基于元胞自动机NaSch模型的多车道手动-自动混合驾驶仿真模型的Matlab实现

模型的建立基本来自于：http://www.doc88.com/p-2078634086043.html

花了一天半的时间用新学会的matlab实现了一下。

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2018-1-31更新：

居然真的有人会看我的博文诶，那我不能就这么不负责任的直接甩代码跑路了，稍微评价一下我自己的代码吧……

1、首先是优点，就是能用（囧），调调参数，几个车道，多少元胞，多少辆车，自动驾驶车手动驾驶车比例，基本都能改。

2、缺点一：各种规则十分不清晰明确，正确性有待商榷……

　　特别是变道规则，又臭又长，我自己写完之后都不想看第二遍，而且我怀疑跟论文里写的规则有出入（虽然我说实话，论文里的变道规则也说的不是很清晰）

3、缺点二：速度贼慢，慢的跟爬一样。因为这个代码是为了数学建模敲的，所以也多考虑优化速度什么的，直接就简单粗暴地写了。

　　这导致了，我在出结果的时候，车道数不敢设大于3，元胞数不敢设大于200，循环时常不敢超过300,；

　　即使这样，初始放入车辆的时候，元胞占用率大于0.3的时候，程序跑的就肉眼可见的慢，如果想跑个几十上百组的数据求平均的话，估计可以打局王者荣耀再来看看结果……

4、稳定性贼差，我算结果的时候，几百组几百组求平均（元胞占用率0.0几的情况下，跑的还是挺快的），结果都稳定不下来……导致我们敏感性分析基本等于瞎扯。

感觉自己是真鸡儿的菜，写了这么久的代码，敲个稍微大点的程序，还是敲得跟坨shit一样

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2018-5-7更新：

emmm发现居然少贴了一个函数的代码，补上了calc_Vave()函数；

然后关于这个模型怎么用……

最简单的用法是：

更改global变量的值（车辆数、车道数、自动驾驶车辆占比等等等等），更改模拟时长T，然后运行NaSch()这个函数，返回的ans答案是整个时长T内所有车辆的平均速度

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NaSch模型主函数：

function [ret_Vave] = NaSch()
rng('shuffle');

global CellsNum; CellsNum = 200; %The number of cells in each lane
global LanesNum; LanesNum = 3; %The number of Lanes
global D; D = 0.02; %The cell occupancy rate
global L; L = 5; %The length of one cell
global CarsNum; CarsNum = round( LanesNum .* CellsNum .* D ); %The number of cars
global SelfRatio; SelfRatio = 0.5; %Self-driving vehicle rate
global Vmin; Vmin = 1; %Minimum speed limit
global Vmax; Vmax = 6; %Maximum speed limit

%Meet the lane changing conditions...
global ChangeRightP; ChangeRightP = 0.5; %The probability of changing into the right lane
global ChangeLeftP; ChangeLeftP = 0.8; %The probability of changing into the left lane

[z,cars] = RoadInit();
cells = z;
cars = CarInit(cars);

T = 1000; %The duration of simulation
Vave = zeros(1,T); %Average velocity per unit time

global loopCars; loopCars = [];
%Start the simulation
for t = 1:1:T

    [cells,cars] = EntryControl(cells,cars);

    %Calculate each distance
    [d,d_safe,d_l_for,d_l_bac,d_r_for,d_r_bac] = calcDist(cells,cars);

    %Get the next state
    for i = 1:1:CarsNum
        if(cars(i).M==1) %Leftmost lane
            [cells,cars] = L_NextState(i,cells,cars,d,d_safe,d_l_for,d_l_bac,d_r_for,d_r_bac);
        elseif(cars(i).M==LanesNum) %Rightmost lane
            [cells,cars] = R_NextState(i,cells,cars,d,d_safe,d_l_for,d_l_bac,d_r_for,d_r_bac);
        else %Middle lane
            [cells,cars] = M_NextState(i,cells,cars,d,d_safe,d_l_for,d_l_bac,d_r_for,d_r_bac);
        end
    end

    cars = RandSlow(cars);
    [cells,cars] = Update(cells,cars);
    cells = cells(1:LanesNum,1:CellsNum); %Control the size of Cells Matrix
    Vave(t) = calc_Vave(cars); %Calculate current average velocity
end

ret_Vave = mean(Vave); %Calculate average velocity
end

初始化函数：

function [cell_mat,car_mat] = RoadInit()
global LanesNum;
global CellsNum;
global CarsNum;

mat = zeros(LanesNum,CellsNum);

Car(1,CarsNum) = struct('ID',[],'V',[],'M',[],'N',[],'Self',[]);
%Vehicle Information: ID, Speed, Position, Whether self driving or not

for i = 1:1:CarsNum
    m=round( 1 + ( LanesNum - 1 ) * rand(1) );
    n=round( 1 + ( CellsNum - 1 ) * rand(1) );
    while( mat(m,n) ~= 0 )
        m = round( 1 + ( LanesNum - 1 ) * rand(1) );
        n = round( 1 + ( CellsNum - 1 ) * rand(1) );
    end
    mat(m,n) = i;

    Car(i).ID = i;
    Car(i).M = m;
    Car(i).N = n;
end

cell_mat = mat;
car_mat = Car;
end

function car_mat = CarInit(Car)
global CarsNum;
global Vmin;
global Vmax;
global SelfRatio;

for i = 1:1:CarsNum
    Car(i).V = round( Vmin + ( Vmax - Vmin ) * rand(1) );
    if(rand(1)<=SelfRatio) Car(i).Self = 1;
    else Car(i).Self = 0;
    end
end

car_mat = Car;
end

入口控制：

function [new_cells,new_cars] = EntryControl(cells,cars)
global loopCars;
global LanesNum;
global Vmin;

while(StackSize(loopCars) > 0)

    if( all( cells(:,1) ~= 0 ) == 1 )
        break
    end

    for i = 1:1:LanesNum
        if(cells(i,1) == 0)
            id = topStack(loopCars); popStack(loopCars);
            cells(i,1) = id;
            cars(id).V = Vmin;
            cars(id).M = i;
            cars(id).N = 1;
            break
        end
    end

end

new_cells = cells;
new_cars = cars;
end

计算各种车距：

function [Ret_d,Ret_d_safe,Ret_d_l_for,Ret_d_l_bac,Ret_d_r_for,Ret_d_r_bac] = calcDist(cells,cars)
global LanesNum;
global CellsNum;
global CarsNum;

d = linspace(-1,-1,CarsNum);
d_safe = linspace(-1,-1,CarsNum);
d_l_for = linspace(-1,-1,CarsNum);
d_l_bac = linspace(-1,-1,CarsNum);
d_r_for = linspace(-1,-1,CarsNum);
d_r_bac = linspace(-1,-1,CarsNum);

for i = 1:1:CarsNum

    m = cars(i).M; %The m_th lane
    n = cars(i).N; %The n_th cell

    %Calculate the distance to front car
    d(i) = inf;
    for f = n+1:1:CellsNum
        if(cells(m,f) ~= 0)
            d(i) = f - n;
            break
        end
    end

    %If the left lane exist
    if( m-1 >= 1 )
        %Forward
        d_l_for(i) = inf;
        for p = n:1:CellsNum
            if( cells( m-1 , p ) ~= 0 )
                d_l_for(i) = p - n;
                break
            end
        end
        %Backward
        for p = n:-1:1
            d_l_bac(i) = inf;
            if( cells( m-1 , p ) ~= 0 )
                d_l_bac(i) = n - p;
                break
            end
        end
    end

    %If the right lane exist
    if( m+1 <= LanesNum )
        %Forward
        d_r_for(i) = inf;
        for p = n:1:CellsNum
            if( cells( m+1 , p ) ~= 0 )
                d_r_for(i) = p - n;
                break
            end
        end
        %Backward
        d_r_bac(i) = inf;
        for p = n:-1:1
            if( cells( m+1 , p ) ~= 0 )
                d_r_bac(i) = n - p;
                break
            end
        end
    end

    %The d_safe of two kinds of cars is different
    if(cars(i).Self == 1)
        d_safe(i) = cars(i).V;
    else
        d_safe(i) = 2 .* cars(i).V;
    end

end

Ret_d = d;
Ret_d_safe = d_safe;
Ret_d_l_for = d_l_for;
Ret_d_l_bac = d_l_bac;
Ret_d_r_for = d_r_for;
Ret_d_r_bac = d_r_bac;
end

加减速规则实现：

function new_cars = Accelerate(id,cars,d,d_Safe)
global Vmax;
global Pa;
Pa = 0.8; %Acceleration probability

if( d(id) > d_Safe(id) && cars(id).V < Vmax )
    if(rand(1) <= Pa)
        cars(id).V = cars(id).V + 1;
    end
end

new_cars = cars;
end

function new_cars = Decelerate(id,cars,d,d_safe)
global Vmax;
global Vmin;

if( d(id) < d_safe(id) && d(id) >= Vmax - Vmin )
    cars(id).V = max( cars(id).V - 1 , Vmin );
elseif( d(id) < Vmax - Vmin )
    cars(id).V = Vmin;
end

new_cars = cars;
end

关于变道的状态更新：

function [new_cells,new_cars] = L_NextState(i,cells,cars,d,d_safe,d_l_for,d_l_bac,d_r_for,d_r_bac)
global Vmax;
global LanesNum;
global loopCars;

if( d_r_for(i) > d_safe(i) ) %与右前方车辆距离大于安全距离
    ok1 = 1;
else
    ok1 = 0;
end

if( d_r_bac(i) > 1 + Vmax - min(cars(i).V+1,Vmax) ) %与右后方车辆安全
    ok2 = 1;
else
    ok2 = 0;
end

if( cars(i).M+2 <= LanesNum && cells(cars(i).M+2,cars(i).N) ~= 0 ) %右边相隔一个车道平行位置有车
    id = cells(cars(i).M+2,cars(i).N); %获取该车编号
    if( min( d_l_for(id) , d_l_bac(id) ) < d_safe(id) ) %判断该车不能向左变道
        ok3 = 1;
    else
        ok3 = 0;
    end
else
    ok3 = 1;
end

ChangeLaneOK = ok1 && ok2 && ok3; %得到是否有变道条件

if( d(i) < d_safe(i) ) %与前车距离小于安全距离，能变道则必须变道
    if(ChangeLaneOK)

        cells(cars(i).M,cars(i).N) = 0;
        cars(i).M = cars(i).M + 1;
        if( cells( cars(i).M , cars(i).N ) ~= 0 ) %撞车控制
            loopCars = pushStack(loopCars,cars(i).ID);
        else
            cells(cars(i).M,cars(i).N) = cars(i).ID; %变道
        end

        cars = Accelerate(i,cars,d,d_safe); %加速
    else
        cars = Decelerate(i,cars,d,d_safe); %减速
    end
else %与前车距离大于等于安全距离
    ChangeLaneDesire = getCLD(i,cars,'R'); %计算变道欲望
    if(ChangeLaneOK && ChangeLaneDesire)

        cells(cars(i).M,cars(i).N) = 0;
        cars(i).M = cars(i).M + 1;
        if( cells( cars(i).M , cars(i).N ) ~= 0 ) %撞车控制
            loopCars = pushStack(loopCars,cars(i).ID);
        else
            cells(cars(i).M,cars(i).N) = cars(i).ID; %变道
        end

        cars = Accelerate(i,cars,d,d_safe); %加速
    else
        cars = Accelerate(i,cars,d,d_safe); %加速
        cars = Decelerate(i,cars,d,d_safe); %减速
    end
end

new_cells = cells;
new_cars = cars;
end

function [new_cells,new_cars] = M_NextState(i,cells,cars,d,d_safe,d_l_for,d_l_bac,d_r_for,d_r_bac)
global Vmax;
global LanesNum;
global loopCars;
%计算中间车道上车辆的下一时刻状态

if( d_l_for(i) > d_safe(i) ) %与左前方车辆距离大于安全距离
    ok1 = 1;
else
    ok1 = 0;
end

if( d_l_bac(i) > 1 + Vmax - min(cars(i).V+1,Vmax) ) %与左后方车辆安全
    ok2 = 1;
else
    ok2 = 0;
end

if( cars(i).M-2 >= 1 && cells(cars(i).M-2,cars(i).N) ~= 0 ) %左边相隔一个车道平行位置有车
    id = cells(cars(i).M-2,cars(i).N); %获取该车编号
    if( min( d_r_for(id) , d_r_bac(id) ) < d_safe(id) ) %判断该车不能向右变道
        ok3 = 1;
    else
        ok3 = 0;
    end
else
    ok3 = 1;
end

ChangeLeftLaneOK = ok1 && ok2 && ok3; %得到是否有向左变道条件

if( d_r_for(i) > d_safe(i) ) %与右前方车辆距离大于安全距离
    ok1 = 1;
else
    ok1 = 0;
end

if( d_r_bac(i) ~= inf && d_r_bac(i) ~= -1 && cells( cars(i).M + 1 , cars(i).N - d_r_bac(i) ) > 0 ) %右后方有车
    id = cells( cars(i).M + 1 , cars(i).N - d_r_bac(i) ); %得到该车的编号
    if( d_r_bac(i) > d_safe(id) ) %与右后方车辆安全
        ok2 = 1;
    else
        ok2 = 0;
    end
else
    ok2 = 1;
end

if( cars(i).M+2 <= LanesNum && cells(cars(i).M+2,cars(i).N) ~= 0 ) %右边相隔一个车道平行位置有车
    id = cells(cars(i).M+2,cars(i).N); %获取该车编号
    if( min( d_l_for(id) , d_l_bac(id) ) < d_safe(id) ) %判断该车不能向左变道
        ok3 = 1;
    else
        ok3 = 0;
    end
else
    ok3 = 1;
end

ChangeRightLaneOK = ok1 && ok2 && ok3; %得到是否有向右变道条件

if( d(i) < d_safe(i) ) %与前车距离小于安全距离

    if(ChangeRightLaneOK) %能够向右变道则向右变道

        cells(cars(i).M,cars(i).N) = 0;
        cars(i).M = cars(i).M + 1;
        if( cells( cars(i).M , cars(i).N ) ~= 0 ) %撞车控制
            loopCars = pushStack(loopCars,cars(i).ID);
        else
            cells(cars(i).M,cars(i).N) = cars(i).ID; %变道
        end

        cars = Accelerate(i,cars,d,d_safe); %加速

    else %不能向右变道则尝试向左变道

        if(ChangeLeftLaneOK == 1) %能向左变道则向左变道

            cells(cars(i).M,cars(i).N) = 0;
            cars(i).M = cars(i).M - 1;
            if( cells( cars(i).M , cars(i).N ) ~= 0 ) %撞车控制
                loopCars = pushStack(loopCars,cars(i).ID);
            else
                cells(cars(i).M,cars(i).N) = cars(i).ID; %变道
            end

        else %两边都不允许变道
            cars = Decelerate(i,cars,d,d_safe); %减速
        end

    end

else %与前车距离大于等于安全距离

    ChangeLaneDesire = getCLD(i,cars,'R'); %计算变道欲望

    if(ChangeRightLaneOK && ChangeLaneDesire) %能够向右变道，且有变道欲望

        cells(cars(i).M,cars(i).N) = 0;
        cars(i).M = cars(i).M + 1;
        if( cells( cars(i).M , cars(i).N ) ~= 0 ) %撞车控制
            loopCars = pushStack(loopCars,cars(i).ID);
        else
            cells(cars(i).M,cars(i).N) = cars(i).ID; %变道
        end

        cars = Accelerate(i,cars,d,d_safe); %加速
    else
        cars = Accelerate(i,cars,d,d_safe); %加速
        cars = Decelerate(i,cars,d,d_safe); %减速
    end

end

new_cells = cells;
new_cars = cars;
end

function [new_cells,new_cars] = R_NextState(i,cells,cars,d,d_safe,d_l_for,d_l_bac,d_r_for,d_r_bac)
global Vmax;
global loopCars;
%计算最右侧车道上车辆的下一时刻状态

if( d_l_for(i) > d_safe(i) ) %与左前方车辆距离大于安全距离
    ok1 = 1;
else
    ok1 = 0;
end

if( d_l_bac(i) > 1 + Vmax - min(cars(i).V+1,Vmax) ) %与左后方车辆安全
    ok2 = 1;
else
    ok2 = 0;
end

if( cars(i).M-2 >= 1 && cells(cars(i).M-2,cars(i).N) ~= 0 ) %左边相隔一个车道平行位置有车
    id = cells(cars(i).M-2,cars(i).N); %获取该车编号
    if( min( d_r_for(id) , d_r_bac(id) ) < d_safe(id) ) %判断该车不能向右变道
        ok3 = 1;
    else
        ok3 = 0;
    end
else
    ok3 = 1;
end

ChangeLaneOK = ok1 && ok2 && ok3; %得到是否有变道条件

if( d(i) < d_safe(i) ) %与前车距离小于安全距离
    ChangeLaneDesire = getCLD(i,cars,'L'); %计算变道欲望
    if(ChangeLaneOK && ChangeLaneDesire)
        cells(cars(i).M,cars(i).N) = 0;
        cars(i).M = cars(i).M - 1;
        if( cells( cars(i).M , cars(i).N ) ~= 0 ) %撞车控制
            loopCars = pushStack(loopCars,cars(i).ID);
        else
            cells(cars(i).M,cars(i).N) = cars(i).ID; %变道
        end
    else
        cars = Decelerate(i,cars,d,d_safe); %减速
    end
else %与前车距离大于等于安全距离
    cars = Accelerate(i,cars,d,d_safe); %加速
    cars = Decelerate(i,cars,d,d_safe); %减速
end

new_cells = cells;
new_cars = cars;
end

计算变道欲望：

function ret = getCLD(id,cars,Type)
%Calculate the desire to change the lane
global ChangeRightP;
global ChangeLeftP;

if(Type == 'R') %To right
    if(cars(id).Self == 1) %Self driving
        ret = 1;
    else %Manual driving
        if(rand(1) <= ChangeRightP)
            ret = 1;
        else
            ret = 0;
        end
    end;
else %To left
    if(cars(id).Self == 1) %Self driving
        ret = 1;
    else %Manual driving
        if(rand(1) <= ChangeLeftP)
            ret = 1;
        else
            ret = 0;
        end
    end;
end

end

随机慢化：

function new_cars = RandSlow(cars)
global CarsNum;
global Vmin;

p=0.1; %手动车慢化概率
q=0.03; %自动驾驶车慢化概率

for i = 1:1:CarsNum
    if(cars(i).Self==1)
        if(rand(1) <= q)
            cars(i).V = max( cars(i).V - 1 , Vmin );
        end
    else
        if(rand(1) <= p)
            cars(i).V = max( cars(i).V - 1 , Vmin );
        end
    end
end

new_cars = cars;
end

状态更新：

function [new_cells,new_cars] = Update(cells,cars)
global CarsNum;
global CellsNum;
global loopCars;

for i = 1:1:CarsNum
    cells( cars(i).M , cars(i).N ) = 0;
    if( cars(i).N + cars(i).V > CellsNum ) %Drive out of the road
        loopCars = pushStack(loopCars,cars(i).ID);
    else
        cells( cars(i).M , cars(i).N ) = cars(i).ID;
    end;
end

new_cells = cells;
new_cars = cars;
end

计算某一时刻的平均车速：

function Ret = calc_Vave(cars)
global CarsNum;

sum = 0;
for i = 1:1:CarsNum
    sum = sum+cars(i).V;
end

Ret = sum./CarsNum;
end

栈模拟：

function newStack = pushStack(Stack,val)
newStack = [val,Stack];
end

function newStack = popStack(Stack)
newStack = Stack(2:end);
end

function ret = StackSize(Stack)
ret = size(Stack,2);
end

function Val = topStack(Stack)
Val = Stack(1);
end

源代码直接下载链接