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
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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
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