How can i find optimal path using particle swarm optimization which is interpolated through the given control(handle) points?
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LAKSHMANAN ADAIKKAPPAN
el 12 de Feb. de 2016
Editada: LAKSHMANAN ADAIKKAPPAN
el 15 de Feb. de 2016
if true
% code
end
%%%%%%%%%%Create model%%%%%%%%%%%
function model=CreateModel()
% Source
xs=1;
ys=1;
% Target (Destination)
xt=10;
yt=5;
xobs=[1 3 6 9 11 1 3 6 9 11 2 4.5 7.5 10 4.5 7.5];
yobs=[9 9 9 9 9 6.5 6.5 6.5 6.5 6.5 2.5 4 4 2.5 1 1];
robs=[0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5];
n=16;
xmin=-10;
xmax= 10;
ymin=-10;
ymax= 10;
model.xs=xs;
model.ys=ys;
model.xt=xt;
model.yt=yt;
model.xobs=xobs;
model.yobs=yobs;
model.robs=robs;
model.n=n;
model.xmin=xmin;
model.xmax=xmax;
model.ymin=ymin;
model.ymax=ymax;
end
%%%%%%%%%%%CreateRandomSolution%%%%%%%%%%%%%%%
function sol1=CreateRandomSolution(model)
n=model.n;
xmin=model.xmin;
xmax=model.xmax;
ymin=model.ymin;
ymax=model.ymax;
sol1.x=unifrnd(xmin,xmax,1,n);
sol1.y=unifrnd(ymin,ymax,1,n);
end
%%%%%%%%%%%%%MyCost%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [z, sol]=MyCost(sol1,model)
sol=ParseSolution(sol1,model);
beta=100;
z=sol.L*(1+beta*sol.Violation);
end
%%%%%%%%%%obstaclefunction%%%%%%%%%%%%%%%%%%%%%%%%%
function J=obstaclefunction(x,w1)
% An example function to represent sensed obstacles:
J=...
w1*max([exp(?0.8*((x(1,1)?20)^2+(x(2,1)?15)^2)),...
exp(?0.8*((x(1,1)?8)^2+(x(2,1)?10)^2)),...
exp(?0.8*((x(1,1)?10)^2+(x(2,1)?10)^2)),...
exp(?0.8*((x(1,1)?12)^2+(x(2,1)?10)^2)),...
exp(?0.8*((x(1,1)?24)^2+(x(2,1)?20)^2)),...
exp(?0.8*((x(1,1)?18)^2+(x(2,1)?20)^2))]);
%%%%%%%%%%%%%%%%%%%ParseSolution%%%%%%%%%%%%%%%%%%%%%%
function sol2=ParseSolution(sol1,model)
x=sol1.x;
y=sol1.y;
xs=model.xs;
ys=model.ys;
xt=model.xt;
yt=model.yt;
xobs=model.xobs;
yobs=model.yobs;
robs=model.robs;
XS=[xs x xt];
YS=[ys y yt];
k=numel(XS);
TS=linspace(0,1,k);
tt=linspace(0,1,100);
xx=spline(TS,XS,tt);
yy=spline(TS,YS,tt);
dx=diff(xx);
dy=diff(yy);
L=sum(sqrt(dx.^2+dy.^2));
nobs = numel(xobs); % Number of Obstacles
Violation = 0;
for k=1:nobs
d=sqrt((xx-xobs(k)).^2+(yy-yobs(k)).^2);
v=max(1-d/robs(k),0);
Violation=Violation+mean(v);
end
sol2.TS=TS;
sol2.XS=XS;
sol2.YS=YS;
sol2.tt=tt;
sol2.xx=xx;
sol2.yy=yy;
sol2.dx=dx;
sol2.dy=dy;
sol2.L=L;
sol2.Violation=Violation;
sol2.IsFeasible=(Violation==0);
% figure;
% plot(xx,yy);
% hold on;
% plot(XS,YS,'ro');
% xlabel('x');
% ylabel('y');
%
% figure;
% plot(tt,xx);
% hold on;
% plot(TS,XS,'ro');
% xlabel('t');
% ylabel('x');
%
% figure;
% plot(tt,yy);
% hold on;
% plot(TS,YS,'ro');
% xlabel('t');
% ylabel('y');
end
%%%%%%%%%%%%%%PlotSolution%%%%%%%%%%%%%%%%%%%%%%%%
function PlotSolution(sol,model)
xs=model.xs;
ys=model.ys;
xt=model.xt;
yt=model.yt;
xobs=model.xobs;
yobs=model.yobs;
robs=model.robs;
XS=sol.XS;
YS=sol.YS;
xx=sol.xx;
yy=sol.yy;
theta=linspace(0,2*pi,100);
for k=1:numel(xobs)
fill(xobs(k)+robs(k)*cos(theta),yobs(k)+robs(k)*sin(theta),[0.5 0.7 0.8]);
hold on;
end
plot(xx,yy,'k','LineWidth',2);
plot(XS,YS,'ro');
plot(xs,ys,'bs','MarkerSize',12,'MarkerFaceColor','y');
plot(xt,yt,'kp','MarkerSize',16,'MarkerFaceColor','g');
hold off;
grid on;
axis equal;
end
%%%%%%%%%%%%%%PSO%%%%%%%%%%%%%%%%%%%%%%%%%%%
clc;
clear;
close all;
%%Problem Definition
model=CreateModel();
model.n=4; % number of Handle Points
CostFunction=@(x) MyCost(x,model); % Cost Function
nVar=model.n; % Number of Decision Variables
VarSize=[1 nVar]; % Size of Decision Variables Matrix
VarMin.x=model.xmin; % Lower Bound of Variables
VarMax.x=model.xmax; % Upper Bound of Variables
VarMin.y=model.ymin; % Lower Bound of Variables
VarMax.y=model.ymax; % Upper Bound of Variables
%%PSO Parameters
MaxIt=10; % Maximum Number of Iterations
nPop=150; % Population Size (Swarm Size)
w=1; % Inertia Weight
wdamp=0.98; % Inertia Weight Damping Ratio
c1=1.5; % Personal Learning Coefficient
c2=1.5; % Global Learning Coefficient
% % Constriction Coefficient
% phi1=2.05;
% phi2=2.05;
% phi=phi1+phi2;
% chi=2/(phi-2+sqrt(phi^2-4*phi));
% w=chi; % Inertia Weight
% wdamp=1; % Inertia Weight Damping Ratio
% c1=chi*phi1; % Personal Learning Coefficient
% c2=chi*phi2; % Global Learning Coefficient
alpha=0.1;
VelMax.x=alpha*(VarMax.x-VarMin.x); % Maximum Velocity
VelMin.x=-VelMax.x; % Minimum Velocity
VelMax.y=alpha*(VarMax.y-VarMin.y); % Maximum Velocity
VelMin.y=-VelMax.y; % Minimum Velocity
%%Initialization
% Create Empty Particle Structure
empty_particle.Position=[];
empty_particle.Velocity=[];
empty_particle.Cost=[];
empty_particle.Sol=[];
empty_particle.Best.Position=[];
empty_particle.Best.Cost=[];
empty_particle.Best.Sol=[];
% Initialize Global Best
GlobalBest.Cost=inf;
% Create Particles Matrix
particle=repmat(empty_particle,nPop,1);
% Initialization Loop
for i=1:nPop
% Initialize Position
if i > 1
particle(i).Position=CreateRandomSolution(model);
else
% Straight line from source to destination
xx = linspace(model.xs, model.xt, model.n+2);
yy = linspace(model.ys, model.yt, model.n+2);
particle(i).Position.x = xx(2:end-1);
particle(i).Position.y = yy(2:end-1);
end
% Initialize Velocity
particle(i).Velocity.x=zeros(VarSize);
particle(i).Velocity.y=zeros(VarSize);
% Evaluation
[particle(i).Cost, particle(i).Sol]=CostFunction(particle(i).Position);
% Update Personal Best
particle(i).Best.Position=particle(i).Position;
particle(i).Best.Cost=particle(i).Cost;
particle(i).Best.Sol=particle(i).Sol;
% Update Global Best
if particle(i).Best.Cost<GlobalBest.Cost
GlobalBest=particle(i).Best;
end
end
% Array to Hold Best Cost Values at Each Iteration
BestCost=zeros(MaxIt,1);
%%PSO Main Loop
for it=1:MaxIt
for i=1:nPop
% x Part
% Update Velocity
particle(i).Velocity.x = w*particle(i).Velocity.x ...
+ c1*rand(VarSize).*(particle(i).Best.Position.x-particle(i).Position.x) ...
+ c2*rand(VarSize).*(GlobalBest.Position.x-particle(i).Position.x);
% Update Velocity Bounds
particle(i).Velocity.x = max(particle(i).Velocity.x,VelMin.x);
particle(i).Velocity.x = min(particle(i).Velocity.x,VelMax.x);
% Update Position
particle(i).Position.x = particle(i).Position.x + particle(i).Velocity.x;
% Velocity Mirroring
OutOfTheRange=(particle(i).Position.x<VarMin.x | particle(i).Position.x>VarMax.x);
particle(i).Velocity.x(OutOfTheRange)=-particle(i).Velocity.x(OutOfTheRange);
% Update Position Bounds
particle(i).Position.x = max(particle(i).Position.x,VarMin.x);
particle(i).Position.x = min(particle(i).Position.x,VarMax.x);
% y Part
% Update Velocity
particle(i).Velocity.y = w*particle(i).Velocity.y ...
+ c1*rand(VarSize).*(particle(i).Best.Position.y-particle(i).Position.y) ...
+ c2*rand(VarSize).*(GlobalBest.Position.y-particle(i).Position.y);
% Update Velocity Bounds
particle(i).Velocity.y = max(particle(i).Velocity.y,VelMin.y);
particle(i).Velocity.y = min(particle(i).Velocity.y,VelMax.y);
% Update Position
particle(i).Position.y = particle(i).Position.y + particle(i).Velocity.y;
% Velocity Mirroring
OutOfTheRange=(particle(i).Position.y<VarMin.y | particle(i).Position.y>VarMax.y);
particle(i).Velocity.y(OutOfTheRange)=-particle(i).Velocity.y(OutOfTheRange);
% Update Position Bounds
particle(i).Position.y = max(particle(i).Position.y,VarMin.y);
particle(i).Position.y = min(particle(i).Position.y,VarMax.y);
% Evaluation
[particle(i).Cost, particle(i).Sol]=CostFunction(particle(i).Position);
% Update Personal Best
if particle(i).Cost<particle(i).Best.Cost
particle(i).Best.Position=particle(i).Position;
particle(i).Best.Cost=particle(i).Cost;
particle(i).Best.Sol=particle(i).Sol;
% Update Global Best
if particle( *if true
% code
end* i).Best.Cost<GlobalBest.Cost
GlobalBest=particle(i).Best;
end
end
end
% Update Best Cost Ever Found
BestCost(it)=GlobalBest.Cost;
% Inertia Weight Damping
w=w*wdamp;
% Show Iteration Information
if GlobalBest.Sol.IsFeasible
Flag=' *';
else
Flag=[', Violation = ' num2str(GlobalBest.Sol.Violation)];
end
disp(['Iteration ' num2str(it) ': Best Cost = ' num2str(BestCost(it)) Flag]);
% Plot Solution
figure(1);
PlotSolution(GlobalBest.Sol,model);
pause(0.01);
end
%%Results
figure;
plot(BestCost,'LineWidth',2);
xlabel('Iteration');
ylabel('Best Cost');
grid on;
%%%%%%%%%%%%%%END PROGRAM%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%I am working on particle swarm optimization(PSO) for to find optimal path for mobile robot. Here, i have attached the code and output images of PSO. Initially, i will give start and end points as input and it will give optimal path which is interpolated through four handle (control) points. In this case, handle(control) points are generated randomly by code.
But in my problem, I will also give number of handle(control) points as a input to the code and the path follow through the given handle points only. I will provide a output image of PSO. In this, how can i give my handle(control) points such as (1,4), (3,5),(6,5), (4,2), (6,2), (8,3), (6,4) as a input for PSO? And how can i find optimal path between start and end points which is interpolated through the given handle(control) points?
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