# Final Project Presentation on autonomous mobile robot - PowerPoint PPT Presentation

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Final Project Presentation on autonomous mobile robot. Submitted to Prof, Jaebyung Park Robotics Lab. Submitted by Ansu Man Singh Student ID (201150875). Outline. Title Objective Procedure Binary Image Attractive Potential field Repulsive Potential field Total field

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Final Project Presentation on autonomous mobile robot

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## Final Project Presentation on autonomous mobile robot

Submitted to

Prof, Jaebyung Park

Robotics Lab

Submitted by

Ansu Man Singh

Student ID (201150875)

### Outline

• Title

• Objective

• Procedure

• Binary Image

• Attractive Potential field

• Repulsive Potential field

• Total field

### Title

• Path planning using attractive and Reflective potential field

### Objective

• To generate a path for mobile robot using attractive and repulsive potential field

### Procedure

Goal Position

Attractive Potential field

Binary Image

Repulsive Potential field

Start Position

Required Path

### Binary Image

• Binary Image of 200 by 200 pixel is taken

• 1’ will represent free space, 0’s will represent obstacle space

• example

Obstacles

### Attractive Potential Field

• The Attractive Potential field is generated using conic and quadratic functions

Conic

### Attractive Potential Field

• Attractive Potential function

Goal Position

### Attractive Potential Field

• Code Section

goal_pos = [180 180];

Uatt = zeros(wSpace_Size);

d_xtrix_goal =3;

K=0.06;

const1 = 0.5*K*d_xtrix_goal^2;

for i=1:wSpace_Size(1)

for j=1:wSpace_Size(2);

A=(goal_pos(1)-i)^2+(goal_pos(2)-j)^2;

distance=sqrt(A);

if(distance > d_xtrix_goal)

Uatt(i,j)=d_xtrix_goal*K*distance -const1;

else

Uatt(i,j)=0.5*d_xtrix_goal*K*distance^2 ;

end

end

end

### Repulsive Potential Field

• Repulsive function used

• Repulsive function is generated by the help of binary image.

• Steps used in generating Repulsive function

• Find the obstacle position in the binary image

• Generate field using the equation for the distance Q* above and below the obstacle pixel position

### Repulsive Potential Field

• Repulsive Potential Field

### Repulsive Potential Field

• Code section

for i=1:wSpace_Size(1)

for j=1:wSpace_Size(2);

if(wSpace_Bin(i,j)==0)

Uref(i,j)=8;

for k= -xtrix_OBS:xtrix_OBS

for p =-xtrix_OBS:xtrix_OBS

if((i+k)>wSpace_Size(1)||(i+k)<1||(j+p)>wSpace_Size(2)||(j+p)<1)

else

if(wSpace_Bin(i+k,j+p)~= 0)

distance2 = sqrt((k)^2+(p)^2);

Uref(i+k,j+p)=Uref(i+k,j+p)+ 0.5*2*(1/distance2 - 1/xtrix_OBS)^2;

else

Uref(i+k,j+p)= 8;

end

end

end

end

else

Uref(i,j) = Uref(i,j) +0;

end

end

end

### Total Field

• Total Potential field is addition of attractive and Repulsive field

+

• Algorithms used to find the path in the field

• Gradient descent always follows negative slope

Input: A means to compute the gradient ∇U (q)at a point q

Output: A sequence of points {q(0), q(1), ..., q(i)}

1: q(0) = qstart

2: i = 0

3: while ∇U (q(i)) ≠= 0 do

4: q(i + 1) = q(i) + α(i)∇U (q(i))

5: i = i + 1 6: end while

• Code section

while(flag)

position(iteration+1,:) = [pos_xpos_yU_tot(pos_y,pos_x)];

flag = 0;

end

if (pos_x>=200||pos_y>=200)

flag =0;

else

iteration= iteration+1;

end

end

• Contour map of field with path

Start point = (0,80)

• Path 2

• Local Minima problem

• Local Minima problem can be using navigation function

A function is called a navigation function if it

• is smooth (or at least Ck for k ≥ 2),

• has a unique minimum at qgoal in the connected component of the free space that contains qgoal,

• is uniformly maximal on the boundary of the free space, and

• is Morse.

• Navigation function on sphere world

• Obstacle functions

• Distance to goal function

• Switch function which is used to map from (0 to infinity) to [0 1]

• Sharpening function to make critical points non-degenerate

• Final navigation function on sphere world

• Implementation of navigation function on sphere world

• Code section

clear all ;

x= -10:0.1:10;

y= -10:0.1:10;

x_goal = 8;

y_goal = 8;

K= 4;

nav_fxn = zeros(length(x),length(y));

lambda = 2;

for i = 1 :length(x)

for j = 1:length(y)

beta = beta_function(x(i),y(j));

dist_goal = norm([x(i)-x_goal y(j)-y_goal],2);

nav_fxn(i,j) = 1;

else

nav_fxn(i,j) = dist_goal^2/(dist_goal^(2*K) + lambda*abs(beta))^(1/K);

end

end

end

• Conversion from star-shaped set to sphere shaped set

• This conversion is essential for representation of object in real world.

### References

• [1] HowieChoset et al, Principle of robot Motion-Theory, Algorithms and Implementation,

• [2]ElonRimon, Daniel E Koditschek, Exact Robot Navigation Using Artificial Potential Functions