MHead - Self-Organized Flocking in Mobile Robot Swarms

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ME 462 Mechatronics Design
Project Report
Self-Organized Flocking in Mobile Robot Swarms
GROUP “2mm”
Samet Baykul
sametbaykul@gmail.com
1. INTRODUCTION
Flocking is the phenomenon in which a large number of individuals, using limited
information, organize into an ordered motion. It is observed very often in the nature and provides
many advantages for individuals within a group. In flocking, total amount of information obtained by
individuals is increased [1].
Craig Reynolds, who was the first to explain the basics of flocking behavior, described this
behavior in three fundamental rules that each individual should have. These are: attraction,
repulsion and alignment [2]. Attraction means each individual to be pulled by its neighbors to keep
the group together. Repulsion means each individual to stay away from its neighbors and obstacles.
Alignment means each individual to match its velocity and heading direction according to its
neighbors.
Nowadays, collective multi-robot studies which are inspired by nature are becoming more
and more attractive. In order to have a more natural flocking behavior implementation, the data
acquisition of each individual robot has to be kept as low as possible. On the other hand, in order
to achieve a successful flocking behavior and to solve a more complex task, the number of
individuals within a swarm robot must be increased. In other words, flocking size should be as much
as possible. Consequently, there is need to develop a new swarm of robot platform that can
demonstrate the solution of complex problems with large amounts of limited information. In order to
achieve this goal, each individual robot should be designed in a minimalistic way and produced as
cheaply as possible.
Property Statement
Data Acquisition of each Individual Robot Should be minimum
Number of Individual within a Group Should be maximum
Table 1. Fundamental Requirements for Swarm Robot Platform
2. LITERATURE SURVEY
2.1. Flocking Behavior Studies in Swarm Robotics
There have been many previous works in which flocking behavior can be fully implemented
with mobile swarm robots. But in most of the studies, the acquisition of individual information is
large, and the group size is generally small.
Mataric [3] proposed a flocking method on behaviors mentioned above. But in this study
predefined collective homing direction was used as an extra information. Kelly [4] proposed a
flocking method based on a leader-following behavior. A RF system was used for dynamically
electing the leader. Electing leader mechanism is also considered as an extra information for
individuals. Hayes [5] used also a similar mechanism. Furthermore, each individual robot is also

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informed via an external computer. Although these studies showed a successful implementation of
self-organized flocking on physical mobile robots, in the nature, individuals are not able to know
their own heading direction from an external source.
Turgut [6] proposed a method based on using a digital compass, wireless communication
module and a proximal control without using of an external source. This can be said for the first fully
implemented study of flocking behavior. But only with a group of seven robots have been showed
in a physical environment due to the limitations of communication range and environmental noise
for the digital compass. Baldassarre [7] proposed a set of basic interactions for analyzing group
behaviors but only four physical robots could be used to show. Ferrante, Turgut, et al. (2012) [8],
with a more minimalistic approach, showed that flocking behavior is possible in a random direction
without an alignment control. Nevertheless, the flocking swarm size did not exceed eight robots.
Moeslinger [9] proposed that there is a much easier way to create flocking behavior by only
discretizing the robots’ sensor fields into sectors and using different distance thresholds for
attraction and repulsion in these sectors. Flocking algorithm was quite efficient concerning with
aggregation of scattered robots. But this proposal was not verified in a physical environment. Also,
the authors reported that there was a significant decreasing in mobility of the swarm due to the
flock’s size.
Most minimalistic approaches like Turgut, et al. (2012) and Moeslinger’s studies seem to be
most valuable studies for the future of this project.
2.2. Mobile Swarm Robot Platforms
There are many swarm robot platforms used for swarm robotic studies. A comparison table
was given in Appendix 1, which indicates released year, cost, size, microprocessor, locomotion
technique, battery, communication modules, other physical components, simulators and other pros.
and cons. for each robot platform. There are many other products, but similar products are not
included in this table.
Five important features of a swarm robot platform can be listed as like this (Showed in Table
2): Construction cost, size, sensing capabilities, easy of manufacturing and easy of using. Although
these platforms are claimed to be low-cost, many of them still quite expensive. Even using of Colias,
which is the cheapest robot, in a one-thousand-swarm causes a very high cost for the study. Small
sizes are also important for the use of a large number of individual robots in a limited space. It is
seen that the vibration locomotion reduces the size but decreases the speed also. However, there
are some successful examples such as Alice and Colias are also available for the speed-size trade-
off. Sensing capabilities should be kept minimum by the nature of swarm robotics studies. Some
platforms have lots of capabilities such as Kobot, Foot-Bot, R-one and e-Puck but relatively
expensive and bigger. Finally, it is often difficult for researchers to produce and using these
platforms by using procedures in provided open sources. Considering all of these features, most
promising platforms seem to Alice, Colias and Kilobots.
Property Best Platform Record Overall Situation
Construction Cost Colias $41
Costs are high but getting cheaper
Nominal cost is about $100
Size Alice 2.2cm Nominal value is 4 cm
Minimalist Sensing
Capabilities
Kilobot 2 sensors Highly variable
Easy of
Manufacturing
Kilobot
n/a h for
construction
Easy for only experienced researchers
Easy of Using e-Puck, R-one
n/a # of
features
Easy for only experienced researchers
Table 2. Overall Situations for Swarm Robotics Platforms

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3. PRELIMINARY DESIGN
In swarm robotic studies, it is hard to test an algorithm by using a large number of individual
robots because of the manufacturing cost and complexity. Simulation tools used to solve this
problem provide limited options due to the inaccuracy. Available robot platforms are still expensive
and over-complicated. To address this problem, this project presents low-cost, autonomous, small-
sized robot platform in order to provide testing of collective algorithms on large number of robots
for people interested in swarm robotic studies. In addition, the new robot platform will be used to
testing of a basic flocking behavior.
3.1. Design Requirements
1. Platform should consist of several robots.
2. Robots should be small enough.
3. Robots should be fast enough.
4. Robots should have enough duty time.
5. Robots should not collide with each other and not move too away from each other.
6. Each robot should be fast and accurate in adjusting of its speed and heading direction
according to swarm.
7. All robots should run autonomously except for leading robots. (For the demo day)
8. Leading robots should be able to sense an external actuator. (For the demo day)
9. Robots should be manufactured at low costs.
In addition, for a more innovative and generic swarm robot platform, some other
requirements should also be considered as follows:
1. Platform should support testing of swarm algorithms in large numbers.
2. Robots should be very small.
3. Robots should be very fast.
4. Robots should have a very long duty time.
5. Robots should be user-friendly.
3.2. Design Criteria’s
Considering the design requirements for only flocking behavior, the robots must have the
following specifications:
1. Platform should consist of at least 2 robots.
2. The diameter of a robot should not exceed 20cm.
3. Robots should be faster than 0.1 robot size/s.
4. In a single session, robots should run for at least 10 min.
5. Each robot should keep the distance between its closest neighbor from 1 to 5 robot sizes.
6. About velocity and heading alignment of each robot, alignment time should not exceed 10
seconds and alignment error should not exceed 90 degrees.
7. In all robots except for 1 robot, the number of external control sources must be 0.
8. Leading robot(s) should sense an external actuator up to a distance of 5 robot size.
9. Total cost of the prototype of a robot should not exceed 300₺.
For additional requirements:
1. Platform should consist of at least 1024 robots.
2. The diameter of a robot should not exceed 3cm.
3. Robots should be faster than 1 robot size/s.
4. In a single session, robots should run for at least 10h.
5. All robots should be charged and programmed simultaneously within a 2h.

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3.3. Conceptual Designs
There are four conceptual designs in order to provide design requirements. For overall view,
some expected features are given in Table 3.
Table 3. Some Expected Features of Conceptual Designs
3.3.1. M-Head (Mushroom Head)
A simple hemisphere shaped design (Figure 1) mobile robot for flocking swarm
implementation. At the bottom side, two micro DC motors are placed in the reversed direction in
order to gain more space. If there is an imbalance in motion due to asymmetry, the number of
wheels can be increased during testing stage. Control board is mounted on the motors. At the top,
there is a battery as an energy source and a swivel cover in order to access the battery easily.
There are IR’s on the front side. An RGB LED is used to communicate with users and it also
indicates the heading direction of the robot.
Figure 1. (Above) M-Head mobile robot. (Below-Left) Locomotion method. (Below-Right) Other basic
components
3.3.2. VS-Cell (Vibrating Solar Cell)
A battery-fee solution with a solar energy cell (Figure 2). Since with two direct contact
vibrating motors and no battery, this is the smallest one among all the concepts. It has also two
IR’s, one LDR and a programmable control board. Control board has also a structural functionality
as a main body element to hold vibrating motors and solar panel. End edge of the control board is
also touching the ground for the static balance.
Figure 2. VS-Cell mobile robot and basic components.
Property VS-Cell V-Cone M-Head
Cost 50₺ 200₺ 300₺
Size 2.0cm 2.5cm 3.0cm
Speed 1cm/s 5cm/s 20cm/s
Duty Time n/a 1-2h 1-2h

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3.3.3. V-Cone
A cone shaped simple design (Figure 3) mobile robot. It consists of two micro DC motors
which are placed at a certain angle, two IR’s, one LDR, one RGB LED and a programmable control
board inside. Battery is placed at the bottom and accessible easily by user. Since shafts of DC
motors touch the ground directly, which is a unique solution, no wheels are used and by this way
size is minimalized.
Figure 3. (Left) V-Cone mobile robot. (Right) Basic components.

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4. DETAILED DESIGN
Red Lines: Needs to be checked and updated
4.1. Short Explanation of the Design
With a direct shaft-contact locomotion technique and simple hemisphere-shaped design, M-
Head (Figure 4) is a relatively cheap, small, fast and user-friendly self-autonomous mobile robot
which is aimed to be used for flocking behavior implementation in swarm robotics. It consists of two
micro DC motors which are placed in a special V-shape at a certain angle (α) to decrease the
required space. There is no gear or wheel inside. Motors are controlled by H-bridge drivers. Unlike
many mobile robots, M-Head has only one pair of IR sensors but still able to perceive its around by
using rotational motion with a special algorithm. It has also an LDR brightness sensor and an RGB
LED light. Batteries are placed at the top and accessible easily by user.
4.1.1. 3D CAD Model
SolidWorks was used for design of M-Head. Related unfinished 3D models are showed in
Figure 4. After the selection of components and compression studies, the general characteristics
are determined as follows (Table 4):
Properties Value
do Diameter 60 mm
h Height 32 mm
W Weight 60 g
t Shell Thickness 2 mm
hg Ground Gap 2 mm
s Shaft Distance 42 mm
α Shaft Angle 57.15°
Table 4. General Design Properties of M-Head
Figure 4. 3D CAD Model of M-Head
4.1.2. Webots Simulation
Webots was used to simulate physical behaviors and control algorithms. Webots is an open
source robot simulator that provides a complete development environment to model, program and
simulate robots. 3D simulation model of M-Head is showed in Figure 5.

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Figure 5. Simplified 3D simulation model of M-Head
4.2. Selection of Components
4.2.1. Selection of Motor
Since there is no need for angular position control on the motor side, stepper and servo
motors are excluded. Among DC motors, brushless motors are not preferred because of their high
costs. As the small size and low cost are high priority for the robot, it is better to use of coreless DC
motors that can be produced in the smallest size in Figure 6.a. But these motors can rotate at very
high speeds with very low power. Considering the required traction and thermal failure limits, regular
micro DC motors (Figure 6.b) is the best option among others. Comparison of technical data for
coreless and regular DC motors are given in the Table 5.
Figure 6. a. Coreless DC motor. b. Regular DC motor
Coreless DC
Motor
1st Micro DC
Motor
2nd Micro DC
Motor
Voltage 6 V 6 V 6-12 V
Current 0.15 mA (?) 35 mA 35 mA
Motor Length 13 mm 22 mm 23 mm
Motor Radius 4 mm 12 mm 12 mm
Shaft Length 3.5 mm 5 mm 5 mm
Shaft Radius 0.7 mm 1 mm 1 mm
Weight 1 g 8 g 10 g
Speed 40,000 rpm (?) 15,000 rpm (?) 15,000 rpm (?)
Max. Temperature (?) 90ºC (?) 90ºC (?)
Torque (?) (?) (?)
Table 5. Technical specifications for selected DC motors

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4.2.2. Selection of Proximity Sensor
In generally, for mobile robots, IR and ultrasonic sensors (Figure 6.a) are used to determine
the distance with neighboring robots. The distance measurement range of the ultrasonic sensors is
greater than the IR sensors (Figure 6.b). However, IR sensors are preferred because IR sensors
give more reliable results in indoor operations. The other reason of using IR sensors instead of
ultrasonic sensors is that IR sensors provide higher precision in near distances for low-budget
range. Technical data comparison of preferred sensors is given in the Table 6.
Figure 6. a. Ultrasonic transmitter and receiver pair. b. IR transmitter and receiver pair
Ultrasonic Sensor
Radius 16mm
Voltage 5 V
Frequency 40 Hz
Precision 68 dB
Resolution 10 mm
Max. Distance 400 cm
Min. Distance 2 cm
Angle of Vision 15º
Operation Temperature -20ºC ~ +80 ° C
Weight 1 g
IR Sensor
Radius 5mm
Voltage 1.35 V
Wavelength 940 nm
Max. Distance 30 cm
Min. Distance 2 cm
Angle of Vision 34º
Operation Temperature -40ºC ~ +85 ° C
Weight <1 g
Table 6. Technical specifications comparison of the ultrasonic sensor and IR sensor
4.2.3. List of Components
All components which are used in the construction of M-head is given in Appendix 2.

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4.3. Compactness
This is the installation of components into the smallest possible volume for M-Head. As a
result, the inner diameter of the hemispherical shell and the axial angle of the motor shaft axis to
the horizontal ground were calculated as respectively 56 mm and 57.15°.
4.3.1. Effect of DC Motor Selection
The effect of motor selection on dimensions was investigated. It was attempted to obtain
more space inside the shell by placing the motors in a V-shape. (Figure 7) In here, inner shell
diameter based on the optimum shaft contact angle was calculated for different motors and
scenarios (with or without middle circuit space). Other geometric limitations are as follows:
• Clearance between the bottom edge of the motor and the ground,
• Clearance between two motors,
• Required circuit space between the motors in the lower area.
Coreless DC motors gives best results because of its very small sizes. But for now, micro
DC motors are selected. Among both micro DC motors, 2nd
DC motor is longer but gives better
results because of the longer shaft length. Difference is not very big but when it is combined with
other factors such as higher torque capacity, durability, quality etc. the use of 2nd
DC motor is more
reasonable. Related works are showed in Appendix 3. All the results are given in Table 8.
Figure 7. Installation of DC Motors
Circuit
Space
Motor
Height
Motor
Dia.
Shaft
Height
Shaft
Dia.
Motor
Gap
Ground
Gap
Thickness α R Di Do
Coreless DC - 12,5 6 5,5 0,8 1 >2 1 46,1 14,17 28,34 30,34
Coreless + 12,5 6 5,5 0,8 10,64 >2 1 55,2 17,94 35,88 37,88
1st Micro DC - 22 12 5 1 1 1 2 55,46 26,08 52,16 56,16
1st Micro DC + 22 12 5 1 2,68 1 2 55,46 26,43 52,86 56,86
2nd Micro DC - 23 12 6 1 1 1 2 49,57 26,13 52,26 56,26
2nd Micro DC + 23 12 6 1 1 0,94 2 49,11 26 52 56
2nd Micro DC + 23 12 6 1 1 2 2 57,15 28 56 60
Table 8. Effect of Motors with Different Sizes on Compactness
(α: angle between axial motor shaft and the ground)

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4.3.2. Installation of Components
SolidWorks is used as a main tool to install all necessary components into the defined
volume which is determined in the section of “Effect of DC Motor Selection” and based on the angle
α (57.15°) and the diameter (56 mm) of the inner robot shell. The results of optimum installations
are given in Appendix 4.
In Appendix 4. Figure 4.1., the DC motors are installed as in the previous. In addition, a
square hole is drilled on the shell for the heat sink. Two wings are added to fix the motor. A bearing
extending from the shell to the shaft will also be attached to hold the motor from the bottom side.
On the upper side an RGB LED is placed between the motors.
In Appendix 4. Figure 4.2., the important point is that particularly the long edges of the
circuits fit into the shell. At the top in the figure (Rear side of the robot), some part of the socket and
the heat sink is opened out of the shell and this is already required. The socket and the Arduino are
inserted end to end. At the bottom in the figure (Front side of the robot), the IR sensor module is
positioned horizontally. In this way, the total length of the socket, Arduino and horizontally
positioned IR module does not exceed the inner diameter of the shell. On the other hand, the motor
driver must not exceed into the motor site (7 mm above and down of the central horizontal axes)
because its thickness (21 mm) is more than the gap between the motors (18 mm). The battery
beds do not pose a problem in this plane view as shown in the next figure. The other important thing
is that the design of the motherboard is determined according to this installation. Optimum design
of the motherboard is given in Appendix 4 Figure 4.2. b.
In Appendix 4. Figure 4.3., the important point is that particularly the thickness of the
components fit into the shell in especially y-axis. Arduino is placed with 2 mm clearance to the
ground. Since the reset button on Arduino is used by the user, it must be placed downwards. The
motherboard is mounted on Arduino. The total thickness of these two circuits should not exceed
6.33 mm, considering the motor installation (Maximum allowable space under the V-shape motor
installation). In the IR module, the potentiometer is facing downwards and again with 2 mm
clearance with respect to the ground. The IR module must not enter the motor site and should be
located below the lower edge of the battery bed. At the right of the figure (Rear side of the robot),
the socket, the motor driver and the heat sink are placed in colinear from the right side. The left
edge of the motor drive must not enter the motor site. The battery beds are located adjacent to the
motor site on both sides. The RGB LED is located at the top. The IR receiver is located over the IR
module. But details about installation of the IR sensors is given in the next section.
4.4. Installation of Sensors
The ability of robots to communicate effectively with each other depends on the effective
use of sensors. Accurate positioning of the sensors in the physical environment is just as important
as their correct usage on the control side. In working principle of IR sensors, the reflection of the
transmitted infrared light from the object is followed by the receiver. Accordingly, the lower the focus
of the reflected infrared light from the center of the receiver and the higher the intensity of the light,
the better the results are obtained. The effects of the sensors on the design can be listed as follows:
• Opening suitable holes on the shell surface according to 5 mm IR sensor pair.
• Choosing smooth white material on the shell surface to provide maximum reflection for
the IR receiver to collect more incensed light.
• Adjustment of position and angles of the IR sensor holes depending on geometry for
required distance range.
The range of the IR sensor module is 2 cm to 30 cm is given by the vendor. However, this
range can be adjusted by the potentiometer which is located below the robot. It should be noted

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that there is an inverse relationship between distance and sensitivity for IR sensors. In this way,
different sensitivities can be obtained for different distances in different swarm studies. In this
project, the distance was taken from 20 mm to 100 mm. Robot distance is determined as 60
mm at peak.
The roll angle of the IR sensors and the distance from the vertical axis of the robot center
are set according to distance of 60 mm (distance between the two robots) in the XZ plane (top
view), the focus of the reflected light passing through the IR receiver's central collection point. As a
result, the roll angle was determined as 7.05 degrees and the distance from the center was 7.8
mm. Likewise, the pitch angle and height of the IR sensors are set according to distance of 60 mm
(distance between two robots) in the YZ plane (side view), the focus of the reflected light passing
through the receiver's central collection point. As a result, the pitch angle was 8.3 degrees and its
height were determined as 13.3 mm. All relevant design parameters are given in Table 9.
Table 9. Design parameters of Sensors
The following table (Table 10) shows important parameters about the IR sensors according
to robot distances from 20 mm to 100 mm. The relevant study was obtained by using geometric
parameters in SolidWorks. Commute Distance of Light is the minimum path the light from the
transmitter should go until it reaches to the receiver. A direct reduction in light intensity is expected,
as this value increases. Focus Distance of Reflected Light to the Receiver refers to the distance
of the reflected light focus to the receiver's center. The proximity of the light focus to the receiver’s
center affects the reliability of the output signal. Diameter of spreading Light indicates the
diameter of the circle formed on the reflection surface. As this value increases, the reflected light
intensity decreases. The results of the last two parameters are tabulated for both planes, separately.
Finally, Non-reflected Light Ratio shows the ratio of the non-reflected light to the total transmitted
light, which cannot be reflected because it cannot contact a surface of the opposite robot. Obviously,
as this value increases, the intensity of the incoming light to the receiver decreases.
Distance of
Robots [mm]
YZ Plane (Side View) XZ Plane (Top View)
Commute
Distance of
Light [mm]
Focus
Distance of
Reflected
Light to the
Receiver
[mm]
Diameter of
Spreading
Light [mm]
Focus Height
of Reflection
Side from the
Ground [mm]
Focus
Distance of
Reflected
Light to the
Receiver
[mm]
Diameter of
Spreading
Light [mm]
Non-
Reflected
Light Ratio
[%]
201
59,66 12,33 17,09 9,69 19,17 13,1 -
22 63,52 12,32 18,2 9,42 18,82 14,22 -
24 67,38 12,24 19,32 9,14 18,4 15,36 -
26 73,24 12,08 20,45 8,86 17,93 16,5 -
28 75,1 11,86 21,58 8,58 17,39 17,65 -
302
78,98 11,55 22,65 8,3 16,79 18,81 -
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The minimum distance which can be measured by the sensors. The visuals of the related studies are given in Appendix
5. Figure 5.1.1 (Side view) and Appendix 5. Figure 5.2.1 (Top view).
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In the side view, the lower boundary of the transmitted light starts to come to the ground instead of the robot surface.
Relevant visual is given in Appendix 5. Figure 5.1.2. In addition, in the top view, at this distance, the focus of the
reflected light passes through the transmitter again. Appendix 5. Figure 5.2.2.
Parameter Design Plane Value
Optimum Robot Distance - 60 mm
Roll Angle
XZ Plane (Top View)
7,05°
Distance from the Center Line 7,8 mm
Pitch Angle
XZ Plane (Top View)
8,3°
Distance from the Bottom Line 13,3 mm

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32 82,86 11,17 23,74 8,02 16,12 19,98 -
34 86,76 10,73 24,99 7,74 15,39 21,17 -
36 90,64 10,21 26,37 7,46 14,6 22,37 -
38 94,54 9,63 27,87 7,18 13,74 23,58 -
40 98,46 8,98 29,48 6,89 12,82 24,81 -
42 102,36 8,25 31,17 6,61 11,83 26,06 -
44 106,28 7,47 32,93 6,33 10,78 27,33 -
46 110,2 6,61 34,76 6,05 9,67 28,62 -
48 114,12 5,68 36,65 5,76 8,49 29,94 -
50 118,06 4,69 38,58 5,48 7,24 31,3 -
52 122 3,63 40,57 5,19 5,92 32,69 -
54 125,94 2,5 45,59 4,91 4,54 34,13 -
56 129,9 1,31 44,65 4,62 3,09 35,64 -
58 133,84 0,04 46,75 4,34 1,57 37,23 -
603
137,8 1,3 48,88 4,05 0 38,94 -
62 141,75 2,71 51,03 3,77 1,71 40,83 -
64 145,74 4,18 53,22 3,48 3,45 43,1 -
66 149,72 5,73 55,44 3,19 5,26 47,12 -
684
153,7 7,35 57,68 2,91 7,17 - 1,43
70 157,7 9,04 59,95 2,62 9,14 - 2,87
72 161,68 10,83 62,24 2,33 11,21 - 4,23
74 165,68 12,67 64,57 2,04 13,34 - 5,67
765
169,7 14,6(3) 66,93 1,75 15,58 - 6,8
78 173,7 16,62 69,31 1,46 17,9 - 8,03
80 177,72 18,7 71,73 1,17 20,31 - 9,2
82 181,74 20,88 74,19 0,88 22,81 - 10,33
84 185,78 23,14 76,69 0,59 25,41 - 11,43
86 189,8 25,49 79,24 0,3 28,1 - 12,5
88 193,84 27,92 81,85 0,01 30,9 - 13,5
906
197,9 30,46 84,52 -0,28(4) 33,79 - 14,4
92 201,94 - 87,28 -0,58 36,82 - 15,46
94 206 - 90,17 -0,87 39,94 - 16,37
96 210,06 - 93,24 -1,16 42,12 - 17,27
98 214,12 - 96,67 -1,46 44,36 - 18,13
100 218,2 - 101,74 -1,75 46,65 - 19
Table 10. Effect of Motors with Different Sizes on Compactness.
Analysis of sensor behaviors according to distances between two neighboring robots is
given in Appendix 5.
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This is the optimum distance. The design parameters for the sensor pair are based on this distance. In both planes (Side
and top views) the focus of the reflected light passes through the IR receiver's center. As it moves away from this
distance, the focal point begins to move away from the IR receiver’s center again. The visuals of the related studies are
given in Appendix 5. Figure 5.1.3 (Side view) and Appendix 5. Figure 5.2.3 (Top view).
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At the top view, a certain portion of the transmitted light starts to miss the surface of the opposite robot. The ratio of
non-reflected light to the total transmitted light is tabulated in the corresponding column (Non-Reflected Light Ratio).
Relevant visual is given in Appendix 5. Figure 5.2.4.
5
At the side view, the focus of the reflected light begins to fall below the shell surface of the light transmitter robot.
Relevant visual is given in Appendix 5. Figure 5.1.4.
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This is considered as the farthest distance to be studied for this project. The visuals of the related studies are given in
Appendix 5. Figure 5.1.5 (Side view) and Appendix 5. Figure 5.2.5 (Top view).

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5. MATHEMATICAL MODEL
5.1. Direct Shaft-Contact Mechanism
Since M-Head has no gear and no wheel, it uses directly motor shafts for traction. Each
motor shaft is in contact with the ground at a certain angle (α = 62.17º). This angle is optimized for
the compactness of the robot. The shaft is rotated at a high speed (up to 15000rpm) on the surface
to provide traction due to the friction force. Since the shaft slides over the surface, the linear speed
of the wheel at the contact point will be different from the overall speed of the robot. Nevertheless,
there is still a correlation between overall robot speed, motor rotation speed, reaction force and
friction coefficient. This correlation can be expressed by the following formula:
!" = $(&) ∙ * ∙ + 1
The total robot weight (W) is about 60g. There are 4 contact point between the robot and
the surface. Then reaction force (N) is 140 mN. Friction coefficient (k) was taken as 0.25. In the
case of insufficient traction, the motor speed can be increased with the motor driver. In the
simulation and in the real world, the relationship between motor speed and traction is obtained and
showed in Table 11 and Table 12.
Motor Speed Robot Speed Stability
2500 rpm 8 cm/s YES
5000 rpm 16 cm/s YES
10000 rpm 21 cm/s NO
15000 rpm 32 cm/s NO
Table 11. Motor Speed vs Robot Speed
()
Table 12. (A test will be done after the manufacturing)
5.2. Thermal Considerations
Since gear regulator is not used, there is a linear relationship between motor speed and
torque. In other words, it is not possible to obtain the necessary traction without increasing the
motor speed. So high speed on the contact point is inevitable. On the other hand, the shaft slides
on the surface as the wheel is not used. Due to friction, it is expected to the shaft heat up. In addition,
because the engines are small, the heat dissipation is low as an extra problem. For these reasons,
the temperature must be kept under control so that the motors can operate safely in the expected
time. So, the motor speed and thus the traction force will be lower than the actual limit to prevent
any thermal failure. Depending on the motor speed, the thermal durability comparison of the motors
is showed in Table 13.
In order to ensure that the heat emitted from the motors and the motor driver is dissipated
by free convection, heat sinks have been placed on ventilation channels on the outer shell of the
robot.
According to the results of the experiment, an embedded thermal control system was also
provided to the robots. Details about this system are included in the control design section.
()
Table 13. (A test will be done after the manufacturing)

14
5.3. Motion Mechanism
5.3.1. Translational Motion
When the two motors rotate in the same direction, the translational motion is achieved.
Rotational motor speed vs overall robot speed change is shown in Table 11 and Table 12.
5.3.2. Rotational Motion
When the two motors rotate in opposite directions, the robot rotates around itself. By using
the simulation tool, the obtained graph of the motor speed and depending angular rotation speed
of the robot is shown in the Table 14.
Motor Speed Period
Physical
Stability
Stability
Duration
Accuracy Results
90 rad/sec 3.200 sec YES 20 sec Not Accurate
450 rad/sec 1.888 sec NO n/a Not Stable (WORST)
120 rad/sec 2.400 sec YES > 3 min +3.1 mm
94 rad/sec 3.040 sec YES > 3 min -2.7 mm
112 rad/sec 2.560 sec YES > 3 min +1.2 mm (BEST)
Table 14. Motor Speed vs Rotational Motion Results

15
5.4. Mechanical Parameters
All the important parameters for optimum traction and overall speed for the robot are given
in the Table 15.
Input/output Parameter Symbols Description Values
Input Values
w Angular velocity of
motor
15000 rpm
(250 rps)
d Diameter of motor
shaft
1 mm
k Friction constant
(Clean-cut steel and
wood)
0.25
W Weight of the robot 60 g
t Operational time 2400 s
Tmax Maximum allowable
temperature
120ºC (?)
Output Values
Vs Max. linear velocity of
the shaft
78.5 cm/s
N Reaction force (for
each shaft)
140 mN
Ff Friction force 35 mN
Ft Traction force (?)
V Max. velocity of robot (?)
Table 15. Mechanical parameters for optimum traction and overall velocity of the M-Head

16
6. CONTROLLER DESIGN
6.1. Low-Level Control Systems
6.1.1. Motor Power Control
When the robot starts first, more power is supplied to the motors. When the robot reaches
the desired speed, the motor power is reduced and stabilized. In this way, both the engine's heating
is delayed, and energy is saved. And this is also required to compensate time loss due to the inertia
effect. Related control diagram has been showed in Figure 8.
Figure 8. Motor Power Control Diagram

17
6.1.2. Initial Calibration Control
In the modeling of most swarm algorithms, it is important to starting of the robots as
simultaneously. However, in the current version of M-head, it is not possible to program the robots
at the same time (They need to be programmed one by one). So, all the robots need to be calibrated
before starting manually.
This could be achieved by using a remote trigger signal which starts the processing at the
same time. As proposed solution in this document, robots use their brightness sensors. The
successive 3 straight-line-light-signal initiates all the robots. The successive 2 straight-line-light-
signal light signals stops the robots. The successive 4 straight-line-light-signal resets the robots.
The corresponding control mechanics were given in Figure 9.
Figure 9. Initial Calibration Control Diagram
6.1.3. Thermal Control
As stated in the Mathematical Model section, the motor shafts slide on the surface. High-
speed rotating shafts lead to increase motor temperature due to friction. Since the heat dissipation
rate of small-sized DC motors is slow, it is critical to control the motor temperatures in order to
prevent any thermal failure. Since the excessive operation time will endanger the motors, thermal
control system turns off the robot motors automatically after 30 (?) minutes from the start. The user
is informed by the RGB LED in this cooling state. As the motors are small, the cooling time does
not last long. After a certain period of time the robot continue to its operation and terminates the
cooling warning state. Related control diagram has been showed in Figure 10.
Figure 10. Thermal Control Diagram

18
6.1.4. Diagnosis Control Mode
This mode is used to verify the operation of basic functions such as motor speed control,
battery status, sensor readings, current heading direction and light sensitivity. Related control
diagram has been showed in Figure 11.
Figure 11. Diagnosis Mode Control Diagram
6.2. High-Level Control Systems
6.2.1. MODE 1: Rotational Period Time Measurement Control
When the robot is started first, it does not have any information about itself and its
surroundings. Firstly, the robot starts to search for an object that it can detect. When it encounters
an object for the first time, it rotates approximately two and a half rounds around itself and learn
one turning period time. Knowing period time provides the necessary heading information
depending on the returning. RPTM is terminated after the period information is learned.
Figure 11. Rotational Period Time Measurement Control Diagram

19
6.2.2. MODE 2: Magnetic Pathfinder Algorithm
Since the robot has a limited perception capability, it must collect information as much as
possible for a proper flocking implementation. Instead of wandering around randomly, the robot
records the places which it travels and the objects it encounters on a map. The contribution of this
algorithm for the flocking implementation can be listed as follows:
• Possibility of encountering increases for robots. This decreases the required time for
aggregation especially for lost robots.
• Robots remember the obstacles they have encountered before and avoid in the next time.
Thus, they do not spend unnecessary time by scanning against the same obstacle. They
gradually begin to give instant responses for the same objects,
• Robots estimate the possible locations of other robots which they encounter. In this way,
swarm cohesion can be increased.
The pathfinder algorithm used in here is specifically developed for this project. There is no
goal for finding the shortest path. It is not designed to find complex paths like labyrinths. It is
designed especially for the paths which have relatively a smaller number of obstacles. Considering
all of these, this algorithm requires less memory and processing power than generic algorithm such
as A * pathfinder algorithm. It is considered as a more optimal option for lower processing power
such as microcontrollers. The differences between the two algorithms are given in Table 16.
Magnetic Pathfinder
(M-Head)
A* Pathfinder
(Generic)
Shortest path results Occasionally Often
Convenience for complex
roads
No Yes
Memory Usage Low High
Processor Usage
Medium (can be
optimized)
High
Usage Area Microcontroller Microprocessor
Table 16. Comparison of Magnetic Pathfinder and A* Pathfinder Algorithms
6.2.3. MODE 3: Path follower Algorithm
It enables the robot to access to a targeted position on the map. It can be used without a
pathfinder algorithm. It works like a joystick in a video game.
6.2.4. MODE 4: Geometry Recognition Algorithm
It can distinguish the objects which are encountered as moving and stationary. The
obstacles can be distinguished as walls, an ordinary obstacle, a robot, a wall corner etc. The related
diagram is given in Figure 12.

20
Figure 12. Geometry Recognition Control Diagram

21
6.2.5. MODE 5: Locking Algorithm
It learns the relative velocity and position vectors of a neighboring robot. This provides the
robot to connect and move with the robot with a proper alignment.
(Not implemented yet)
6.2.6. Finetuning
Property Name Description
Optimal
Value for
Webots
Optimal
Value for
Real World
UPDATE_DELAY
Defines the expected time delay between two
operations for the microcontroller
32 30
MAP_WIDTH
Defines the cell number of the arm that opens to
the sides of the map. Total number of the cells in
the map, C is as follows
C = (MAP_WIDTH x 2 + 1)2
The map always defines a 2D square area.
3 6
TARGET_WIDTH
Defines the width of the scanned sub-map in
pathfinding mode. Total number of the cells in
the target map, T is as follows
T = (TARGET_WIDTH x 2 + 1)2
The target map always defines a 2D square
area.
2 3
PATH_LONG
Defines the total memory for the pathfinder. It
has a direct impact on the processing power.
25 10?

22
SPEED_MAX
Defines the maximum speed. The robot uses
this speed when it is lost in panic and is sure
where to go.
260 260?
SPEED_NOM
Defines the nominal speed for a calm
wandering.
130 130?
SPEED_MIN
Defines the minimum speed. The robot uses this
speed when it is not sure where it will go.
65 65?
SPEED_ROT
Defines the rotation speed. This speed must be
optimized for smooth scanning operations.
112 112?
SEGMENT
(CELL_WIDTH)
Defines the width of each of the cells on the
map. The map should be optimized with
MAP_WIDTH when describing the real area. For
example: On low-resolution maps, this value
must be increased in order to cover the entire
area.
23 23?
FIRST_APPROACH
Defines the value of the maximum interference
of IR rays when an obstacle is first encountered.
600 600?
DS_TOLERANCE Defines the tolerance range for the IR sensor. 150 150?
DIAGNOSIS Starts the robot with diagnostic services. - -
DIAG_PERIOD
It is used for optimization of the parameter,
SPEED_ROT.
- -
Table 17. Finetuning Parameters

23
6.2.7. General Control Diagram
Figure 13. General Control Diagram

24
Experimental Results (2 pages)
Put tables and figures summarizing the results here. Put relevant graphs. Discuss the results,
specifically focusing on the effect of controller parameters on the performance of your design.
Compare the results of simulation and real robot experiments.

25
Discussion and Conclusion (1 page)
Discuss the results in general. Summarize the procedure you followed. Make general conclusions.
Put future work. Discuss the results in general. Summarize the procedure you followed. Make
general conclusions. Put future work. Discuss the results in general. Summarize the procedure
you followed. Make general conclusions. Put future work.

26
REFERENCES
[1] Clark, C. W., & Mangel, M. (1984). Foraging and flocking strategies: information in an
uncertain environment. The American Naturalist, 123(5), 626-641.
[2] Reynolds, C. W. (1987, August). Flocks, herds and schools: A distributed behavioral model. In
ACM SIGGRAPH computer graphics (Vol. 21, No. 4, pp. 25-34). ACM.
[3] Mataric, M. J. (1993, April). Designing emergent behaviors: From local interactions to collective
intelligence. In Proceedings of the Second International Conference on Simulation of Adaptive
Behavior (pp. 432-441).
[4] Kelly, I. D., & Keating, D. A. (1996). Flocking by the fusion of sonar and active infrared sensors
on physical autonomous mobile robots. In Proceedings of The Third Int. Conf. on Mechatronics
and Machine Vision in Practice (Vol. 1, pp. 1-4).
[5] Hayes, A. T., & Dormiani-Tabatabaei, P. (2002). Self-organized flocking with agent failure: Off-
line optimization and demonstration with real robots. In Proceedings 2002 IEEE International
Conference on Robotics and Automation (Cat. No. 02CH37292) (Vol. 4, pp. 3900-3905). IEEE.
[6] Turgut, A. E., Çelikkanat, H., Gökçe, F., & Şahin, E. (2008). Self-organized flocking in mobile
robot swarms. Swarm Intelligence, 2(2-4), 97-120.
[7] Baldassarre, G., Nolfi, S., & Parisi, D. (2003). Evolving mobile robots able to display collective
behaviors. Artificial life, 9(3), 255-267.
[8] Ferrante, E., Turgut, A. E., Huepe, C., Stranieri, A., Pinciroli, C., & Dorigo, M. (2012). Self-
organized flocking with a mobile robot swarm: a novel motion control method. Adaptive
Behavior, 20(6), 460-477.
[9] Moeslinger, C., Schmickl, T., & Crailsheim, K. (2009, September). A minimalist flocking
algorithm for swarm robots. In European Conference on Artificial Life (pp. 375-382). Springer,
Berlin, Heidelberg.
[10] Turgut, A. E., Gokce, F., Celikkanat, H., Bayindir, L., & Sahin, E. (2007). Kobot: A mobile
robot designed specifically for swarm robotics research. Middle East Technical University, Ankara,
Turkey, METU-CENG-TR Tech. Rep, 5(2007).
[11] Brutschy, A., Pini, G., & Decugniere, A. (2012). Grippable objects for the foot-bot. Technical
Report TR/IRIDIA/2012-001). IRIDIA, Université Libre de Bruxelles, Brussels, Belgium.
[12] Garnier, S., Tache, F., Combe, M., Grimal, A., & Theraulaz, G. (2007, April). Alice in
pheromone land: An experimental setup for the study of ant-like robots. In 2007 IEEE Swarm
Intelligence Symposium (pp. 37-44). IEEE.
[13] Arvin, F., Murray, J., Zhang, C., & Yue, S. (2014). Colias: An autonomous micro robot for
swarm robotic applications. International Journal of Advanced Robotic Systems, 11(7), 113.
[14] Droplets. (2014, May 03). Retrieved from http://correll.cs.colorado.edu/?page_id=2687
[15] Szymanski, M., Breitling, T., Seyfried, J., & Wörn, H. (2006, September). Distributed shortest-
path finding by a micro-robot swarm. In International Workshop on Ant Colony Optimization and
Swarm Intelligence (pp. 404-411). Springer, Berlin, Heidelberg.

27
[16] Rubenstein, M., Ahler, C., Hoff, N., Cabrera, A., & Nagpal, R. (2014). Kilobot: A low cost
robot with scalable operations designed for collective behaviors. Robotics and Autonomous
Systems, 62(7), 966-975.
[17] One. (n.d.). Retrieved from http://mrsl.rice.edu/projects/r-one
[18] Cianci, C. M., Raemy, X., Pugh, J., & Martinoli, A. (2006, September). Communication in a
swarm of miniature robots: The e-puck as an educational tool for swarm robotics. In International
Workshop on Swarm Robotics (pp. 103-115). Springer, Berlin, Heidelberg.
[19] What is an Ultrasonic Sensor? (n.d.). Retrieved from
http://cmra.rec.ri.cmu.edu/content/electronics/boe/ultrasonic_sensor/1.html

28
APPENDIX 1:
Comparison of Robot platforms
Picture Platform Released Cost Size Microprocessor Locomotion Battery Communication
Other
Components
Simulator Comments
Kobot
[10]
2007 $800 12cm
20 MHz 8-bits
14.3KB
PIC18F4620A
2 x DC
Motors with
2 x Wheels
2000 mAh
LiPo
Battery
Operation:
10h
8 x IR Proximity
IEEE
802.15.4/ZigBee
Compliant XBee
Wireless Module
(Range: 20m)
Digital
Compass
Camera
CoSS
+ Group Programming
+ Kin-detection
- Replaceable battery
which is recharged
manually
Foot-Bot
[11]
2012 ? 17cm ? Treels ?
24 x IR
Proximity
12 x RGB LEDs
Turret force
sensor
Camera
Gripper
ARGoS
+ Rotatable turret that
consists of a grippable
ring and a gripper.
Alice
[12]
2007 ? 2.2cm
20 MHz 8-bit
14KB
PIC16LF877
2 x Swatch
Motors
Speed:
4cm/s
LiPo
Battery
Operation:
10h
4 x IR Proximity
RF Modem
ANT Module
(Optional)
Camera
(Optional)
Gripper
(Optional)
Webots
+ A very small
package size
+ Kin-detection
+ Employed
in various swarm
research applications,
such as the
embodiment of
cockroach
aggregation
- The commercialized
Alice was previously
around a few hundred
pounds

29
Colias
[13]
2013 $41 4cm
8 MHz 8-bits
ATMEL AVR 8
2 x Micro
DC Motors
H Bridge DC
Motor Driver
Speed:
35cm/s
600 mAh
LiPo
Battery
Operation:
1-3h
IR Proximity Light ?
+ Colias uses three IR
proximity sensors to
avoid collisions with
obstacles and other
robots within less than
10 mm.
+ Motors are
controlled individually
using a pulse-width
modulation (PWM)
technique
Droplets
[14]
? ? 4.4cm ?
Vibration
Motors
Operation:
24h
? Light ?
+ Large-scale
swarming researches
+ Droplet-to-droplet
reprogramming
Jasmine
[15]
2006 $130 3.5cm
20 MHz 8-bits
32KB
Atmega328
2 x Small
Gear-Head
Motors
2 x Wheels
LiPo
Battery
Operation:
1-2h
6 x IR Proximity
Light
(Optional)
Color
(Optional)
Gripper
Breve
Simulation
Environment
+ Group Charging
+ Aluminum Structure
+ Kin-detection
+ Played the role of a
honeybee
in several aggregation
(BEECLUST)
scenarios
Kilobot
[16]
2013 $120 3.3cm
20 MHz 8-bits
32KB
Atmega328
2 x Sealed
Coin
Shaped
Vibration
Motors
Speed:
1cm/s
Operation:
3-24h
IR Proximity
RGB LED
Light ?
+ Group Charging
+ Group Programming
+ It uses a slip-stick
principle for motion
which reduces its
cost, since the robot
does not use motors
or wheels.
- The motion method
has several
drawbacks, such as
that the achieved
speed is low, which
limits its application in
swarm scenarios.

30
R-one
[17]
2012 $220 10cm
50MHz 32-bits
256KB ARM
Cortex M3
Speed:
25cm/s
2000 mAh
LiPo
Battery
Operation:
4h
8 x IR Proximity
12 x RGB LEDs
RF Modem
Light
4 x Analog
Cds
3D Gyro
3D
Accelerometer
Encoders
3 x User
Mode Buttons
?
+ Research and
teaching purposes. It
was used in several
studies on swarm
robotics.
e-Puck
[18]
? $1300 7.5cm
30 MHz 16-bits
144KB
PIC30F6014A
2 x Stepper
Motors
Speed:
13cm/s
Operation:
1-10h
8 x IR Proximity
Bluetooth
802.15.4 ZigBee
Camera
Speaker
3 x
Microphones
Accelerometer
Webots
+ Mainly designed for
education in the
engineering field
+ Bluetooth
Programming
- $400 is needed to
obtain an additional
range
and bearing module

31
APPENDIX 2:
Component List
Picture Component Dimensions Description
2 x Micro DC Motor
Motor:
D: 12 mm
H: 23 mm
W: 10 g It is used for traction.
Shaft:
D: 1 mm
H: 6 mm
Arduino Pro Mini
328 5V 16MHz
l: 33 mm
w: 18 mm
t: 3 mm
W: 2 g
Arduino Pro Mini is
used as a main
microprocessor.
LM393 IR Sensor
Module
l: 48 mm
w: 15 mm
t: 8 mm
W: 3 g
It is used for obstacle
detection
FT232RL Converter No effect on design
FTDI is used as a
converter from USB
to TTL in order to
program Arduino
from an external
computer
TB6612FNG DC
Motor Driver
l: 21 mm
w: 21 mm
t: 3 mm
W: 2 g
DC Motor Driver is
used to control
speed of DC motors.
2 x CR2032 3V – 210
mAh Coin Battery
D: 20 mm
t: 3.2 mm
W: 3 g
It is used to energy
source for the robot.
6-pin Female
Header Socket
l: 16 mm
w: 8,5 mm
t: 2,6 mm
W: 1 g
This header is used
as a connector from
FTDI to Arduino Pro
Mini.
2 x CR2032 Vertical
Coin Battery Bed
l: 22 mm
w: 23 mm
t: 6.4 mm
W: 2 g
Battery bed is used
to hold battery and
provides energy
transmission from
battery to circuits.

32
3mm Brightness
Sensor
D: 5 mm
t: 2 mm
W: 1 g
A 3mm diameter light
sensor is used to
allow light-sensitive
control programming.
RGB LED
D: 5 mm
h: 8.7 mm
W: 1 g
A 5mm diameter
RGB LED is used to
communicate with
the user
1 x 14x14x6 mm Al
Heat Sink
2 x 8x8x6 mm Al
Heat Sink
-
Smaller heat sinks
are used to increase
heat dissipation rate
of DC motors. Bigger
one is used for the
motor driver.

33
APPENDIX 3:
Effect of DC Motor Selection on the Compactness
Figure 3.1. Coreless DC Motor without Circuit Space (α = 46.1°, Rin = 14.17 mm, Dout = 30.34)
(Best Choice but not selected because of thermal and traction limits)
Figure 3.2. Coreless DC Motor without Circuit Space (α = 55.2°, Rin = 17.94 mm, Dout = 37.88)

34
Figure 3.3. 1st
Micro DC Motor without Circuit Space (α = 55.46°, Rin = 26.08 mm, Dout = 56.16)
Figure 3.4. 1st
Micro DC Motor with Circuit Space (α = 55.46°, Rin = 26.43 mm, Dout = 56.86)

35
Figure 3.5. 2nd
Micro DC Motor without Circuit Space (α = 46.57°, Rin = 26.13 mm, Dout = 56.26)
Figure 3.6. 2nd
Micro DC Motor with Circuit Space (α = 49.11°, Rin = 26 mm, Dout = 56)
(Optimum Choice)

36
APPENDIX 4:
Installation of Components
Figure 4.1. Installation view on xz-plane: RGB LED is at the top, DC Motor is at the side and contacts with inner surface of the shell, aluminum
heat sink is mounted on the motor, required circuit space is at the middle of bottom

37
Figure 4.2. a. Installation view on xz-plane: All end points of all the components are adjusted with respect to the inner surface of the shell.

38
Figure 4.2. b. Optimum design of Motherboard

39
Figure 4.3. Installation view on yz-plane. All components are mounted with respect to others and the limits of inner shell diameter.

40
APPENDIX 5:
5.1. Behaviors of IR Sensors with respect to Different Distances on Side View (YZ Plane)
Figure 5.1.1. Side view of two robots (YZ Plane). Distance between robots is 20 mm. Commute distance is 2 x 29.83 mm. The spreading
distance is 17.09 mm. Focus distance is 12.33 mm. This is the minimum distance which can be measured by the sensors.

41
distance is 22.65 mm. Focus distance is 11.55 mm. The lower boundary of the transmitted light starts to come to the ground instead of the
opposite robot surface.

42
distance is 48.88 mm. Focus distance is 1.3 mm. This is the optimum distance for the current sensor design. The design parameters for the
sensor pair are based on this distance. The focus of the reflected light passes through the IR receiver's center. As opposite robot moves away
from this distance, the focal point begins to move away from the IR receiver’s center again.

43
distance is 66.93 mm. Focus distance is 14.6 mm. At this distance, the focus of the reflected light begins to fall below the shell surface of the
light transmitter robot.

44
distance is 84.52 mm. Focus distance is 30.46 mm. This is considered as the farthest distance to be studied for this project.

45
5.2. Behaviors of IR Sensors with respect to Different Distances on Top View (XZ
Plane)
Figure 5.2.1. Top view of two robots (XZ Plane). Distance between robots is 20 mm. The
spreading distance is 13.1 mm. Focus distance is 19.17 mm. This is the minimum distance which
can be measured by the sensors.

46
spreading distance is 18.81 mm. Focus distance is 16.8 mm. At this distance, the focus of the
reflected light passes through the transmitter again

47
spreading distance is 38.94 mm. Focus distance is 0 mm. This is the optimum distance for the
current sensor design. The design parameters for the sensor pair are based on this distance. The
focus of the reflected light passes through the IR receiver's center. As opposite robot moves away
from this distance, the focal point begins to move away from the IR receiver’s center again.

48
spreading distance is 48.16 mm. Focus distance is 7.17 mm. After this distance, a certain portion
of the transmitted light starts to miss the surface of the opposite robot. The ratio of non-reflected
light to the total transmitted light is tabulated in the corresponding column (Non-Reflected Light
Ratio) in Table 10.

49
Figure 5.2.5. Top view of two robots (XZ Plane). Distance between robots is 90 mm. Focus
distance is 33.79 mm. This is considered as the farthest distance to be studied for this project.

MHead - Self-Organized Flocking in Mobile Robot Swarms

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