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# Monthly Archives: January 2014

## Distance Transform Path Planning Algorithm

clc;close all;clear all;

Input Map

```RGB = imread('Mapn.png');
figure('Position',[600 0 600 1000],'color','k');
image(RGB);
hold on;
axis off
axis image
hold off;
% Convert to binary image matrix and inverse matrix values
I = rgb2gray(RGB);
binaryImage = im2bw(RGB, 0.3);
binaryImage = 1-binaryImage;
% Inital pose
xs = 540; ys = 750;
% Goal Pose
xg = 150; yg = 150;```

Distance to Goal

```sz  = size(binaryImage);
for i = 1:sz(1)
for j = 1:sz(2)
rg(i,j) = sqrt((i-yg)^2 +(j - xg)^2);
end
end
% Pose Matrix
pose = zeros(sz(1),sz(2));
pose(ys,xs) = 1;
pose(yg,xg) = 1;```
```Di = 15; % Distance of influence of the obstacles
% Compute for every pixel the distance to the nearest obstacle(non zero
% elements which after inversion corespondent to the obstacles)
[D,IDX] = bwdist(binaryImage);
for i = 1:sz(1)
for j = 1:sz(2)
rd = D(i,j);
if (rd <= Di)
rg(i,j)  = 1e6;
end
end
end```

Distance Transform Path Planning Algorithm

```figure('Position',[600 0 600 1000],'color','k');
hold on;
image(RGB);
colormap gray
contour(rg,15);
spy(pose,'*r');
axis off
axis image
title('Distance Transform Path Planning Algorithm','color','w');
x = xs; y = ys;
last = rg(y-1,x-1);
while (x ~= xg)||(y ~= yg)
dis =[ rg(y-1,x-1), rg(y-1,x),rg(y-1,x+1);
rg(y,x-1), rg(y,x) ,rg(y,x+1);
rg(y+1,x-1), rg(y+1,x),rg(y+1,x+1)];
m = min(dis(:));
[r,c] = find(dis == m);
rg(y,x) = 1E6;
y = y-2+r;
x = x-2+c;
pose(y,x) = 1;
end
spy(pose,'.r');
set(gcf, 'InvertHardCopy', 'off');
hold off;```

## Voronoi Road Map, Path Planing

clc;close all;clear all;

Input Map

```RGB = imread('Map.png');
figure('Position',[100 0 600 700],'color','k');
imagesc(RGB);
axis image
title('Input Map','color','w');
axis off
set(gcf, 'InvertHardCopy', 'off');
hold off;```

Convert to binary image matrix and inverse matrix values

```I = rgb2gray(RGB);
binaryImage = im2bw(RGB, 0.3);
sz  = size(binaryImage);```

Inital pose

```xs = 225; ys = 355;
% Goal Pose
xg = 50; yg = 50;
% Pose Matrix
pose = zeros(sz(1),sz(2));
pose(ys,xs) = 1;
pose(yg,xg) = 1;```

```figure('Position',[100 0 600 700],'color','k');
hold on;
set(gcf, 'InvertHardCopy', 'off');
sk = 1;
for i = 1:sz(1)
for j = 1:sz(2)
if(binaryImage(i,j) == 1 )
xv(sk) = j;
yv(sk) = i;
sk = sk+1;
end
end
end
[vrx,vry]  = voronoi(xv,yv);
set(gca,'YDir','Reverse');
plot(xv,yv,'y.',vrx,vry,'b-');
axis tight
%axis([1 sz(2) 1 sz(1) ]) ;
axis image
'* - Represents Starting and Goal Position '},'color','w');
axis off
spy(pose,'*r');```

Robot Path

```x = xs; y = ys;
indk = 1;
while (abs(x - xg) > 5)||(abs(y - yg)> 5)
path(:,indk) = [x y];
dist = sqrt((vrx - x).^2+(vry - y).^2);
goal = sqrt((xg - x).^2+(xg - y).^2);
% Find closest vertices of the Voronoi edges
[mn ind] = min(dist(:));
xt = vrx(ind);
yt = vry(ind);
goalj = sqrt((xg - xt).^2+(xg - yt).^2);
if (goalj < goal )
x = xt;
y = yt;
vrx(ind) = 1E6;
vry(ind) = 1E6;
indk = indk +1;
else
vrx(ind) = 1E6;
vry(ind) = 1E6;
end
end
path(:,indk) = [xg yg];
plot(path(1,:),path(2,:),'-r');
title({'Voronoi Road Map and Robot Path';
'* - Represents Starting and Goal Position '},'color','w');```

## Potential Field Path Planning

clc;close all;clear all;

Input Map

```RGB = imread('Mapn.png');
figure('Position',[600 0 600 1000],'color','k');
image(RGB);
hold on;
axis off
axis image```

Convert to binary image matrix and inverse matrix values

```I = rgb2gray(RGB);
binaryImage = im2bw(RGB, 0.3);
binaryImage = 1-binaryImage;
% Inital pose
xs = 540; ys = 750;
% Goal Pose
xg = 150; yg = 150;```

Attractive potential

```sz  = size(binaryImage);
for i = 1:sz(1)
for j = 1:sz(2)
rg = sqrt((i-yg)^2 +(j - xg)^2);
U_att(i,j) = 0.5*rg^2;
end
end
contour(U_att,40);

set(gcf, 'InvertHardCopy', 'off');
% Pose Matrix
pose = zeros(sz(1),sz(2));
pose(ys,xs) = 1;
pose(yg,xg) = 1;
spy(pose,'*r');
title({'Attractive Potential Field';...
'Circles Center Corespondents to the Goal Position '},'color','w');
hold off;```

Repulsive potential

```Di = 35; % Distance of influence of the object
% Compute for every pixel the distance to the nearest obstacle(non zero
% elements which after inversion corespondent to the obstacles)
[D,IDX] = bwdist(binaryImage);
for i = 1:sz(1)
for j = 1:sz(2)
rd = D(i,j);
if (rd <= Di)
U_rep(i,j)  = 0.5*(rd - Di)^2;
else
U_rep(i,j)  = 0;
end
end
end
figure('Position',[600 0 600 1000],'color','k');
hold on;
colormap jet;
contourf(U_rep,5);
spy(pose,'*r');
axis off
axis image
set(gcf, 'InvertHardCopy', 'off');
title('Repulsive Potential Field','color','w');
hold off;```

Summary Potential Field

```k_s  = 2; % Scaling factor
U_sum = U_rep/max(U_rep(:))+k_s*U_att/max(U_att(:));
figure('Position',[600 0 600 1000],'color','k');
hold on;
contourf(U_sum,15);
spy(pose,'*r');
axis off
axis image
title('Summary Potential Field','color','w');
set(gcf, 'InvertHardCopy', 'off');
hold off;```

Potential Field Path Planning

```figure('Position',[600 0 600 1000],'color','k');
hold on;
contourf(U_sum,15);
spy(pose,'*r');
axis off
axis image
title('Potential Field Path Planning,*Note the Potential Trap','color','w');
x = xs; y = ys;
last = U_sum(y-1,x-1);
while (x ~= xg)||(y ~= yg)
dis =[ U_sum(y-1,x-1), U_sum(y-1,x),U_sum(y-1,x+1);
U_sum(y,x-1), U_sum(y,x) ,U_sum(y,x+1);
U_sum(y+1,x-1), U_sum(y+1,x),U_sum(y+1,x+1)];
m = min(dis(:));
[r,c] = find(dis == m);
U_sum(y,x) = inf;
y = y-2+r;
x = x-2+c;
pose(y,x) = 1;
end
spy(pose,'.r');
set(gcf, 'InvertHardCopy', 'off');
hold off;```

## Computing a Skeleton of a Map for Mobile Robots,Path Planning

clc;close all;clear all;

Input Map

```RGB = imread('Map1.png');
figure('Position',[0 0 800 800]);
imshow(RGB);```

Convert to binary image matrix and inverse matrix values

```I = rgb2gray(RGB);
binaryImage = im2bw(RGB, 0.3);
binaryImage = 1-binaryImage;
figure('Position',[0 0 800 800]);
imshow(binaryImage);```
```Warning: Image is too big to fit on screen; displaying at
50%```

Compute for every pixel the distance to the nearest obstacle(non zero elements which after inversion corespondent to the obstacles)

```[D,IDX] = bwdist(binaryImage);
figure('Position',[0 0 800 800],'color','k')
colormap bone
image(D);
axis off          % Remove axis ticks and numbers
axis image
set(gcf, 'InvertHardCopy', 'off');```

Taking the Laplacian of the distance transform. Play with the treshold value 0.15 to remove or add more futures in skeleton

```lap = del2(D);
sz  = size(lap);
for i = 1:sz(1)
for j = 1:sz(2)
if( abs(lap(i,j)) < 0.15)
lap(i,j) = 0;
end
end
end
lap = flipdim(lap ,1);           %# vertical flip
figure('Position',[0 0 800 800],'color','k');
colormap winter;
contour(lap,'DisplayName','lap');
axis off
axis image
set(gcf, 'InvertHardCopy', 'off');```

## Swirl,Matlab Code

```clc; clear all; close all;
x = -20:0.1:20;
sz = size(x);
ind = 0;
b = 6
for n = 1:15 %
for i = 1:sz(2)
for j = 1:sz(2)
sw(i,j) = sin(b*cos(sqrt(x(i)^2+x(j)^2))-n*atan2(x(i),x(j)));
end
end
ind = ind +1;
fig = figure('Position',[0 0 800 800]);
hold on;
imagesc(sw);
colormap bone;
axis off;
set(fig, 'color', [0 0 0]);
set(gcf, 'InvertHardCopy', 'off');
hold off;
%print(fig,['Sw',num2str(ind)],'-djpeg  ','-r300');
close all;
end```