置，将个体和个体极值或个体与群体极值进行交叉，对于获得的新粒子采取保留优秀原则，只有当新粒子适应度值优于旧粒子的适应度值时才可更新。Select two intersection positions, cross the individual and the individual extreme value or the individual and the group extreme value, adopt the principle of retaining the excellence for the new particles obtained, and update only when the fitness value of the new particle is better than the fitness value of the old particle. .

步骤4.6，变异操作Step 4.6, mutation operation

选择粒子个体内部的两个变异位置st1和st2，所选的两个位置互换，对于获得的新粒子同样采取保留优秀原则，只有当新粒子适应度值优于旧粒子的适应度值时才可更新。Select the two mutation positions st1 and st2 within the particle individual, and the two selected positions are exchanged. The principle of retaining excellence is also adopted for the new particles obtained. Only when the fitness value of the new particle is better than the fitness value of the old particle. Updatable.

进一步的，通过混合粒子群算法中的寻优特性，得到的迭代次数与适应度值的关系如图3所示，得到的适应度求得不同车速下的换道纵向轨迹长度以及换道所需时间，如下表所示，进而得到最优超车轨迹函数。Further, through the optimization feature in the hybrid particle swarm algorithm, the obtained relationship between the number of iterations and the fitness value is shown in Figure 3. The obtained fitness is used to obtain the length of the longitudinal trajectory of lane changing and the required length of lane changing at different vehicle speeds. time, as shown in the following table, and then obtain the optimal overtaking trajectory function.

进一步的，选择高速、中速、低速三种典型的车速进行研究，所得到的超车轨迹曲线如图3所示。Further, three typical vehicle speeds of high speed, medium speed and low speed are selected for research, and the obtained overtaking trajectory curve is shown in Figure 3.

表1轨迹优化结果Table 1 Trajectory optimization results

Figure BDA0002722586030000105
Figure BDA0002722586030000105

Figure BDA0002722586030000111
Figure BDA0002722586030000111

以上所述仅是本发明的优选实施方式，应当指出，对于本技术领域的普通技术人员来说，在不脱离本发明原理的前提下，还可以做出若干改进和润饰，这些改进和润饰也应视为本发明的保护范围。The above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the principles of the present invention, several improvements and modifications can be made. It should be regarded as the protection scope of the present invention.

Claims (5)

1.一种基于混合粒子群算法的智能车超车轨迹优化方法，其特征在于，包括如下步骤：1. an intelligent vehicle overtaking trajectory optimization method based on hybrid particle swarm algorithm, is characterized in that, comprises the steps: 步骤1：信息采集，根据摄像头采集的道路信息，包括障碍物位置信息、车道限速信息，激光雷达采集的前车车辆与自车车辆信息以及车辆传感器单元采集的车辆状态信息确定大地坐标系与车辆坐标系，建立超车安全距离模型；Step 1: Information collection, according to the road information collected by the camera, including obstacle position information, lane speed limit information, the preceding vehicle and ego vehicle information collected by lidar, and the vehicle status information collected by the vehicle sensor unit to determine the geodetic coordinate system and Vehicle coordinate system to establish a safe distance model for overtaking; 步骤2：超车决策的判定，车辆电子控制单元通过判断自车与前车的实际距离Sreal与超车安全距离Sf的差值，记作a；通过摄像头检测道路信息，识别出车道限制速度vl；通过摄像头检测左侧车道是否存在障碍物，当自车与前车的实际距离满足超车安全距离，两车车速均在车道限制速度内，且左侧超车道无障碍物时，车辆电子控制单元发信号给车辆执行机构，开始超车；车辆电子控制单元将超车信号发送给车辆执行机构；Step 2: Judgment of overtaking decision, the vehicle electronic control unit judges the difference between the actual distance S real and the overtaking safe distance S f between the vehicle and the preceding vehicle, denoted as a; detects the road information through the camera, and identifies the lane limit speed v l ; Use the camera to detect whether there are obstacles in the left lane. When the actual distance between the vehicle and the vehicle in front meets the safety distance for overtaking, the speed of the two vehicles is within the lane limit speed, and the left overtaking lane is free of obstacles, the electronic control of the vehicle The unit sends a signal to the vehicle executive agency to start overtaking; the vehicle electronic control unit sends the overtaking signal to the vehicle executive agency; 步骤3：超车轨迹函数建立，建立五次多项式超车轨迹函数，确定初始时刻状态
Figure FDA0003409657190000011
与结束时刻状态
Figure FDA0003409657190000012
中各项的数值，将以上各数值代入五次多项式超车轨迹函数，可得到含有初始车速、换道纵向轨迹长度、换道所需时间三个参数变量的函数式；Step 3: Establish the overtaking trajectory function, establish the quintic polynomial overtaking trajectory function, and determine the initial time state
Figure FDA0003409657190000011
and end time state
Figure FDA0003409657190000012
By substituting the above values into the quintic polynomial overtaking trajectory function, a functional formula containing three parameter variables of initial vehicle speed, length of lane-changing longitudinal trajectory, and time required for lane-changing can be obtained; 步骤4：参数变量的优化，利用混合粒子群算法对换道纵向轨迹长度、换道所需时间两个参数变量进行参数优化，即可得到不同初始车速下的最优超车轨迹。Step 4: Optimization of parameter variables, using the hybrid particle swarm algorithm to optimize the parameters of the two parameter variables, the length of the longitudinal trajectory of the lane change and the time required for the lane change, to obtain the optimal overtaking trajectory under different initial vehicle speeds. 2.根据权利要求1所述的一种基于混合粒子群算法的智能车超车轨迹优化方法，其特征在于，所述步骤1中摄像头将采集到的道路信息、激光雷达将采集到的前车与自车相对位置以及前车速度、加速度信息传到车辆电子控制单元中，车辆传感器包括车速传感器、前轮转角传感器以及加速度传感器分别采集车辆的速度、前轮转角以及加速度，同时将得到的信息传到车辆电子控制单元中。2. a kind of intelligent vehicle overtaking trajectory optimization method based on hybrid particle swarm algorithm according to claim 1, is characterized in that, in the described step 1, the road information that the camera will collect, and the preceding vehicle and the laser radar that will collect will be collected. The relative position of the vehicle, the speed and acceleration of the preceding vehicle are transmitted to the electronic control unit of the vehicle. The vehicle sensors include vehicle speed sensor, front wheel angle sensor and acceleration sensor to collect the vehicle speed, front wheel angle and acceleration respectively, and transmit the obtained information at the same time. into the vehicle electronic control unit. 3.根据权利要求1所述的一种基于混合粒子群算法的智能车超车轨迹优化方法，其特征在于，所述步骤2的超车安全距离模型为：3. a kind of intelligent vehicle overtaking trajectory optimization method based on hybrid particle swarm algorithm according to claim 1, is characterized in that, the overtaking safety distance model of described step 2 is:
Figure FDA0003409657190000013
Figure FDA0003409657190000013
 式中，vf为自车车速，vr为自车与前车相对速度，μ为道路附着系数，g为重力加速度，t1为驾驶员反应延迟时间，t2为制动器起作用时间，d为最小停车距离。In the formula, v f is the speed of the ego vehicle, v r is the relative speed of the ego vehicle and the preceding vehicle, μ is the road adhesion coefficient, g is the acceleration of gravity, t 1 is the driver’s response delay time, t 2 is the brake action time, d is the minimum parking distance. 4.根据权利要求1所述的一种基于混合粒子群算法的智能车超车轨迹优化方法，其特征在于，所属步骤3的具体实现包括首先将超车轨迹函数分为换道、超越、并道三个阶段函数，为了减小计算量，将换道阶段轨迹与并道阶段轨迹看作是相对称的，超越阶段轨迹为一条直线无需优化，因此，只对换道阶段进行优化即可得到整个超车轨迹，建立五次多项式换道轨迹函数：4. a kind of intelligent vehicle overtaking trajectory optimization method based on hybrid particle swarm algorithm according to claim 1, is characterized in that, the concrete realization of belonging step 3 comprises at first dividing the overtaking trajectory function into three lanes, overtaking, and merging lanes. In order to reduce the amount of calculation, the trajectory of the lane-changing phase and the trajectory of the merging phase are regarded as relatively symmetrical, and the trajectory of the overtaking phase is a straight line without optimization. Therefore, only the lane-changing phase can be optimized to obtain the entire overtaking phase. trajectories, establish a quintic polynomial lane-changing trajectory function:
Figure FDA0003409657190000021
Figure FDA0003409657190000021
 式中,a0,a1,a2,a3,a4,a5,b0,b1,b2,b3,b4,b5表示上述多项式函数的各项系数，确定初始时刻t0状态为：
Figure FDA0003409657190000022
结束时刻tz状态为：
Figure FDA0003409657190000023
In the formula, a 0 , a 1 , a 2 , a 3 , a 4 , a 5 , b 0 , b 1 , b 2 , b 3 , b 4 , b 5 represent the coefficients of the above polynomial functions, and determine the initial time The t 0 state is:
Figure FDA0003409657190000022
The end time t z state is:
Figure FDA0003409657190000023
 则多项式的各项系数可表示为：Then the coefficients of each polynomial can be expressed as: a0＝0,a1＝v0,a2＝0,a3＝10(xz-v0tz)/tz 3,a4＝-15(xz-v0tz)/tz 4,a5＝6(xz-v0tz)/tz 5 a 0 =0,a 1 =v 0 ,a 2 =0,a 3 =10(x z -v 0 t z )/t z 3 ,a 4 =-15(x z -v 0 t z )/t z 4 ,a 5 =6(x z -v 0 t z )/t z 5 b0＝0,b1＝0,b2＝0,b3＝10yz/tz 3,b4＝-15yz/tz 4,b5＝yz/tz 5 b 0 =0,b 1 =0,b 2 =0,b 3 =10y z /t z 3 ,b 4 =-15y z /t z 4 ,b 5 =y z /t z 5 式中，v0表示自车初始时刻的纵向车速，xz表示换道纵向轨迹长度，tz表示换道所需时间，yz表示车道宽度，取3.75m，则可以求出换道曲线函数为：In the formula, v 0 represents the longitudinal speed of the own vehicle at the initial moment, x z represents the length of the longitudinal trajectory of lane changing, t z represents the time required for lane changing, y z represents the lane width, taking 3.75m, the lane changing curve function can be obtained. for:
Figure FDA0003409657190000024
Figure FDA0003409657190000024
 由于超车轨迹中第三阶段函数与第一阶段函数互相对称，则可得超车轨迹函数为：Since the third-stage function and the first-stage function in the overtaking trajectory are symmetrical to each other, the overtaking trajectory function can be obtained as:
Figure FDA0003409657190000025
Figure FDA0003409657190000025
Figure FDA0003409657190000031
Figure FDA0003409657190000031
 式中，t1,t2,t3分别表示超车第一阶段、第二阶段、第三阶段的结束时间。In the formula, t 1 , t 2 , and t 3 represent the end time of the first stage, the second stage and the third stage of overtaking, respectively. 5.根据权利要求1所述的一种基于混合粒子群算法的智能车超车轨迹优化方法，其特征在于，所属步骤4的具体实现包括：5. a kind of intelligent vehicle overtaking trajectory optimization method based on hybrid particle swarm algorithm according to claim 1, is characterized in that, the concrete realization of belonging step 4 comprises: 步骤4.1，种群初始化与个体编码Step 4.1, Population Initialization and Individual Encoding 在一定的搜索空间中，初始化微粒数目为n的种群，第i个粒子代表一个m维的向量
Figure FDA0003409657190000032
粒子所在的位置都是方程的解，第i个粒子在搜索空间中运动的速度也是m维的向量，为
Figure FDA0003409657190000033
对种群中的粒子个体采用编码的方式，每个粒子包含换道纵向轨迹长度，换道总时间两个参数变量；In a certain search space, initialize a population of n particles, and the ith particle represents an m-dimensional vector
Figure FDA0003409657190000032
The position of the particle is the solution of the equation, and the speed of the i-th particle moving in the search space is also an m-dimensional vector, which is
Figure FDA0003409657190000033
The method of coding is adopted for the individual particles in the population, and each particle contains two parameter variables: the length of the longitudinal trajectory of the lane change and the total time of the lane change; 步骤4.2，个体适应度值计算Step 4.2, individual fitness value calculation 粒子个体的适应度值计算公式表示如下:fitness＝min(J)，The calculation formula of the fitness value of the individual particle is expressed as follows: fitness=min(J), J表示目标函数，利用其来确定参数变量纵向轨迹长度，换道总时间，J represents the objective function, which is used to determine the length of the longitudinal trajectory of the parameter variables, the total time of lane changing, ay可由以下公式直接求二次导数获得，a y can be obtained by directly calculating the second derivative of the following formula,
Figure FDA0003409657190000034
Figure FDA0003409657190000034
 ωr可由以下公式获得，ω r can be obtained by the following formula,
Figure FDA0003409657190000035
Figure FDA0003409657190000035
 其中，vx是车辆纵向速度，R为车辆转向半径；Among them, v x is the longitudinal speed of the vehicle, and R is the turning radius of the vehicle; β可由以下公式获得，β can be obtained by the following formula,
Figure FDA0003409657190000036
Figure FDA0003409657190000036
 δ可由以下公式获得，δ can be obtained by the following formula,
Figure FDA0003409657190000037
Figure FDA0003409657190000037
 其中
Figure FDA0003409657190000041
k1,k2表示前轮与后轮的侧偏刚度，a,b分别表示质心至前轴和后轴的距离，L表示轴距，m表示汽车总质量，i为汽车转向系传动比，取i＝17；in
Figure FDA0003409657190000041
k 1 , k 2 represent the cornering stiffness of the front and rear wheels, a, b represent the distance from the center of mass to the front and rear axles, respectively, L represents the wheelbase, m represents the total mass of the vehicle, i is the transmission ratio of the steering system of the vehicle, take i=17; 由此可建立目标函数表达式：From this, the objective function expression can be established:
Figure FDA0003409657190000042
Figure FDA0003409657190000042
 式中，xz表示换道纵向轨迹长度，ay表示换道任意时刻侧向加速度，ωr表示换道任意时刻横摆角速度，β表示换道任意时刻质心侧偏角，δ表示换道任意时刻前轮转角，xamax、aymax、ωrmax、βmax、δmax分别表示所有换道轨迹中所允许的最大纵向轨迹长度、最大侧向加速度、最大横摆角速度、最大质心侧偏角和最大前轮转角，ω1、ω2、ω3、ω4、ω5为权值系数，且ω1+ω2+ω3+ω4+ω5＝1；In the formula, x z represents the length of the longitudinal trajectory of the lane change, a y represents the lateral acceleration at any time of the lane change, ω r represents the yaw rate at any time of the lane change, β represents the side-slip angle of the centroid at any time of the lane change, and δ represents the arbitrary time of the lane change. Front wheel rotation angle at time, x amax , a ymax , ω rmax , β max , δ max represent the maximum longitudinal track length, maximum lateral acceleration, maximum yaw rate, maximum center of mass slip angle and Maximum front wheel rotation angle, ω 1 , ω 2 , ω 3 , ω 4 , and ω 5 are weight coefficients, and ω 1 +ω 2 +ω 3 +ω 4 +ω 5 =1; 即粒子的适应度值为目标函数的最小值，将
Figure FDA0003409657190000047
带入目标函数即可求得该粒子对应的适应度值，根据所求的适应度值来判定解的优劣；That is, the fitness value of the particle is the minimum value of the objective function, and the
Figure FDA0003409657190000047
The fitness value corresponding to the particle can be obtained by bringing in the objective function, and the pros and cons of the solution can be determined according to the obtained fitness value; 步骤4.3，寻找个体极值和群体极值Step 4.3, looking for individual extremum and group extremum 通过计算每个粒子的适应度值以及粒子所经历过的位置，则可以得到粒子的个体极值与群体极值，令第i个粒子搜索到的最优位置为
Figure FDA0003409657190000043
在全局中搜索到的最优位置为
Figure FDA0003409657190000044
将粒子当前适应度值与粒子经过最优位置
Figure FDA0003409657190000045
的适应度值比较，根据比较结果选择其作为粒子当前最优位置，同时，将粒子当前适应度值比较，根据比较结果选择其作为粒子全局最优位置，上述可由以下公式确定：By calculating the fitness value of each particle and the position experienced by the particle, the individual extreme value and the group extreme value of the particle can be obtained, and the optimal position searched by the ith particle is
Figure FDA0003409657190000043
The optimal position searched in the global is
Figure FDA0003409657190000044
Compare the particle's current fitness value with the particle's optimal position
Figure FDA0003409657190000045
Compare the fitness values of the particles, select it as the current optimal position of the particle according to the comparison result, and at the same time, compare the current fitness value of the particle, and select it as the global optimal position of the particle according to the comparison result. The above can be determined by the following formula:
Figure FDA0003409657190000046
Figure FDA0003409657190000046
 其中，Xi(t+1)表示第i个粒子t+1时刻的s维向量，Pi(t)表示第i个粒子在搜索空间中的最优位置；Among them, X i (t+1) represents the s-dimensional vector of the ith particle at time t+1, and P i (t) represents the optimal position of the ith particle in the search space; 步骤4.4，更新粒子的速度和位置Step 4.4, update particle velocity and position 通过以下公式对粒子进行更新操作：The particles are updated by the following formula: vim(t+1)＝vim(t+1)+c1r1m(t)(pim(t)-xim(t))+c2r2m(t)(pgm(t)-xgm(t))v im (t+1)=v im (t+1)+c 1 r 1m (t)(p im (t)-x im (t))+c 2 r 2m (t)(p gm (t) -x gm (t)) xim(t+1)＝xim(t)+vim(t+1)x im (t+1)=x im (t)+v im (t+1) 式中：vim(t+1)表示第i个粒子在t+1时刻的速度，xim(t)表示第i个粒子在t+1时刻的位置，i＝[1,n],s＝[1,m]学习因子c1和c2为非负常数；r1与r2为相互独立的伪随机数，服从[0,1]上的均匀分布，vim∈[-vmax,vmax],其中，vmax是由自己设定的常数；In the formula: vi im (t+1) represents the velocity of the ith particle at time t+1, x im (t) represents the position of the ith particle at time t+1, i=[1,n],s =[1,m] The learning factors c 1 and c 2 are non-negative constants; r 1 and r 2 are mutually independent pseudo-random numbers, obeying the uniform distribution on [0,1], vi im ∈[-v max , v max ], where v max is a constant set by itself; 步骤4.5，交叉操作Step 4.5, Crossover Operation 选择两个交叉位置，将个体和个体极值或个体与群体极值进行交叉，对于获得的新粒子采取保留优秀原则，只有当新粒子适应度值优于旧粒子的适应度值时才可更新；Select two intersection positions, cross the individual and the individual extreme value or the individual and the group extreme value, adopt the principle of retaining the excellence for the new particles obtained, and update only when the fitness value of the new particle is better than the fitness value of the old particle. ; 步骤4.6，变异操作Step 4.6, mutation operation 选择粒子个体内部的两个变异位置st1和st2，所选的两个位置互换，对于获得的新粒子同样采取保留优秀原则，只有当新粒子适应度值优于旧粒子的适应度值时才可更新；Select the two mutation positions st1 and st2 within the particle individual, and the two selected positions are exchanged. The principle of retaining excellence is also adopted for the new particles obtained. Only when the fitness value of the new particle is better than the fitness value of the old particle. updatable; 确定初始状态和目标函数，考虑到汽车稳定性问题，基于纵向位移，侧向加速度，横摆角速度，质心侧偏角和前轮转角建立目标函数，通过混合粒子群算法对目标函数的换道纵向轨迹长度和换道所需时间两个参数变量进行优化，最后得到最优超车轨迹；Determine the initial state and objective function, consider the vehicle stability problem, establish an objective function based on longitudinal displacement, lateral acceleration, yaw rate, center of mass slip angle and front wheel rotation angle, and use the hybrid particle swarm algorithm to change lanes of the objective function longitudinally The two parameter variables, the trajectory length and the time required to change lanes, are optimized, and finally the optimal overtaking trajectory is obtained; 通过混合粒子群算法中的寻优特性，求得不同车速下的换道纵向轨迹长度以及换道所需时间，进而得到最优超车轨迹函数。Through the optimization feature in the hybrid particle swarm optimization algorithm, the length of the longitudinal trajectory of lane-changing and the time required for lane-changing under different vehicle speeds are obtained, and then the optimal overtaking trajectory function is obtained.
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