Report Project 3

8/2/2019 Report Project 3

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Ashish Lal

Project 3

MTRN3100

Ashish Lal

10/22/2010


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Ashish Lal

Contents

1. Introduction......................................................................................................................................... 3

2. Generating a real map from a mobile robots laser scans.................................................................... 3

3. Path finding......................................................................................................................................... 5

a) Dijkstras Algorithm ................................................................................................................... 5

4. Fail-Safe Methods for the Robot......................................................................................................... 5

a) Implementation of the Barrier and Rings Method................................................................... 5

5. Discussion ........................................................................................................................................... 7

6. Conclusion .......................................................................................................................................... 8

7. Appendix ............................................................................................................................................. 8

a) Appendix 1 .................................................................................................................................. 8

b) Appendix 2.................................................................................................................................. 9

c) Appendix 3................................................................................................................................ 10


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1. Introduction

The objective of this project is to design a map which takes real time simulated data

from the robots scan. A path finding technique should also be developed, where a user can

specify a desired destination along with fail-safe measures. It is also essential to take in

account of the robot size.

2. Generating a real map from a mobile robots laser scans

To create a 2D map (OG grid) for the robot, data is collected from the LMS200 laser.

This data is further processed in real time displaying the obstacles, safe and unsafe area on

the map for the robot. The figure below shows the complete map of the area with obstacle

information once the robot has moved around the room scanning the area.

Fig 1 and Fig 2 (different colour map) shows the occupancy grid with each grid resolution of

10cm by 10 cm and the dimensions of the grid as 300 by 300 (cells).

The occupancy grid (Fig 1 & Fig 2) is obtained after a devised algorithm is applied.

When a single beam of laser hits and obstacle it stops there and that is how an obstacle is


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determined. Since the area the laser travelled through before hitting obstacle is seen as an

empty area a certain way is devised to clear this area in the OG.

Firstly, while considering the robot to be stationary (Fig XX) a vector is defined with a

specifiedANGLE. This vector is then accessed in loop where l (the y value) is set to increase

and decrease, this way all the cells can be accessed in front of the reference cell and given a

value depending if its and obstacle, unknown or known areas on the map.

Fig 2 shows vector from the astationary robot

Fig 3 shows vector from the a mobile robot

However, since the robot is moving in the 2-D space, problems occur when the robot

scans a location that is behind it due to the actual vector (i.e. vector which normally is

defined from laser sensor to the location of the obstacle it scanned.) Becoming inverted and

pointing the wrong way and clearing spaces behind the robot. To overcome this dilemma, the

directions of the vectors are checked before the spaces are declared as clear. If the vector is

negative, its direction is inverted to the correct orientation as shown in Fig 3, so it points from

the reference point toward the obstacle.


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3. Path finding

a) Dijkstras Algorithm

It works for a given point in a map; the algorithm finds the path with lowest cost (i.e.

the shortest path) between the two specified points. However this technique accounts for

points only. Designing fully functional autonomous software for the robot would require

considering the volume of the trolley itself. There are two ways of applying the solution, one

is to modify the map, taking in account of the robot size and the other more difficult approach

is modifying the algorithm. Modifying the algorithm would require the process to be

performed on a series of different cells of the occupancy grid (which define the robot)

increasing the time taken to find a feasible path to the desired destination. Therefore more

feasible approach would be constructing barriers around the obstacles in the OG.

4. Fail-Safe Methods for the Robot

a) Implementation of the Barrier and Rings Method

Fig 4 The OG with Barriers(199) only Fig 5 The OG with Rings and Barriers


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The implementation of the barriers and rings (fig 5) occur before the path finding

function is called. The obstacle (200) and the barrier (199) are set in the OG with a high value

so that under no circumstances the path finding algorithm will travel though that area.

However to be cautious, the implementation of the rings is essential since these essentially

provide more safety feature for the robot to navigate around an obstacle. The level of safety

can be set according to how many rings surround the barriers. The source code for the

implementation of the barriers and rings are provided in appendix 2 and appendix 3

respectively.

The dimensions of the barrier will be consistent to the dimensions of the robot.

Specifically, the barrier will be half the width of the robot because this is the distance from

the centre of the robot to its edge. However if the robot is not a perfect square, it can get very

close to the wall or obstacles. To avoid this situation the maximum dimension of the robot

can be chosen, but this will restrict the robot going through narrow corridors where it would

actually fit in reality (e.g. navigating in a crowded hallway of the hotel). A better solution is

to implement rings (fig 6 & 7) around the barriers which has a cost low enough to be a

feasible path when there is no other path.

Fig 6 Shows the path generated on the OG Fig 7 shows the robot moving through the

narrow space.


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Fig 8 shows topographic map i.e. the cost

function with destination where red =expensive and blue = cheap route.

Fig 9 is a zoomed in version of the

topographic map.

The cost to go function in Fig 8 & 9 shows the topographical cost map to go to each

location. The scale is set where the blue indicates the easy to go to place therefore the

cheaper place, while the red indicate the places its hard to get to i.e. more expensive. The

blue areas can be seen close to the point since this area is easier and faster to get to and the

robot has to avoid fewer obstacles. The red areas are further away from the origin of the robot

since it would take longer to get to those points and it would have to avoid a greater number

of obstacles to get to that point.

5. Discussion

This software developed for the robot is capable of running on a real-life robot;

however its processing time is not as quick as expected in the real world industrial

application. As development goes on for this software in the future, one could look into

implementing software which considers the robot size in the Dijkstras algorithm, this would

be a difficult task but if successful it will increase the efficiency of the robot. Another


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limitation for this software is it doesnt take in account for the driving and manoeuvring

capabilities of the robot and only gives a straight lined path (fig 9).

6. Conclusion

The project was a success where a consistent map was generated from the mobile

robots laser scans. Dijkstras algorithm was used in combination to determine path finding.

Fail-safe measures such as the applying barriers and rings around obstacles were

successfully in implemented and was fully functional. The robots size was also taken into

consideration and it could also travel through narrow spaces within the map without causing

any damage to the robot itself and the surroundings.

7. Appendix

a)Appendix 1This source code outlines the reversing of the vector and converting the map to a global axis.

timeLaser =double(Data.time);a = MyAPI.ReadPose() ; % read all new position records since last reading

if a.n>1, % any new records?% yes, there are 'n' new readingstimePose = a.Data(1:a.n,1) ; % timestamps of the readings.

% estimate (in this case just interpolate) the robot's pose at% the time of the laser measurement

if timeLasertimePose(end), continue ; end ;

% [Lx,Ly,Lh] are (x,y,heading) at time=timeLaserLx = interp1(timePose,a.Data(1:a.n,2),timeLaser) ;Ly = interp1(timePose,a.Data(1:a.n,3),timeLaser) ;Lh = interp1(timePose,a.Data(1:a.n,7),timeLaser) ;

% however the position corresponds to the centre of the back% axis, ==> I need to translate it to the laser position (front% of the robot)

Lx = Lx + H*cos(Lh) ;

% translate the point to the laser position (H meters aheadthe robot's position)


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Ly = Ly + H*sin(Lh) ;else,

continue ;end;

% I convert the local laser readings --> global.

aa2 = aa+Lh-pi/2+OffsetLaserAngle ;cosaa = cos(aa2) ;sinaa = sin(aa2) ;xx = Lx + Ranges.*cosaa ;yy = Ly + Ranges.*sinaa ;% xx[],yy[] are the laser's points expressed in the global% coordinate frame

X = xx; % laser in globalY = yy;

for u=1:length(X);l = abs(Y(u)-(Ly));

%define vector length of laser globally as the distance to the%obstacle minus the robots current headingth = atan((X(u)-Lx)/(Y(u)-Ly));%angle of laser vector also defined globallya=1;if Y(u)-(Ly) 0.1OG_x = floor((Lx+a*l*tan(th))*10+150);OG_y = floor((Ly+a*l)*10);

if OG_x>0 && OG_x0 && OG_y0 && OG_x0 && OG_y


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wr=60; br=60;%create barrier around obstacle

left_right=ceil((wr/wg)/2);front_back=ceil((br/bg)/2);i_i=1:left_right;i_j=1:front_back;

%create barrier around obstaclefor b_i=1+left_right:300-left_rightfor b_j=1+front_back:300-front_back

if OG(b_i,b_j) == 200%implement barrier%left and rightOG(b_i+i_i,b_j)=199;OG(b_i-i_i,b_j)=199;%above belowOG(b_i,b_j+i_j)=199;OG(b_i,b_j-i_j)=199;%top left top rightOG(b_i-i_i,b_j+i_j)=199;

OG(b_i+i_i,b_j+i_j)=199;%bottom left bottom rightOG(b_i-i_i,b_j-i_j)=199;OG(b_i+i_i,b_j-i_j)=199;

endend

end%barrier ends here

c) Appendix 3This source code outlines Implementation of the rings method.

%% Analogue Bubble

%decrementer 3,2,1for ring = 3:-1:1;

%analogue bubbleif ring==1

intermediate = 90;elseif ring == 2

intermediate = 50;else

intermediate = 10;endfor r_i = 1+max(ring):300-max(ring)

for r_j = 1+max(ring):300-max(ring)%if barrierif OG(r_i,r_j) == 199

for k = -1:1if OG(r_i-ring,r_j+k) < intermediate;

OG(r_i-ring,r_j+k) = intermediate;endif OG(r_i+ring,r_j+k) < intermediate;

OG(r_i+ring,r_j+k) = intermediate;endif OG(r_i+k,r_j-ring) < intermediate;

OG(r_i+k,r_j-ring) = intermediate;end


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if OG(r_i+k,r_j+ring) < intermediate;OG(r_i+k,r_j+ring) = intermediate;

endend

endend

enden %Analogue Bubble ends here

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