a documented MSc thesis on this project.

Design and Analysis of a Robotic Duct
Cleaning System
by
Siamak Ghorbani Faal
A thesis
Presented to Sharif University of Technology, International Campus, Kish Island
in partial fulfillment of the
requirements for the degree of
Master of Science
in
Mechanical Engineering
(Mechatronics)
Supervisor: Prof. Gholamreza Vossoughi
Co-supervisor: Dr. Kambiz Ghaemi Osgouie
Kish Island, Iran, 2011
© Siamak Ghorbani Faal, 2011
i
Sharif University of Technology
International Campus, Kish Island
This is to certify that the Thesis Prepared,
By:
Siamak Ghorbani Faal
Entitled:
Design and Analysis of a Robotic Duct Cleaning System
and submitted in partial fulfillment of the requirements for the Degree of
Master of Science
complies with the regulation of this university and meets the accepted standards with respect
to originality and quality.
Signed by the final examining committee:
Supervisor:
Co-Supervisor:
External Examiner:
Internal Examiner:
Session Chair:
ii
AUTHOR'S DECLARATION
I hereby declare that I am the sole author of this thesis. The work described in this thesis has
not been previously submitted for a degree in this or any other university, and unless
otherwise referenced it. This is a true copy of the thesis, including any required final
revisions, as accepted by my examiners. I understand that my thesis may be made
electronically available to the public.
iii
Abstract
Design and Analysis of a Robotic Duct Cleaning
Siamak Ghorbani Faal, M.Sc.
Sharif University of Technology, International Campus, Kish Island, 2011
Supervisor: Prof. Gholamreza Vossoughi
Co-supervisor: Dr. Kambiz Ghaemi Osgouie
Delivering high quality and clean air into occupied spaces is the main goal of Heating,
Ventilation and Air Conditioning (HVAC) systems. HVAC systems draw supply air which
usually contains fungi and moisture. Fungi and moisture plus organic materials create a good
bed for mold growth. Studies prove that duct cleaning process can definitely reduce the
amount of pollutants present in the ducts. Hence, it has positive impact on human lives both
regarding psychological and physical points of view. Duct cleaning method‟s application
difficulties and ducts‟ unreachable environments motivated duct cleaning firms to employ
robots for duct cleaning tasks. Although there are considerable numbers of Duct Cleaning
Robots (DCRs) available on the market, they are not dexterous enough to be widely used by
the companies requiring this service. The main reason is that they are unable to maneuver in
vertical ducts.
This thesis focuses on designing a novel DCR which doesn‟t have the limitations of current
DCRs. First, a literature review on DCRs is presented in order to find their requirements and
limitations. Additionally, a literature review on climbing robots is presented in order to find
an appropriate structure serving as a DCR. By considering different duct conditions and
DCRs requirements, a conceptual design of a climbing DCR (named as Duct-Sweeper) is
proposed. Moreover, an optimization problem is formulated and solved to find the optimal
robot geometry. The results of the optimization are used to design a prototype. Finally,
different maneuvers and path plantings of the robot are discussed.
iv
Although the introduced robot is designed to serve as HVAC DCR, small changes to the
adhesion system and wheeled locomotion system of the robot can make it suitable for
industrial duct systems as well.
Key words: Duct cleaning robots, Climbing robots, Conceptual design, Design optimization,
Prototype design, Path planning
v
Acknowledgements
This dissertation would not have been possible without the guidance and help of several
individuals who contributed their valuable assistance throughout this study.
Foremost, I would like to express my sincere appreciation to my supervisor Prof. Gholamreza
Vossoughi for his patience, motivation and immense knowledge. His guidance and support
helped me throughout this research and the preparation of this thesis.
My special thanks also go to my Co-Supervisor Dr. Kambiz Ghaemi Osgouie for his support,
motivation and knowledgeable guidance.
My sincere thanks also go to my friends in Sharif University of Technology, International
Campus-Kish Island: Mozhgan Azimpour Kivi, Kaveh Bidarmaghz and Navid Kermanshahi
who always took the time to listen to me and share their knowledge.
Last but not the least; I would like to thank my parents, Maghsoud Ghorbani Faal and Nasrin
Basharkhah, for their endless support and love they have provided me throughout my life. I
would also like to thank them for encouraging and supporting me to pursue my Master‟s
study. My brother, Babak Ghorbani Faal, and my sister, Parisa Ghorbani Faal, deserve my
wholehearted thanks as well.
vi
Dedication
This thesis is dedicated to my parents who have never failed to give us financial and moral
support and for showing me the worth of knowledge. It is also dedicated to all my teachers
throughout my life that helped me to pursue my studies. Finally, this thesis is dedicated to all
those who never stop believing in the richness of learning.
vii
Table of Contents
Sharif University of Technology ............................................................................................... ii
AUTHOR'S DECLARATION ................................................................................................. iii
Abstract .................................................................................................................................... iv
Acknowledgements .................................................................................................................. vi
Dedication ............................................................................................................................... vii
Table of Contents ................................................................................................................... viii
List of Figures ........................................................................................................................... x
List of Tables ........................................................................................................................... xii
List of Abbreviations .............................................................................................................. xiii
Chapter 1 Introduction............................................................................................................... 1
1.1 The necessity of duct cleaning ........................................................................................ 1
1.2 Proposed method ............................................................................................................. 3
1.3 Chapter organization ....................................................................................................... 4
Chapter 2 Literature review of current duct cleaning and climbing robots ............................... 5
2.1 Literature review on duct cleaning robots ....................................................................... 5
2.2 Literature review on climbing robots .............................................................................. 9
Chapter 3 Conceptual Design .................................................................................................. 15
3.1 Structure concept of the Duct-Sweeper ......................................................................... 15
3.2 Duct-Sweeper waist mechanism‟s workspace requirements ......................................... 16
3.3 Conceptual design of the waist mechanism................................................................... 22
3.4 Conceptual design of wheeled locomotion.................................................................... 26
3.5 Conceptual design of adhesion system .......................................................................... 28
3.5.1 Duct construction materials .................................................................................... 28
3.5.2 Adhesion technology suitable for Duct-Sweeper ................................................... 29
3.5.3 Vacuum system design ........................................................................................... 30
3.5.4 Adhesion system leveling mechanism.................................................................... 36
3.6 Summary of Duct-Sweeper‟s conceptual design ........................................................... 37
Chapter 4 Kinematics and static force analysis of Duct-Sweeper ........................................... 39
4.1 Kinematic analysis of Duct-Sweeper ............................................................................ 39
4.1.1 Solving waist‟s kinematics using SSM .................................................................. 39
4.1.2 Mapping PP kinematics to SSM ............................................................................. 41
4.1.3 Forward and inverse kinematics of the waist ......................................................... 43
4.1.4 Velocity analysis .................................................................................................... 47
viii
4.2 Jacobian and static force analysis .................................................................................. 49
4.3 Suction cup force analysis ............................................................................................. 50
Chapter 5 Design optimization and prototype design ............................................................. 55
5.1 Definition of parameters used in optimization .............................................................. 55
5.2 Optimization formulations............................................................................................. 58
5.3 Applying optimization to prototype design ................................................................... 61
5.3.1 Evaluating constant values ..................................................................................... 61
5.3.2 Solving optimization problem ................................................................................ 64
5.4 Prototype design ............................................................................................................ 66
5.4.1 Cart design .............................................................................................................. 66
5.4.2 Adhesion module design ........................................................................................ 67
5.4.3 Waist design ........................................................................................................... 68
5.4.4 Overall robot assembly ........................................................................................... 70
Chapter 6 Path planning .......................................................................................................... 72
6.1 Transition schemes ........................................................................................................ 72
6.2 Transition combinations ................................................................................................ 79
Chapter 7 Conclusions and future works ................................................................................. 82
7.1 Future work ................................................................................................................... 84
Appendix A ............................................................................................................................. 85
Appendix B.............................................................................................................................. 86
References ............................................................................................................................... 91
ix
List of Figures
Figure ‎3.1. Conceptual scheme of structure and its expected maneuvers in 2D plane ............ 16
Figure ‎3.2. Geometric parameters of the robot; (a): side and (b): top views of the robot,
respectively.............................................................................................................................. 18
Figure ‎3.3. RA, OA and PP transitions of the robot with some other maneuvers ................... 19
Figure ‎3.4. Passing through a corner; first approach. .............................................................. 20
Figure ‎3.5. Passing through a corner; second approach. ......................................................... 20
Figure ‎3.6. Extreme conditions of the waist ............................................................................ 21
Figure ‎3.7. The concept and prototype of the proposed parallel mechanism for the waist of the
robot ........................................................................................................................................ 23
Figure ‎3.8. 2-DOF mechanism that satisfies 2 DOFs of the waist .......................................... 24
Figure ‎3.9. Enhanced version of the mechanism used to provide 2DOF for waist ................. 25
Figure ‎3.10. The proposed structure for the waist of Duct-Sweeper ....................................... 26
Figure ‎3.11. Two approaches to adapt wheels with substrate plane ........................................ 27
Figure ‎3.12. Finalized concept of the wheeled locomotion system employed in each cart..... 27
Figure ‎3.13. Pneumatic circuit diagram .................................................................................. 36
Figure ‎3.14. Proposed mechanism for adhesion subsystem .................................................... 37
Figure ‎3.15. Finalized concept of the Duct-Sweeper .............................................................. 38
Figure ‎4.1. Coordinates assigned to FSM ............................................................................... 40
Figure ‎4.2. Kinematic model used in PP analysis ................................................................... 42
Figure ‎4.3. Adhesion system worst case scenarios used to determine suction cup sizes ........ 50
Figure ‎4.4. Coordinate system, geometric properties and forces for case 6 ............................ 52
Figure ‎5.1. Parameters assigned to linear electromechanical actuator .................................... 55
Figure ‎5.2. Common design of EWGs .................................................................................... 56
Figure ‎5.3. Sample design to locate Extra-Limb in the middle of two linear actuators .......... 56
Figure ‎5.4. Parameters assigned to Extra-Limb ...................................................................... 57
Figure ‎5.5. Two critical transitions of robot and the parameters used to define their constraints
................................................................................................................................................. 57
Figure ‎5.6. Different algorithms approach to find minimum value for cost function ............. 65
Figure ‎5.7. Isometric view of the designed cart ...................................................................... 67
Figure ‎5.8. Trimetric exploded view of the cart ...................................................................... 67
Figure ‎5.9. Isometric and trimetric exploded views of the adhesion module .......................... 68
Figure ‎5.10. Mechanical design of waist, excluding linear actuators ...................................... 68
Figure ‎5.11. Isometric exploded view of the waist, excluding linear actuators ...................... 69
x
Figure ‎5.12. Linear electromechanical actuator which is used to actuate waist of the robot .. 69
Figure ‎5.13. Exploded view of the linear electromechanical actuator .................................... 70
Figure ‎5.14. Completed design of Duct-Sweeper.................................................................... 71
Figure 6.1. Scenes from Parallel Plane transition of the Duct-Sweeper .................................. 73
Figure ‎6.2. Scenes from Right Angle transition of the Duct-Sweeper .................................... 74
Figure ‎6.3. Scenes from Open Angle transition of the Duct-Sweeper .................................... 75
Figure ‎6.4. Scenes from On-Plane to Counter-Mode transition of the Duct-Sweeper ............ 76
Figure ‎6.5. Passing through a turn with hollow space in between .......................................... 78
Figure ‎6.6. Passing through different conditions by combining basic transitions ................... 79
xi
List of Tables
Table 1.1 - Parameters regarding air quality, hygiene and impurities presented in air ducts
before and after cleaning [1]...................................................................................................... 2
Table ‎2.1. Sample commercial DCRs, their manufacturers and images ................................... 6
Table ‎2.2. Locomotion system and physical properties of sample DCRs ................................. 7
Table ‎2.3. Facilities and tools available on the sample DCRs................................................... 8
Table 2.4. Specifications of the climbing robots under review. ................................................ 9
Table ‎3.1. Industrial suction cups‟ shapes, names and applications, courtesy of VACCON Co.
[60]. ......................................................................................................................................... 31
Table 3.2: A review on materials used in vacuum cup technology ......................................... 33
Table ‎4.1. Link parameters of FSM......................................................................................... 40
Table 5.1. Standard rectangular air duct sizes presented in [69] ............................................. 62
Table 5.2. Regular rectangular air duct sizes based on Engineering Toolbox suggestion [71] 63
Table ‎5.3. Design variables computed by different algorithms ............................................... 66
Table ‎6.1. Definition of symbols used in Figure ‎6.6 ............................................................... 79
xii
List of Abbreviations
Cases
DCR: Duct Cleaning Robot ....................................................................................................... 3
DH: Denavit-Hartenberg ......................................................................................................... 39
DOF: Degree of Freedom .......................................................................................................... 5
EWG: Electric motors with Worm-gear Gearboxes ................................................................ 26
FSM: Fully Serial Mechanism................................................................................................. 39
HVAC: Heating, Ventilation and Air Conditioning .................................................................. 1
NFPA: National Fire Protection Association .......................................................................... 28
PP: Parallel Portion ................................................................................................................. 39
SQP: Sequential Quadratic Programming ............................................................................... 65
SSM: Serial Substitute Mechanism ......................................................................................... 39
UL: Underwriters‟ Laboratory ................................................................................................ 28
ZMP: Zero Moment Point ....................................................................................................... 77
xiii
Chapter 1
Introduction
1.1 The necessity of duct cleaning
Heating, Ventilation and Air Conditioning (HVAC) systems are designed to deliver fresh air
into buildings and guarantee comfort of their residents. Air ducts are the primary facilities in
ventilation systems that provide air flow paths. Air always contains various amounts of
chemical substances, moisture, fungus, dusts and odor sources [1]. Thus air ducts not only
provide a path for air flow but also they provide a way for transmitting substances and micro
particles which are existent in air. While some of these extraneous materials recirculate in
ventilation paths, others dwell in air ducts. Fungi and moisture plus organic materials create a
good bed for mold; therefore, air duct environments are excellent places for mold growth [2].
A research done by Angui Li et al [3] shows that there is a positive correlation between dust
quantity and the number of micro-organisms. They also declared that: “the organic
compounds composing the dust in supply air duct also had great impact on microbial growth”.
A simple solution to eliminate pollutants in the ducts is to filter out the particles in air. In a
research, Gabriel Beko et al [4] studied the effect of filtration of particles in air both from
economic and social health points of views; and they concluded that the overall running costs
associated with particle filtration will compensate the initial investments by decreasing
occupant morbidity and mortality.
However filtration cannot completely eliminate
extraneous materials from air ducts because of two principal reasons: 1) today common
particle filters cannot completely filter out all small particles and microorganisms from
outdoor air and allow amount of microbial to penetrate into air ducts; 2) Construction and
duct installation phases may cause accumulation of dust and other contaminations inside air
ducts [1].
1
Sirpa Kolari et al. [1] have done valuable research on the effect of duct cleaning on work
environment and employees. Table 1.1 shows some parameters regarding air quality, hygiene
and impurities present in ducts before and after cleaning as presented in their research. As
indicated in this table, duct cleaning significantly decreased dust deposition and viable
microbial counts.
Table 1.1 - Parameters regarding air quality, hygiene and impurities presented in air ducts before and
after cleaning [1].
Variable
Temperature a [C]
Relative humidity a [%]
Air flow [L/s/Person]
Ventilation rate [1/h]
Particle mass concentration [µg/m3]
Airborne viable microbes [cfu/m3]
Fungi (MEA)b
Fungi (DG18)c
Bacteria (THG)d
Before cleaning
Mean
SD
22.9
1.5
32
15
26.3
13.7
2.3
1.3
6.5
4.1
43
27
27
After cleaning
Mean
SD
22.3
1.0
25
15
26.9
9.6
2.4
1.0
7.6
4.0
50
36
30
23
22
64
Viable microbial count f [cfu/cm2]
Fungi (MEA)b
8
10
2
Fungi (DG18)c
17
40
2
d
Bacteria (THG)
1200
3500
5
e
3
TVOC concentration [µg/m ]
73
46
66
CO2a [ppm]
480
29
470
Dust deposition f [g/m2]
8.8
6.6
1.7
a
Measured from indoor air.
b
Malt extract agar.
c
Dichloran glycerol agar.
d
Tryptone glucose yeast agar.
e
TVOC = Total concentration of volatile organic compounds.
f
Measured from inner duct surface.
20
20
95
3
2
7
79
40
1.2
They also declared that “the duct cleaning had a positive impact on perceived work
environment and the prevalence of work-related symptoms in studied offices. Cleaning
especially decreased stuffiness and sensation of dry air. A decrease in nasal symptoms and
concentration difficulties was also observed after the duct cleaning”.
2
This introduction proves the positive effect of duct cleaning process on the quality of
ventilation air and residents‟ physical and psychological health. It also clarifies the necessity
of such a process in modern buildings.
With all the importance of duct cleaning process, there are still a number of unsolved
problems in this industry. Vernard D. Holden [2] states that even though there are rules
available for duct cleaning, unfortunately many firms that are active in this industry do not
actually obey them. He also mentions a big market that is occupied by this industry.
Limitations imposed by human body also affect duct cleaning process. Human cannot access
all the internal surface of duct assembly to do a perfect cleaning; and even if this limitation is
ignored, manual duct cleaning process is time-consuming and expensive. These issues
highlight the requirement of an autonomous or semi-autonomous agent to be able to clean
ducts based on pre-defined rules, efficiently and as fast as possible. Robots are the exact
agents which are specialized to solve these problems.
1.2 Proposed method
Since 1960‟s robots have become an identifiable agent in industrial automation [5]. To date,
they have been employed to perform many tasks such as automations [6], [7], [8]; servicing:
[9], [10], [11], [12]; human assisting: [13], [14], [15]; discovering: [16], [17]
and a large
number of other tasks. Similar to others, duct cleaning firms have shown an extensive interest
to robots that are specialized for duct cleaning task. To date, many commercial versions of
Duct Cleaning Robots (DCRs) have been introduced by different robotic industries.
Unfortunately, as covered in chapter 2, almost all of these robots lack the ability to climb
vertical paths due to their simple locomotion systems. Thus, they are unable to navigate
between different levels of multilevel buildings or clean vertical ducts. Besides, these robots
are not autonomous and they need an operator to control them via teleportation techniques.
Thus problems regarding human resources and time expenses remain unsolved. To provide
them electric power and pressurized air, tethers are obligatory facilities of DCRs introduced
3
so far. Like many other experts in duct cleaning business, Pat Johnson declares that the
available robots are still unable to do the process of duct cleaning perfectly and many
companies just take advantage of them to attract more customers but they actually do not use
them [15]. These issues simply imply that, although there are many commercial robots
available for duct cleaning task, they are not dexterous enough to perform a perfect process.
This research aims to analyze available duct cleaning and climbing robots, highlight the main
requirements of a climbing DCR and propose a design to solve current concerns of this field.
1.3 Chapter organization
The necessity of duct cleaning process and its current concerns are covered in Chapter 1.
Literature reviews on current commercial duct cleaning and climbing robots are presented in
Chapter 2. Chapter 3 focuses on the conceptual design of the proposed robot, its maneuvers
and design constraints. Kinematic and static force analyses required for the design phase are
presented in Chapter 4. Design optimization and a prototype design of the robot are covered
in Chapter 5. Detailed descriptions of the robot transitions and path planning are covered in
chapter 6. Finally, Chapter 7 addresses the most important outcomes of this research, the
lessons learned and conclusions.
4
Chapter 2
Literature review of current duct cleaning and climbing robots
Two categories of duct cleaning and climbing robots are reviewed. By these reviews, we seek
to find answers for following concerns: Facilities, components and dexterity of available
DCRs; available climbing structures and their potential to serve as the structure of a duct
cleaner robot.
2.1 Literature review on duct cleaning robots
There are lots of companies that perform duct cleaning process all around the globe. Most of
these firms have employed robots to do this tedious task. While numbers of DCRs have been
designed by companies that are experts of robots design, others are designed by engineers of
duct cleaning firms. This section aims to categorize structures, facilities and tools of DCRs.
Unfortunately, these robots are not discussed in any scientific article, thus all the information
presented in this section is gathered from robot designers‟ and duct cleaning companies‟
websites. Since most of the models available take advantage of similar structures and
facilities, a set of 10 different robots is chosen to be representative of the others.
Table 2.1 introduces names, manufacturers and pictures of the robots under review.
Simplicity of the locomotion systems used in these robots proves their inability to climb
vertical ducts. All the introduced models use either two wheeled, four wheeled or tracked
differential drive locomotion system to transport robot‟s facilities. Some models are equipped
with a manual or actuated one degree of freedom (DOF) arm to adjust position of duct
cleaning tools. Other physical and structural properties of the robots are tabulated in
Table 2.2.
5
Table ‎2.1. Sample commercial DCRs, their manufacturers and images
Robot’s‎name
Manufacturer
Inspector Robot III [18]
Indoor Environmental
Solutions, Inc.
Deluxe [18]
Indoor Environmental
Solutions, Inc.
OmniBot MI-6000 [19]
LLOYD‟S systems
MicroInspector MI-180
[20]
LLOYD‟S systems
ANATROLLER ARI-10
[21]
Robotics Design Inc.
ANATROLLER ARI-50
[22]
Robotics Design Inc.
6
Image
ANATROLLER ARI100 [23]
Robotics Design Inc.
Multi-Purpose Robot
[24]
Danduct Clean
XPW-301 [25]
Hanlim Mechatronics Co.,
Ltd.
XPW-501 [26]
Hanlim Mechatronics Co.,
Ltd.
Table ‎2.2. Locomotion system and physical properties of sample DCRs
Robot‟s Name
Inspector Robot III
Deluxe
OmniBot MI-6000
MicroInspector MI-180
ANATROLLER ARI-10
ANATROLLER ARI-50
ANATROLLER ARI-100
Multi-Purpose Robot
XPW-301
XPW-501
Locomotion
System
4W
Tracked / 4W
4W
4W
2W
Tracked
Tracked / 4W
4W
4W
6W
Speed
[m/s]
INA
0.381
INA
INA
0.91
0.18
0.18
INA
INA
INA
*
Dimensions [mm]
Length
Width
177.80
177.80
460
285
440
380
180
180
177.8
177.8
279.4
89 ~ 127
292.1
179 ~ 216
303 ~ 760
300
360
200
460
210
The whole package weight (Package: robot, duct cleaning facilities, control unit and casing)
INA: Information Not Available
W: Wheels
7
Height
76.20
153
310
80
127
127
127
145
210
390
Weight
[Kg]
3.63
17.2*
29*
2.3
5
5
8
10 ~ 21
INA
INA
Facilities and tools available on reviewed DCRs are tabulated in Table 2.3.
Following points are concluded regarding DCRs after summarizing data presented in
Table 2.1, Table 2.2 and Table 2.3:

Locomotion is generated with either wheeled or tracked differential drive system.

These robots, averagely, speed up to 1.5 Km/hr.

Vision is transferred via a color camera located in front of the robot.

A lightening system with adjustable lumens is provided to compensate darkness in
the ducts and reflections from the ducts‟ surfaces.

Robots carry at least two of the four main duct cleaning tools.










: Available
: Not Available
: Available on Request
?: Information Not Available
: Fixed Color camera
: Adjustable Color camera
: Black and white camera
: Adjustable Lumens Light
M: Manual
* Adjustable camera and lightening system of the model can rotate 360°
8

M


M
?




Rotating Brush
Spray Tip
Air nuzzle










Air Whip

?




?



Tool Adjustment
Rear Light


?
?
?
?
?
?
*
*
Internal battery



?




*
*
Front Light










Rear Camera










Recording Capability
Inspector Robot III
Deluxe
OmniBot MI-6000
MicroInspector MI-180
ANATROLLER ARI-10
ANATROLLER ARI-50
ANATROLLER ARI-100
Multi-Purpose Robot
XPW-301
XPW-501
Front Camera
Robot Name
Hand Held Controller
Table ‎2.3. Facilities and tools available on the sample DCRs
Duct cleaning tools








?















?















2.2 Literature review on climbing robots
Because of their vast application area, climbing robots have been one of the prevalent
research topics among categories of mobile robots. To date, many designs, approaches and
prototypes are introduced in the literature. The importance of the topic has yielded a number
of symposiums focusing on climbing robots (e.g. CLAWAR).
Here, to give insight regarding climbing robots, statistical analysis and comparison, a number
of climbing robots and their features are tabulated in Table 2.4. Labels and abbreviations used
in this table are described in what follows.
Active DOFs
Mechanism type
Adhesion technology(s)
Hybrid action
Bio-Model
Transitions
Workplace Geometry
Reference
RGR
Q
L4, W1
S
VW
No
Gecko
No
P
[27]
3DCLIMBER
B
W4
S
CF
No
‒
RA, OA, PP
S
[28]
SURFY
B
W3
S
VC
No
‒
No
PO
[29]
Raupi
B
W6
S
CF
M
Inchworm
RA, OA, PP
S
[30]
Untitled
B
W5
S
CF, VC, EM
M
Inchworm
RA, OA, PP
S
[31]
Untitled
SF
WH2
‒
BE
No
‒
No
P
[32]
Untitled
B
L4, W2
S
VC
No
‒
No
PX
[33]
Wall Climber
H
L18
S
EM
No
Insects
No
PX
[34]
Untitled
H
L18
S
VC
No
Insects
RA, OA
S
[35]
Mini-Whegs
Q
WL4
‒
CH
WL
Insects
RA
P
[36]
Pipe Robot
O
L16
S
CF
No
Insects
RA, OA
PD
[37]
Untitled
SF
L4, W3
S
VC
No
‒
No
PX
[38]
Untitled
B
L3
S
VC
WL
‒
RA, OA, PP
S
[39]
Untitled
1
Q
W3
S
VC
No
‒
No
P
[40]
Untitled
B
W3
S
VC
No
‒
No
PO
[41]
SAFARI
SF
W4
P
VC
No
‒
No
P
[42]
Robug II
Q
L12, W1
S
VC
No
‒
RA, OA
S
[43]
NINJA-1
Q
L12
P
VC
No
‒
RA, OA
S
[44]
Robot‟s Name
Structure type
Table 2.4. Specifications of the climbing robots under review.
9
Untitled
B
W6
P
CF3
No
‒
RA, OA 4
S
[45]
Inchworm
B
W4
S
EM
No
Inchworm
RA, OA, PP
S
[46]
Untitled
B
W5
S
VC
No
‒
RA, OA, PP
S
[47]
W-Climbot
B
W5
S
VC
M
‒
RA, OA, PP
S
[48]
BIT Climber
SF
WH2
‒
VC
No
‒
No
P
[49]
City-Climber
SF
W1, WH2
S
VC
WL
‒
RA, OA
PO
[50]
Untitled2
SF
WH4
‒
EMW
No
‒
No
PX
[51]
S
EMW
WL
‒
RA, OA
S
[52]
PX
[53]
Untitled
SF
Alicia3
SF
L2, WH4
6
L2, WH6
S
VC
WL
‒
RA, OA
5
1
The robot‟s quadruped structure performs like a biped.
Since the main article which describes the structure of the robot is written in Japanese, Structural properties of
the robot retrieved from [51] based on engineering assumptions and judgments.
3
The adhesion technology of the robot is not covered in related article. Counterforce technology is assumed based
on the images presented in [45].
4
Because of the low workspace of the parallel waist, this robot can perform transitions in specific conditions.
5
The structure of the robot has the potential to perform these transitions. But in the prototype introduced in [53],
the workspaces of the joints are so small to allow the robot to perform the transitions.
6
This robot also has 4 other actuators for its steering system.
2

Structure type: different structures that have been proposed for the robots to generate
the climbing.

B (Biped): Robot structure that benefit from two distinct feet for locomotion.

Q (Quadruped): Robot structure that benefit from four distinct feet for
locomotion.

H (Hexapod): Robot structure that use six distinct feet for locomotion

O (Octopod): Robot structure that use eight distinct feet for locomotion.

SF (Sliding Frame): Robot structure moves parallel to the substrate surface
[42]. This could be achieved by either using wheels or legs.

Active DOFs: Number of actuated degrees of freedom at each part of structure.

Lx: legs of the robot consist of totally „x‟ active DOFs.

Wy: Waist of the robot consists of „y‟ active DOFs.
10

WHz: Structure consists of „z‟ number of wheels. Note that this number
necessarily does not equal the number of actuators.

WLp: Structure consists of „p‟ number of legs that behave like wheels. Note
that this number necessarily does not equal the number of actuators.

Mechanism type: Type of mechanisms used to provide dominating DOFs of the
structure.


S: Serial mechanisms

P: Parallel mechanisms

H: hybrid mechanisms
Adhesion technology(s): Technology(s) used in the robot to produce required
adhesion during climb. There is a possibility that specific robot simultaneously takes
advantage of many adhesion technologies.

VC: Adhesion generated by air pressure difference generated by vacuum
pumps or compressors.

CF: Friction, generated due to counterforces on substrate imposed by jaws of
a gripper or pushing feet toward different walls, produce required adhesion
for robot.

EM: Electromagnetic forces are used to generate normal forces between robot
feet and surface that yield enough friction forces to hold the robot on a
vertical surface.

VW: Van Der Waals forces (attractions between molecules) are used to
generate required adhesion. This technology mostly applied to bio inspired
climbing robots which are lightweight and do not carry large payloads [27].
11

BE: Based on Bernoulli‟s equation, in an ideal incompressible and inviscid
fluid which does not gain or lose any power due to work, increase in the
velocity yields a decrease in pressure. This reduction in pressure is used to
generate adhesion for robot [32].

CH: Robot generates required adhesion using chemical substances, like the
materials used in glues [36].


EMW: Robots adhere to substrate surface using magnetic wheels.
Hybrid action: Ability of the robot to use different locomotion systems.

No: Robot only moves using a single locomotion system, either legged or
wheeled.

M: Robot has modular structure design. Thus, potentially it can change its
locomotion system.

WL: Wheeled-Legged hybrid system allows robot to move either using its
wheels or its legs.

Bio-Model: The biological creature from which the robot structure is inspired.

Transitions: Capabilities of robot of transfering itself between different surfaces.
Unfortunately these transitions are not covered in most of the articles and robots‟
capabilities are identified by engineering judgments.

No: Robot is only able to move on the surface which initially starts its motion
on.

RA (Right Angle): A transition which allows robot to transfer itself between
two perpendicular planes.
12

OA (Open Angle): Open angle transition allows robot to transfer itself
between two planes with 270° angle in between.

PP (Parallel Plane): Ability of the robot to transfer itself from one plane to
another which is parallel to the first one.

Workplace Geometry: The space that robot is designed to work in. These data are
provided either from related articles or by the author‟s engineering judgments.

P: Planar or wall type.

PO: Planar with small obstacles.

PC: Planar with relatively large curvature.

PD: Planar which is closed from both sides (e.g. duct)

PX: Planar with large curvature and small obstacles.

S: Three-dimensional surfaces.
Besides becoming familiar with a variety of design ideas, reviewing these 27 robots yielded a
number of key points regarding their structures and adhesion technologies. These issues are
listed in what follows.

Biped structure with an appropriate waist mechanism is more versatile than
quadrupled, hexapod and octopod structures with an inappropriate legs mechanism.
For example a biped robot with 4 active DOFs [28] can perform all three transitions
and move freely in three-dimensional space, while a hexapod robot with 18 active
DOFs [34] only can move on plane with obstacles and large curvatures.

Among all the models introduced, inchworm inspired robots show higher
performance and versatility with smaller number of active degrees of freedom.

Vacuum based adhesion is the most preferred method for climbing robot design.
13

Electromagnetic adhesion systems can tolerate various surface conditions, but they
are only applicable for surfaces with ferromagnetic materials.

Electromagnetic wheels have the advantages of wheeled locomotion system on
ferromagnetic vertical planes, but they need extra mechanism to pass over obstacles
or perform transitions [52].

Same as electromagnetic wheels, combination of vacuum systems with wheeled
locomotion systems allow robot to move on vertical surfaces without concerns for
surface conditions or materials. Some examples of this type of robots are introduced
in [49], [50] and [53]. But the sealing used to maintain pressure difference wears
eventually and leads to high maintenance cost of this approach [53].

Bio inspired adhesions, like the methods introduced in [27], are still in development
phase. They can tolerate small forces and need special gait strategy.

Although generating adhesion by introducing counterforces on substrate is the most
efficient approach, its application requires specific surface geometries and
dimensions.
14
Chapter 3
Conceptual Design
This chapter covers conceptual design of a novel DCR, the Duct-Sweeper. First, conceptual
designs of different modules of the robot are introduced; then, a complete conceptual scheme
of the robot is presented.
3.1 Structure concept of the Duct-Sweeper
As an industrial DCR, Duct-Sweeper must satisfy constraints regarding maneuvers, speed and
efficiency with minimum possible number of active DOFs. Reducing number of active DOFs
has three main positive impacts, which are: 1) reducing total cost of the robot; 2) increasing
reliability of the robot due to reduction in weight [40], [54]; 3) reducing drive and control
complexities. The following guidelines are considered to select appropriate structure for the
Duct-Sweeper:
I.
Robot should be able to move on vertical and horizontal planes and cylindrical
surfaces and perform transitions between different planes.
II.
Robot must have desired dexterity with minimum possible number of active DOFs.
III.
Efficient locomotion methods are desired in order to minimize power consumption.
IV.
Duct-Sweeper is going to be available on industrial market, thus construction costs
must be minimized.
As discussed before, biped structure can produce high maneuverability with small number of
active DOFs. Thus it is reasonable to use biped structure as the main structure of the robot.
Employing biped structure in a DCR has the following disadvantages:
I.
II.
Legged locomotion is not as efficient as wheeled locomotion [55].
Duct-Sweeper is destined to be an autonomous robot; but, there may be conditions
that require complete supervision and control of an operator. Like any other legged
system, controlling a biped system via joysticks is a challenging task.
15
III.
Duct cleaning is a time consuming process and needs fast movements of the robot.
On the other hand, controlling robot gaits, with current technologies, is a time
consuming and slow process.
IV.
Robot feet must adhere to the wall surface during a climb. This requires an active
adhesion technology which further increases power consumption.
An articulated wheeled structure can eliminate such disadvantages of biped structure. In this
case, wheels increase drive-simplicity, efficiency and speed of the robot while articulated
structure increases its maneuverability and versatility. An articulated (hybrid) system can also
eliminate the need of active adhesion during climbing phase. Friction generated by pushing
wheels toward opposite sides of duct allows robot to climb vertical paths without active
adhesion system. Note that active adhesion system is still required for robot transitions.
Conceptual scheme of the structure in 2D plane is illustrated in Figure 3.1. In this figure, solid
black color indicates activated adhesion system.
Carts
(feet)
Waist
Wheels
Adhesion
system
g
Figure ‎3.1. Conceptual scheme of structure and its expected maneuvers in 2D plane
As long as wheels and adhesion system have the ability to adapt with substrate surface, an
articulated wheeled locomotion allows the robot to move in both rectangular and cylindrical
ducts. These adaptations are discussed in sections 3.4 and 3.5.4.
3.2 Duct-Sweeper waist mechanism’s‎workspace‎requirements
As mentioned before, limbs workspace highly affects versatility of a climbing robot. Many
duct conditions, which robot may encounter during its journey through air ducts, are studied
16
in detail to identify proper workspace requirements for Duct-Sweeper waist. Possible
maneuvers of the robot to pass each condition are studied. To minimize the number of active
DOFs and size of the workspace, those maneuvers that require minimum number of active
DOFs with smallest workspace are selected. The selected maneuvers proved that, if robot can
perform three main transitions, it can successfully pass all the encountered conditions in air
ducts. These three main transitions are: Right Angle, Open Angle and Parallel Plane
transitions that are described in section 2.2. The model used when studying robot maneuvers
is presented in Figure 3.2. This figure illustrates parameters assigned to robot geometry and
its joint variables. As shown in this figure, robot structure is composed of three sections: a
waist and two distinct carts. Carts carry wheels, adhesion system, duct cleaning tools and
other facilities. Waist connects two carts to each other and provides necessary DOFs between
them. Waist‟s joint variables are defined in two coordinate systems {A} and {B} which are
connected to carts A and B, respectively. Parameter S is the linear joint variable and
represents distance between origins of {A} and {B} measured in coordinate system {A}.
Parameters θxA, θyA and θzA are the angles between S and xA, yA and zA axes, respectively. The
angles between extension of S and xB, yB and zB axes are called θxB, θyB and θzB, respectively.
Note that θxA and θxB are not illustrated in Figure 3.2. Parameter L represents the length of the
supporting section that should keep its contact with the substrate surface to provide required
adhesion. Distance between substrate surface and the origin of the reference frames {A} and
{B} along z axis is indicated by h. Distance a is measured from the back of the supporting
section to waist connection point along xA or xB axis. The width of the robot is indicated by w
and measured along yA axis. Parameter T is the smallest distance between back of each cart
and supporting section along xA or xB axis. F represents the distance between waist connection
point and front of each cart along xA or xB axis.
17
θyB
S
zB
xB
xB
zA
-θzB
B
xA
{B}
{B}
θzB
T
{A}
B
xA
h
a
A
yB
a
-θyA
yA
S
{A}
F
A
L
w
(a)
(b)
Figure ‎3.2. Geometric parameters of the robot; (a): side and (b): top views of the robot, respectively
Three main transitions and sample maneuvers of the robot are denoted in Figure 3.3. This
figure is used to demonstrate that the robot can maneuver through all conditions encountered
in a 2D duct environment if it can perform all three transitions discussed earlier. A complete
discussion on this issue is available in Chapter 6. Climbing vertical paths by pushing wheels
against duct walls is also illustrated in this figure. Figure 3.3 does not cover details of
transitions and maneuvers, but blue and magenta lines are used to indicate approximate paths
of carts A and B, respectively. Also note that for better understanding of image, carts
positions are shifted in some maneuvers. Studying these transitions shows that the waist
should have at least three DOFs to provide independent rotations of two carts and allow for
adjusting the distance between them. These results are in agreement with the general notation
that a system should have at least three DOFs to freely move in 2D space.
Robot needs dexterity in 3D environments as well as 2D environments. The only uncovered
3D condition is the robot penetration in directions perpendicular to the 2D plane. Two such
maneuvers for passing this condition are illustrated in Figure 3.4 and Figure 3.5.
18
Parallel Plane Transition
Open Angle Transition
Climbing an arc
with inchworm
motion profile
Passing a
gap with
inchworm
motion
profile
Ascending,
descending
Right Angle Transition
and turning in vertical
ducts
by
generating
counterforce on substrate
Passing an step
Figure ‎3.3. RA, OA and PP transitions of the robot with some other maneuvers
19
Figure ‎3.4. Passing through a corner; first approach.
Figure ‎3.5. Passing through a corner; second approach.
Considering 2D and 3D motions, Duct-Sweeper‟s waist should have at least 4 active DOFs.
Referring to Figure ‎3.2 DOFs include rotations about yA and yB axes, a displacement on xA-zA
plane and rotation about zA axis. Rotation about zA causes movements of cart B along yA axis
which is required for turning the robot. Since this DOF alters both orientation and position of
cart B, rotation about zB is not required during robot transitions. Extreme configurations of
the robot, which are indicated in Figure 3.6, are studied to arrive at a suitable waist
workspace. The following equations show the distances between two coordinate systems {A}
and {B} which are attached to the corresponding carts for each of the three configurations
shown in Figure 3.6. Since Δx3 is zero, it is not illustrated in Figure ‎3.6.
20
(3.1)
{
(3.2)
(3.3)
(3.4)
(3.5)
(3.6)
In above equations Smin represents the minimum value of S. This minimum value depends on
mechanical design of the waist mechanism and it should be equal or greater than 2×F.
zA
Δx1
θ1
xA
xB
A
S1 max
B
zB
Δz1
θ3
Δz2
zB
B
B
xB
Δx2
zA
S2 max
Δz3
θ2
H
S3 max
θ3
xA
A
zB
zA
A
xA
xB
Figure ‎3.6. Extreme conditions of the waist
The relations between Δxi, Δzi (i=1 to 3) and joint variables are defined by following
equations:
√
(3.7)
(
)
(3.8)
Boundary values of the joint angles are determined by substituting equations (3.1) to (3.6) into
(3.7) and (3.8). Doing so, following expressions are obtained:
√(
)
21
(
)
(3.9)
,
√(
)
(
(3.10)
)
(3.11)
(
{
)
(
(3.12)
(3.13)
)
(3.14)
Due to the symmetry of the robot, extreme values of θyA are equal to extreme values of θyB
with a sign change. Considering the fourth DOF of the system, minimum required waist
workspace is defined as:
(
(
)
(3.15)
)
(3.16)
(3.17)
(
)
(3.18)
3.3 Conceptual design of the waist mechanism
Simultaneous activation of all the actuators of parallel mechanism to handle each one of its
maneuvers leads to their high accuracy and payload to weight ratio. Due to these two
outstanding characteristics, parallel mechanisms have been employed in many applications
such as: flight simulation, quality check, manipulation, manufacturing and machining,
satellite dishes and telescopes adjustment mechanisms, etc. Since high payload to weight ratio
is also desirable in mobile robots, parallel robots have been used in different parts of robots
such as legs [44] or waist [45]. Thus it is also desirable to employ parallel mechanism as the
waist of Duct-Sweeper. In order to reach this goal many parallel robot structures are studied.
Most of the considered structures are covered in [56] which is an outstanding and state of the
art text on parallel robots. On the other hand, parallel robots suffer from two main
disadvantages that prevent their globalization. The workspace of parallel robots is relatively
small and there is no systematic type synthesis algorithm for their design. Although many
22
attempts have been taken to solve these issues, still no global and effective solution is
introduced in literature. Unfortunately, efforts taken to find an appropriate parallel structure,
which satisfies number of DOFs and workspace requirements of the Duct-Sweeper‟s waist,
remained inconclusive. The author has also developed a novel parallel robot structure. The
conceptual design and prototype of this mechanism are illustrated in Figure 3.7 (a) and (b),
respectively. But its singularity problems have remained unsolved and prevent its usage as the
waist mechanism for the Duct-Sweeper robot.
(a)
(b)
Figure ‎3.7. The concept and prototype of the proposed parallel mechanism for the waist of the robot
Since efforts of the author to find a fully coupled mechanism for the Duct-Sweeper‟s waist
have failed, partially decoupled mechanisms are considered. For this purpose, two DOFs that
need relatively large workspace (θyA and θyB) are provided by revolute joints, serially.
Remaining two DOFs are provided by means of a parallel mechanism. These latter two
degrees of freedom are related to both adjusting the distance between coordinate systems {A}
and {B} and a rotation of origin of {B} about zA. A design that perfectly satisfies these DOFs
is illustrated in Figure 3.8. In this figure, revolute joints are indicated with solid black circles.
23
yB
xB
yA
{B}
C
{A}
xA
Figure ‎3.8. 2-DOF mechanism that satisfies 2 DOFs of the waist
Proposed mechanism of Figure 3.8 is composed of 3 revolute and 2 prismatic joints. This
mechanism is not one of the contradictory examples of Grübler-Kutzbach mobility criterion,
thus it is possible to use this criterion to validate the number of DOFs of the mechanism.
Based on Grübler-Kutzbach mobility criterion, DOF of a mechanism is defined as [57]:
(
)
∑
(3.19)
In (3.19), F represents DOF of the system. Permitted relative motion of joint i is indicated by
fi. Number of links of the mechanism (including fixed link) is denoted by n. parameter λ
specifies number of DOFs of the working space of the mechanism (λ is equal to 3 and 6 for
planar and spatial mechanism, respectively). Finally, j symbolizes number of joints in the
mechanism. For the mechanism introduced in Figure 3.8, λ is 3, n is 5, j is 5 and ∑
is equal
to 5. Substituting these values into equation (3.19) yields to F = 2, which verifies the desired
number of DOFs of the mechanism. The problem with this structure is that rotation takes
place about an axis parallel to zA that passes through point C. To solve this problem another
passive limb has been introduced. The extra passive limb (named as Extra-Limb from this
point on) introduces two outstanding features to the mechanism that are:
I.
It corrects the offset introduced in the axis of rotation.
24
II.
In practice, ball screws, lead screws or rack and pinion mechanism are used in the
design of actuated prismatic joints. These mechanisms are only able to tolerate axial
loads and any bending moment critically decreases their performance and service life.
It is possible to design Extra-Limb in a way that eliminates any undesired load
exerted on actuated joints.
Figure 3.9 shows the proposed mechanism armed by Extra-Limb. Once again, to validate the
number of DOFs of the mechanism Grübler-Kutzbach criterion is used. For the case of
finalized mechanism, n is 7, j is 8 and ∑
is equal to 8. Substituting these values into (3.19)
yields to F = 2. In Figure 3.9, the active prismatic joints are indicated by double-sided dashed
arrows and all the remaining joints are passive.
yB
xB
{B}
yA
{A}
xA
Figure ‎3.9. Enhanced version of the mechanism used to provide 2DOF for waist
Combining this mechanism with two serial active revolute joint provides all the required
DOFs of the waist. Though this structure introduces an offset for rotation about zA axis, this
offset does not affect maneuvers of the Duct-Sweeper. The finalized version of the
mechanism for Duct-Sweeper‟s waist is illustrated in Figure 3.10. In this figure, dashed lines
and double sided dashed arrows are used to indicate revolute and prismatic joints,
respectively. Blue and green colors are used to indicate passive and active joints, respectively.
25
xB
yB
zB
B
zA
yA
A
xA
Figure ‎3.10. The proposed structure for the waist of Duct-Sweeper
Since the distance between coordinate systems {A} and {B} is relatively large, comparatively
huge torques are required to rotate two serial revolute joints. Two Electric motors with
Worm-gear Gearboxes (EWG) are considered to actuate these two joints. Worm-gear gearbox
provides high gear ratio in relatively small space. Also, the self-locking characteristic of this
gearbox introduces flexibility in path planning of the robot.
3.4 Conceptual design of wheeled locomotion
To find the appropriate design, properties, requirements and constraints of wheeled
locomotion system of the Duct-Sweeper are studied. The conclusions of these studies are
discussed in what follows. As illustrated in Figure 3.3, there are conditions in which one of
the carts carries the other one atop itself. Although, during transitions, one of the carts is
adhered to substrate surface via adhesion system, robot can move with its wheeled
locomotion while the zero moment point of the system is located in support convex polygon
of the supporting cart. Thus static stability should be provided by the means of the wheels
available on each cart. These maneuvers also highlight the need of having actuated wheels in
both carts. Since wheels are employed to increase the speed of the robot, they should provide
26
necessary DOF to allow robot‟s movements and rotations on different planes. Although
holonomic locomotion system is a bonus, a nonholonomic locomotion system with steering
capability is sufficient. Turning capability with zero radius of curvature is required to allow
robot to turn in narrow ducts. In addition, wheels should be able to adapt themselves with
both cylindrical and rectangular duct profiles. To do so, one approach is to use flexible wheel
axel. Alternatively, one may use wheels with an appropriate profile; enabling them to
maintain proper contact with the duct inner surface. These two approaches are illustrated in
Figure 3.11.
Spherical wheels
Flexible axis
Figure ‎3.11. Two approaches to adapt wheels with substrate plane
Considering all the discussed conditions, 2-wheeled differential drive system with one extra
passive wheel (to provide static stability for each cart) and spherical wheels is preferred to be
employed in each one of the carts. The finalized concept of the wheeled locomotion system,
employed in each cart, is illustrated in Figure 3.12.
Wheel actuators
Omnidirectional
wheel
Wheels with proper profile
Figure ‎3.12. Finalized concept of the wheeled locomotion system employed in each cart
27
3.5 Conceptual design of adhesion system
It is necessary to define constraints that adhesion system must satisfy in order to find a
suitable adhesion technology. Duct-Sweeper is a HVAC DCR which is expected to maneuver
in almost any duct with any orientation. Robot maneuvers and some ducts conditions are
discussed thus far. Remaining conditions and constraints that are related to adhesion system
are covered in the following subsections.
3.5.1 Duct construction materials
Since most of the adhesion technologies‟ effectiveness depends on type of material which
they adhere to, identifying materials used in air duct construction is unavoidable. A
classification of duct systems based on smoke developed and flame spread of the duct
material is presented by Underwriters‟ Laboratory (UL) [58]. According to this standard, duct
materials are categorized in three classes:

Class 0 - Zero flame spread, zero smoke developed.

Class 1 - A flame spread rating of not more than 25 without evidence of continued
progressive combustion and a smoke developed rating of not more than 50.

Class 2 - A flame spread of 50 and a smoke developed rating of 100.
Standard 90A of National Fire Protection Association (NFPA) specifies following materials
to be used in air ducts [58]: iron, steel (including galvanized sheets), aluminum, concrete,
masonary and clay-tile. These materials are considered as class 0 of UL standard. However,
use of Class 1 materials is allowed for ducts for temperatures less than 121°C or ducts that do
not serve as risers for more than two floors is allowed by UL standard 181 [58]. Factory
fabricated fibrous glass and many flexible ducts are approved as class 1 of UL standard.
Although safety is the most important factor for selecting appropriate duct material, number
of other features such as cost, surface roughness and resistance to corrosion should be
considered as well. Since moisture is always present in air duct systems, duct material should
have a good resistance to corrosion. Surface roughness affects duct friction and causes
28
pressure drop in air ducts [59]; thus, materials with smooth surfaces are preferred in duct
design. Considering all these subjects, it seems judicious that the galvanized steel is the
standard and most common material used in air duct construction [59]. But, other materials
such as: Polyurethane and Phenolic insulation panels with aluminum coating, black carbon
steel, stainless steel, plastics and fabrics are also used for specific and infrequent applications.
3.5.2 Adhesion technology suitable for Duct-Sweeper
Duct-Sweeper maneuvers, duct conditions and duct materials are discussed in the previous
sections. Requirements and constraints that adhesion technology should provide and satisfy
are discussed in this and following sections. The requirements of the adhesion system are:

Adhesion technology must prevent corresponding cart‟s motion while it is active.

When deactivated, adhesion system should not disturb wheeled locomotion system.

Adhesion system must be applicable on different duct profiles.

Since moisture is presented in air ducts, it should not affect the performance of the
adhesion system.

Although duct surfaces are smooth, dirt and fungi can affect surface roughness. Thus,
adhesion systems effectiveness should not be impaired under rough surface
conditions.

As discussed in section 3.5.1, common material in air ducts construction is galvanized
steel which is ferromagnetic material. However, there are also nonmagnetic materials
used in their construction. Thus providing adhesion on different materials can
increase application domain of the robot.

Duct-Sweeper is expected to serve as an industrial servicing robot. Thus the
reliability of the adhesion system is of vital importance.
Common adhesion technologies, employed on different climbing robots, are described in
Chapter 2. Among all the introduced technologies, electromagnetic, vacuum and gripping
29
systems are the most common methods used in industrial robots designs. Thus, to date, their
reliability has been continuously enhanced and improved.
Main pros and cons of these three approaches are:

Although magnetic systems can tolerate any surface condition and geometry, they are
only applicable for ferromagnetic materials.

Like magnetic systems, generating adhesion by introducing counterforce on substrate
can tolerate any surface condition. Additionally, the material properties do not affect
effectiveness of this approach. But, when it is implemented by grippers, it can only
tolerate geometries with relative curvature more than or equal to 1 (Relative curvature
is defined by the quotient of the diameter of substrate and width of the robot) [31].

Adhesion systems based on pressure difference can tolerate ferromagnetic as well as
nonmagnetic materials. Also, as long as substrate plane provides required area, this
approach can tolerate different geometries. But, porous surfaces dramatically affect
their performance.
Considering Duct-Sweepers requirements, both vacuum and electromagnetic adhesion
technologies are suitable. Although robot benefits counter-force method during its maneuvers
in vertical ducts, this method is not applicable for robot transitions. The reason is: only one of
the carts has contact with the duct surface during transitions, thus relatively large grippers are
required to fix corresponding cart in its location. Since working in both magnetic and
nonmagnetic ducts is desired, adhesion system based on vacuum is selected to be employed in
Duct-Sweeper. Many successful implementations of vacuum systems in climbing robots‟
design, presented in literature, prove reliability of this approach.
3.5.3 Vacuum system design
Generally, vacuum based adhesion system is composed of a number of vacuum cups, one or
more vacuum pump(s), vacuum sensors, number of directional valves and connection tubes.
30
Each one of these components is studied in order to design an efficient and reliable adhesion
system.
3.5.3.1 Suction cups’ shapes and applications
This section covers common industrial cup models that are commercially available. Various
types of suction cups for different industrial applications have been developed by different
manufacturers. Table 3.2 tabulates cups‟ shapes, names and applications that are
manufactured by VACCON Company [60] (Note that, there are many companies in the world
that manufacture and/or distribute suction cups. Most of these companies produce variety of
cups with standard shapes and profiles. VACCON is selected just as an example).
Table ‎3.1. Industrial suction cups‟ shapes, names and applications, courtesy of VACCON Co. [60].
Suction cup shape
Cup‟s name and its application
Name
Flat suction cup
These cups are suitable for lightweight lifting applications.
Inexistence of cleats makes them highly flexible.
Cleats increase rigidity of the cup and allow it to lift heavy
Flat cups with
cleats
without the cup "peeling" away from the object surface or
causing deformation in it. These cups are suitable for
gripping smooth, flat, heavy objects (e.g. steel, glass,
television picture tubes, and coated corrugated).
Pliable outer rim of this type of cups allows it to conform to
curved or uneven surfaces. Bellows sections of this cup
Single-Bellows
cup
compensate for varying stack heights. When vacuum is
applied, the accordion-style bellows cup contracts like a
prismatic joint with very small stork, thus lifts the object for
a short distance. This action may save the need for a distinct
lifting mechanism.
Multi-Bellows
cup
This cup acts similar to Single-Bellows cup, but it has larger
stork for its prismatic action under vacuum.
31
Universal cup
These cups are used in handling objects with flat or slightly
curved surfaces.
Oval cups have heavy load carrying capabilities because of
Oval cup
their rigid design and large vacuum work area, similar to flat
cups with cleats.
These cups are applicable for curved and uneven surfaces.
Deep cup
They are not recommended for flat surfaces. This design is
capable of handling objects over corners and edges and it is
excellent for handling porous objects such as golf balls, etc.
Ultra-Miniature
cup
UH Rigid Cup
Due to their small dimensions, these cups are perfect in
handling extremely small objects (e.g. computer chips,
wafers and electronics components).
Rigid design of these cups makes them ideal for porous
material handling applications.
Besides the properties mentioned in Table 3.2, the presence of cleats in cups introduce other
outstanding features that are not mentioned in VACCON, FIPA, ANVER, Vi-Cas and other
vacuum cup manufacturing companies‟ technical documents. In [61] Failli, and Dini used
cleats to eliminate imprinting effect on the leather surface. They also have shown that cleats
have a positive effect on normal force handling capacity of the cup. Likewise, cleats highly
increase lateral force handling capacity. The reasons of these positive effects are not covered
in [61]. To investigate the reasons, model introduced by Jihong et al [62] is used.
Traditionally, normal force of suction cup is calculated by multiplying gauge pressure and
surface area of the cup; but, Jihong et al presented a more accurate model that compensates
deformations of the cup due to vacuum. In their model, normal force is calculated using
effective area of the cup which is calculated by compensating its deformations. In the case of
simple flat suction cup, as the vacuum in the cup increases, deformation of the cup increases
32
and causes decrease in effective area. But cleats prevent deformations in the presence of
vacuum and keep effective area of the cup close to its initial value and consequently increase
normal force generated by pressure difference. Since friction force is proportional to normal
force, cleats also increase lateral force handling capacity of the cup.
Considering information provided in Table 3.2 and above discussion, it is concluded that Flat
Cup with cleats and Multi-Bellows Cup are most suitable models for Duct-Sweeper. The
advantage of multi-Bellows cup is its adaptability to surface with the aid of accordion type
body. This body acts like a 3-DOF mechanism which is composed of a universal joint
followed by a prismatic joint. Unfortunately, adding cleats to Multi-Bellows cup, to have
simple and cost effective cup model, is impossible. But, it is possible to design a mechanism
to simulate the effect of accordion body for flat cup with cleats. This approach is used in the
design of Duct-Sweeper.
3.5.3.2 Suction cup materials
To select correct material for Duct-Sweeper, a review on common industrial materials used in
vacuum cup industry is presented in Table 3.2. Material name, properties and comments are
courtesy of ANVER industry [63].
Table 3.2: A review on materials used in vacuum cup technology
Material name
Shore A
Hardness
(Durometer)
+/-5
Temperature
Range (°C)
Abrasion
Wear
Resistance
Oil,
Grease
Resistance
UV
Weather
Aging
Resistance
Nitrile (Buna-N)
Neoprene (Chloroprene)
Polyurethane (Anverflex)
Silicone (Translucent clear)
Vinyl
40 – 60
40 – 60
30 – 65
40 – 60
30 – 70
-40 to +110
-40 to +110
-25 to +180
-70 to +316
0 to +70
●●●●
●●●●
●●●●
●●●
●●●●
●●●●
●●●●
●●●●
●●●●
●●
●●●
●●●
●●●
●●●●
●●
● Poor, ●● Good, ●●● Very Good, ●●●● Excellent
Since oil and moisture presented in the air ducts, Duct-Sweeper‟s suction cup material should
be resistant to oil and grease and tolerate dirt. Cups repeatedly loaded during robot transitions
and inch-worm motions; thus, cup material should have excellent wear resistance. Since air
33
ducts‟ temperature is expected to be in the normal range and sun light does not penetrate into
air ducts, cups‟ material do not need UV or critical-temperature resistances. Considering these
issues, Nitrile, Neoprene and Polyurethane are suitable choices for Duct-Sweeper‟s cups.
3.5.3.3 Decisions on required number of suction cups
Bending moments and torsions critically reduce suction cups‟ performance. To find minimum
number of suction cups required to provide stability without tolerating torsions and moments,
suction cups are modeled with spherical joints. Then, Grübler-Kutzbach mobility criterion is
used to define the number of joints required. Spherical joint is one of the specific joint types
that introduce error in Grübler-Kutzbach mobility approach. These joint pairs introduce a
degree of redundancy to the system which is named as passive degree of freedom [57]. The
reason for this nomination is that the DOFs produced are not controllable. An example of the
passive DOF is the redundancy produced in body which is anchored to the ground via a
spherical joint and a revolute joint in which its axis passes through spherical joint. Other joint
pairs that produce passive DOF are as follow: Spherical-Spherical, Spherical-Plane and
Plane-Plane. These joints also produce passive DOF while they are used as terminal joints in
a kinematic chain [57]. In the method presented in [57], passive DOFs are subtracted from
mobility, F, to provide number of active DOFs. But here, complete stability of the system is
desired. Thus passive DOFs should also be considered.
Since the system under study is composed of 2 distinct bodies (robot cart and ground) that
form a closed kinematic chain in 3D space, Spherical-Spherical pairs can produce only 1
passive DOF. Substituting corresponding values and F = 0 into (3.19) yields to:
∑
Solving equation (‎3.20) and substituting ∑
(‎3.20)
by 3j, the minimum number of joints required
to provide stability is computed as:
34
(‎3.21)
Since number of joints must be integer, j is rounded up to 3. Thus, minimum number of
suction cups required to keep the stability of the robot is 3.
As mentioned before, the force exerted by a single suction cup depends on its effective
chamber area. Since smaller suction cups require smaller substrate area, miniaturizing cup
dimensions increases reliability of the system on discrete surfaces. For a symmetric design
and to maintain small cup sizes, four suction cups are desired to be used in adhesion system
of the Duct-Sweeper. The necessity for use of 4 suction cups and force analysis of suction cup
system for various maneuvers and transitions is addressed in section 4.3.
3.5.3.4 Vacuum Pump
Using vacuum pumps and vacuum valves are two main industrial approaches for generating
required vacuum level for suction cups. A promising method to generate vacuum in suction
cups by vibrations is also presented in literature [64], [65]. This approach is still in
development phase and its reliability in industrial environments is not proven. Using
stationary vacuum pumps or pressurized air source that feeds vacuum valves are not good
practices in design of a mobile climbing robot. Long tubes that connect robot to the stationary
facilities increase robot weight. Also, Long tubes cause air pressure drop and reduce
efficiency. A possible solution is to use self-contained vacuum based adhesion system as
discussed in [66]. Aslam and Dangi developed and tested a self-contained robot foot that uses
a miniature diaphragm vacuum pump to generate required vacuum. Test results presented in
[66] proves applicability and reliability of this approach. To eliminate tethers and
consequently decrease robot‟s weight and increase its efficiency, miniature diaphragm
vacuum pumps are used in Duct-Sweeper‟s adhesion system design.
35
3.5.3.5 Pneumatic circuit of the adhesion system
Adhesion is generated because of negative pressure difference between cups‟ chambers and
the surrounding environment by pumping air off the suction cups. To deactivate generated
adhesion, the introduced pressure difference must be removed. Miniature vacuum pumps only
provide flow in one direction and a path is required to allow air flow into the cups‟ chambers.
A simple and cost effective solution is to use a 2/2 directional valve. Figure 3.13 shows
pneumatic circuit diagram for Duct-Sweeper‟s vacuum system. To increase reliability and
speed, each pump drives two of the four suction cups of each cart.
M
Figure ‎3.13. Pneumatic circuit diagram
3.5.4 Adhesion system leveling mechanism
Four main tasks of leveling mechanism are: 1) Adjusting distance between suction cups and
substrate surface; 2) Simulating the effect of accordion body of the Multi-Bellows cup; 3)
Adjusting cart‟s height (h) during robot maneuvers; and 4) Compensating lateral inclines of
duct surfaces. Figure 3.14 illustrates the proposed adhesion system leveling mechanism. To
compensate lateral inclines of air ducts‟ surfaces, mechanism is divided into two distinct
similar modules that work independently. Each module is composed of two cylindrical joints,
two spherical joints, two suction cups, a lead screw, a rotary actuator, a vacuum pump (not
illustrated in the figure), and other pneumatic modules introduce in Figure 3.13. Since two
cylindrical joints provide mobility between two rigid components, they lose one of their DOF
and act as a single prismatic joint. This joint is responsible to adjust level of the suction cups
and height of the cart. Lead screw is used to convert rotary to linear motion and actuate the
36
prismatic joint. Spherical joints are added to allow suction cups adjust themselves with
substrate surface, passively.
Lead screw
Rotary actuator
Cylindrical
joint
Spherical
joint
Suction cup
Figure ‎3.14. Proposed mechanism for adhesion subsystem
3.6 Summary of Duct-Sweeper’s‎conceptual design
In this chapter, each part of the robot studied in detail and a conceptual design is introduced
based on robot‟s requirements and air ducts conditions. The results of each section are listed
here as a summary to complete conceptual design of the robot.

A biped structure with a hybrid articulated wheeled system is proposed as the main
locomotion system of the robot. The structure is composed of three distinct parts,
namely, two carts and a waist. Carts are responsible to carry wheeled locomotion
components, adhesion system components, duct cleaning facilities and electronic
parts. Waist is responsible to provide the required DOFs between two carts to allow
the robot pass through a network of air ducts.

A hybrid waist mechanism is proposed to increase waist‟s load carrying capacity. The
parallel portion of the mechanism is composed of two RPR limbs and one RP limb.
Serial portion of the mechanism is composed of two revolute joints that connect
parallel portion to each one of the robot‟s carts.
37

Wheeled locomotion of the robot is provided by a 2-wheeled differential drive system
with extra omnidirectional wheel.

Four flat cups with cleats, two miniature diaphragm vacuum pumps, two 2/2
directional valves, two rotary actuators, four cylindrical joints, four spherical joints
and two lead screws form two adhesion modules and their leveling mechanisms of
each cart.
A complete conceptual design of the robot is illustrated in Figure 3.15.
Extra-Limb
Linear actuators
EWGs
Figure ‎3.15. Finalized concept of the Duct-Sweeper
38
Chapter 4
Kinematics and static force analysis of Duct-Sweeper
Kinematic analysis of the waist of Duct-Sweeper is required in order to control the gait
sequence of the robot. Forward and Inverse kinematics of the robot and its static force
analysis are covered in this chapter. Analyses of static forces that govern size of the suction
cups of the robot are also presented in this chapter.
4.1 Kinematic analysis of Duct-Sweeper
As mentioned before, Duct-Sweeper is a biped robot with a hybrid serial-parallel waist
mechanism. This mechanism is used to manipulate two robot carts (feet) and locate them in
appropriate positions and orientations. Due to hybrid structure of the waist, using straight
forward approaches for its kinematic analysis is impossible. To solve this issue, during
kinematic analysis of the robot, Parallel Portion (PP) of the mechanism is replaced by a Serial
Substitute Mechanism (SSM). Doing so, the waist converts to a Fully Serial Mechanism
(FSM) that can be analyzed with available tools. The kinematic analysis‟ results of fully serial
and hybrid waits are convertible to each other by translating kinematics of PP to kinematics of
SSM.
4.1.1 Solving waist’s kinematics using SSM
The kinematics of SSM and PP must give equivalent results. Analyzing PP of the waist shows
that SSM already exists in the structure of the waist. Since the Extra-Limb controls kinematic
behavior of PP, it is the best SSM nominate. By substituting PP with Extra-Limb as SSM,
FSM of Figure ‎3.1 is produced. Denavit-Hartenberg (DH) method, introduced in [5], is used
to derive transformation matrices between terminal coordinate systems of the resulting FSM.
Figure 4.1 also indicates coordinate system assigned to each joint of the mechanism. In
39
addition to compatibility with DH method, the coordinate assignment matches with
coordinates previously assigned to the carts.
θ 4 x4
x3
y4
z3
x5
z5
z4
y5
y3
d3
z2
y1 z0
y2
θ2
C
x2
x1
y0
x0
θ1
z1
Figure ‎4.1. Coordinates assigned to FSM
The DH parameters of the linkage are tabulated in Table 4.1. Equation (4.1) [5] is used to
calculate transformation matrices between coordinate systems {0} to {5}. In the following
equations, sθi and cθi represent sine and cosine of θi, respectively.
Table ‎4.1. Link parameters of FSM
i
αi-1
ai-1
di
θi
1
2
3
4
5
π/2
-π/2
-π/2
-π/2
-π/2
0
C
0
0
0
0
0
d3
0
0
θ1
θ2
-π/2
θ4
0
[
]
40
(4.1)
The transformation matrix which maps the positions in {5} to positions in {0} is computed by
multiplying sequential transformation matrices as indicated by (4.2) [5].
is defined as:
(4.2)
[
As discussed in [5],
is the inverse of
(
)
(
)
(
)
(
]
)
]
(4.3)
and is equal to:
[
(4.4)
4.1.2 Mapping PP kinematics to SSM
Figure 4.2 illustrates kinematic model of PP. In order to simplify equations derived in this
section, coordinates assigned to PP do not match with coordinate assignment of Figure 4.1.
Correction equations are introduced to eliminate the effect of this assignment mismatch. The
values for Si (i=1 and 2) are defined as:
‖
‖
(4.5)
The following equation is used to map PiN, defined in coordinate system {N}, to
corresponding point in coordinate system {M}.
(4.6)
The rotation matrix
and distance between origins of {M} and {N} defined in {M} (MPN)
are equal to:
[
]
*
41
+
(4.7)
(4.8)
yN
𝑀
⬚𝑃 𝑀
𝑃 𝑀𝑥
𝑃 𝑀𝑦
𝑃 𝑀𝑧
S2
𝑃 𝑁𝑥
𝑃 𝑁𝑦
𝑃 𝑁𝑧
𝑁
⬚𝑃 𝑁
xN
{N}
yM
φ
d3
xM
{M}
S1
𝑁
⬚𝑃 𝑁
𝑀
⬚𝑃 𝑀
𝑃 𝑀𝑥
𝑃 𝑀𝑦
𝑃 𝑀𝑧
𝑃 𝑁𝑥
𝑃 𝑁𝑦
𝑃 𝑁𝑧
Figure ‎4.2. Kinematic model used in PP analysis
Value of Si as a function of d3 and φ is obtained by substituting equations (4.6), (4.7) and (4.8)
into (4.5):
‖
*
+
[
]
‖
(‎4.9)
Although d3 is already defined, relation between φ and θ2, introduced in section 4.1.1, is:
(‎4.10)
Equation (4.9) defines the values of S1 and S2 as functions of d3 and φ which are required for
inverse kinematics of the waist. For the forward kinematics, d3 and φ must be calculated as
functions of S1 and S2. As explicit solution could not be found for d3 and φ as functions of S1
and S2, the values of d3 and φ could be calculated using numerical methods. Since gait control
requires explicit solutions for inverse kinematics, using numerical methods for the forward
kinematics will not be problematic.
Using (4.9), Jacobian of PP (JPP) is computed as:
42
̇
* +
̇
̇
+[ ̇ ]
*
⏟
(
)
(4.11)
(
)
√(
(
))
(
(
))
(4.12)
√(
(
))
(
(
))
(4.13)
(
)
(
)
√(
(
))
(
(
))
(4.14)
√(
(
))
(
(
))
(4.15)
4.1.3 Forward and inverse kinematics of the waist
The inverse and forward kinematics of the robot are divided into two sub categories: 1) Cart
A is fixed and the waist manipulates cart B; 2) Cart B is fixed and the waist manipulates cart
A. Both of these conditions are covered here.
4.1.3.1 Fixed cart A – Floating cart B
In this condition, coordinate system {0} is fixed and the position of coordinate system {5} is
controlled by joint variables of the waist. Forward kinematics of this condition is simply
solved by multiplying
to any position vector defined in {5}. The position of an arbitrary
point 5P, which is defined in {5}, is defined by:
[
]
[
]
(4.16)
In (4.16), 0P is the position of 5P that is defined in {0}. The last rows are added to position
vectors to allow matrix multiplications, as suggested in [5]. Substituting
previously defined in (4.3), into (4.16) yields to:
43
, which is
(
)
(
)
(
)
[
]
(
)
(
)
(
(4.17)
)
Equation (4.17) maps any arbitrary point that is defined in {5} to corresponding point defined
in {0} for any arbitrary joint variables of the waist. The rotation matrix, that defines the
orientation of cart B with respect to cart A, is already defined by
. Corresponding rotation
matrix presented in rows 1 to 3 and columns 1 to 3 of the transformation matrix
[5]. This
rotation matrix, presented in (4.18), and the matrix presented in (4.17) provide solution for the
forward kinematics of the robot when cart A is fixed.
[
]
(4.18)
Desired position and orientation of the floating cart are used to solve the inverse kinematic
problem. The waist design only allows controlling pitch (rotation about y axis) and yaw
(rotation about z axis) orientations of the floating cart. To find values of joint variables that
put cart B in desired orientation, a unit vector along xB direction is considered. Then this
vector is rotated by a rotation matrix which is constructed with desired rotations about z and y
axes. Equations (4.19) and (4.20) describe desired rotation matrix (RdB) and rotated vector
(VdB), respectively. In these equations α and β symbolize rotations about zB and yB axis,
respectively.
[
][
]
[
[
][ ]
]
[
]
(4.19)
(4.20)
Equation (4.21) presents a unit vector along xB direction which is rotated by rotation matrix
indicated by (4.18) .
44
̂
[
]
(4.21)
To adjust cart B in desired orientation, vectors VdB and WdB must be parallel. Based on vectors
algebra, two nonzero vectors are parallel when their cross product is zero. Thus, vectors VdB
and WdB are parallel if:
[ ]
(4.22)
A set of three equations is obtained by substituting corresponding values of VdB and WdB into
(4.22):
(
)
(
)
(
)
(
)
[ ]
(4.23)
Since θ1 is related to position of cart B as well, three equations of (4.23) have only two
unknown variables. If two out of three components of nonzero vectors cross product are equal
to zero, the third component will be zero as well. A proof for this claim is presented in
Appendix A. Two of three equations of (4.23) are solved by Weierstrass substitutions and
four different sets of solutions are obtained. Two vectors can be parallel but point to opposite
directions. Thus, dot product of VdB and WdB is considered and only solution sets that result
VdB.WdB = 1 are considered. The two acceptable solution sets are:
Solution set #1:
(
(
)
(
)
)
(4.24)
(4.25)
Where νB is equal to:
√
(4.26)
Solution set #2:
45
(
(
)
(
)
(4.27)
(4.28)
)
Consider PBx, PBy and PBz as components of position of the origin of coordinate system {5} in
coordinate system {0}. This position is already defined in transformation matrix
PBx, PBy and PBz with corresponding components of
. Equating
yields:
(
)
(
)
(4.29)
Solving these equations yields definitions of θ1 and d3 for the desired position of cart B.
Substituting value of θ2 defined by (4.24) and (4.27) into (4.29) results in complicated
equations as functions of θ1 and d3. In order to avoid this complexity, corresponding term that
contains θ2 is evaluated from the equations describing x and z components of position.
Consequently, θ1 and d3 are defined by following equations:
(4.30)
√
(4.31)
By calculating θ1 and d3, all the variables of the inverse kinematic of the robot for fixed cart A
are clarified. The summary of the steps required for solving the inverse kinematics is listed in
what follows.
I.
II.
Solve (4.30) using desired position of cart B and calculate θ1.
Use calculated θ1 and desired orientation of cart B (which is defined by α and β) to
calculate two sets of solutions of θ2 and θ4 defined by (4.24) to (4.28).
III.
Select appropriate solution that matches with limitations of joint variables.
IV.
Compute d3 using (4.31).
46
Use (4.9) and (4.10) to convert d3 and θ2 to S1 and S2.
V.
4.1.3.2 Fixed cart B – Floating cart A
Approaches used to solve inverse and forward kinematics for fixed cart B is similar to those
used for fixed cart A. The only difference is that instead of transformation matrix
transformation matrix
,
is used. Solutions for forward kinematics of the robot are computed
as:
(
)
(
)
(
)
[
]
(
)
(
)
[
(
]
(4.32)
)
(4.33)
In (4.32), 0Px, 0Py and 0Pz are three components of 0P which is the position of an arbitrary point
defined in coordinate system {0}.
When cart B is fixed θ4 is related to position of cart A and θ1 controls the orientation of cart
A. Similar to the previous section, values for θ2 and θ1 are obtained by solving the following
set of equations.
(
(
)
)
(
(
)
)
[ ]
‎4.34)
The values for θ4 and d3 are computed as follows:
(4.35)
√
(4.36)
4.1.4 Velocity analysis
Similar to inverse and forward kinematics, velocity analysis of the robot must be divided into
two subsections, in which either cart A or B is fixed. Due to similarity of the approaches, only
47
velocity analysis of the robot for fixed cart A is presented. The approach could be simply
adapted to analyze robot velocity when cart B is fixed. Based on the method introduced in [5],
the velocity of each coordinate system assigned to waist of the robot is computed by
following sets of equations:
If joint i+1 is revolute:
̇
̂
(4.37)
(
)
(4.38)
If joint i+1 is prismatic:
(4.39)
(
̇
)
̂
(4.40)
In these equations, iωi and ivi represent angular and linear velocities of coordinate system {i},
respectively. Rotation matrix that maps coordinate system {i} to {i+1} is indicated by
.
Distance between origins of {i} and {i+1} that is defined in {i} is indicated by iPi+1. Using equations
(4.37) to (4.40), velocity of cart B (coordinate system {5}) is computed as:
̇ (
̇
)
̇
̇ (
(4.41)
̇
)
̇
̇
̇
̇
̇
(4.42)
Multiplying
̇
to these velocities maps them into corresponding velocities defined in
coordinate system {0}. The computed velocities that are defined in {0} are:
(
) ̇
̇
̇
(
̇
̇
) ̇
(4.43)
̇
̇
̇
̇
̇
̇
̇
̇
(4.44)
48
4.2 Jacobian and static force analysis
Similar to the previous section, due to similarity of the approaches, Jacobian and force
analysis is provided only for the case when cart A is fixed.
In robotics, Jacobian is used to relate velocities in joint space and Cartesian space [5] and it is
defined as:
( ) ̇
(4.45)
In (4.45), 0v is the velocity vector that contains both linear and angular velocities in Cartesian
space; Θ is the vector that contains joint variables of the robot. By rewriting (4.43) and (4.44)
into the form defined by (4.45), the Jacobian for the waist of Duct-Sweeper for fixed cart A is
computed as:
̇
̇
̇
[⏟
]
[
⏟
]
̇ ]
[⏟
(4.46)
̇
( )
Jacobian provides a simple approach to drive expressions of the forces which are exerted by
joints of the robot due to hold external loadings. The relation between Jacobian and forces in
Cartesian and joint spaces is [5]:
( )
(4.47)
In this equation, τ represents a vector of forces and moments tolerated by prismatic and
revolute joints, respectively. Vector
contains forces and moments that are defined in
coordinate system {0} and exerted to the origin of coordinate system {5}. Substituting
from (4.46) into (4.47) yields to:
49
( )
( )
[ ]
(4.48)
[
(
)
]
(
)
[ ]
(4.49)
[
]
4.3 Suction cup force analysis
Static analyses of different conditions of the robot are required to be able to determine cups‟
diameters. Figure 4.3 illustrates 6 severe conditions for the adhesion system of the robot.
Case 1
LCM
Fb
Fb
Ff
Ff
Mg
LCM
LS
LCM
Ff
Fb
Case 2
Mg
LCM
Fl
Ff
Mg
bCM
wS
Fr
Mg
Fb
Mg
Case 3
h
h
Case 4
Case 5
LS
ff
ff
fb
wS
fb
Mg
LCM
aS
Case 6
Figure ‎4.3. Adhesion system worst case scenarios used to determine suction cup sizes
Note that, case 4 represents the configuration of the robot in which the gravitational force is
exerted parallel to xA and xB axes; But in case 5, the gravitational force is parallel to yA and yB
axes. Thus, the force distribution on suction cups is different in these two cases. In case
50
number 6, only the suction cups that are illustrated on the hatched area are active. Except for
the case number 6, a simple assumption makes all other cases statically determinate. This
assumption is: two cups which are located on the same line, parallel to yA and yB axes, tolerate
equal forces. Figure 4.3 shows forces exerted from the ground to the suction cups. Thus, the
sizes and gage pressure of the cups should produce forces pointing toward the substrate
surface. The results of static force analysis of the cases 1 to 5 are listed in what follows. In
these equations, Fni represents adhesion forces which must be generated by individual suction
cup for case i.
(4.50)
(
)
(
(
(4.51)
))
(
)
(
)
(4.52)
(4.53)
(4.54)
Since case 6 is statically indeterminate, forces exerted to cups in this case are computed by
the method introduced in [67]. The presented method is aimed to solve shear in bolts with
eccentric loading. Since the geometric conditions and assumptions in both situations (shear in
bolts and tangential forces of suction cups) are equivalent, it is reasonable to apply the
method here. Based on the approach, shear force at each joint is divided into two components.
One corresponds to force itself while the other takes into account the moment generated due
to eccentric nature of the load. To calculate the resultant force at each joint (suction cup), the
center of relative motion must be evaluated. Considering suction cups as tightly fitted pins,
this center lies on centroid of the cups. The centroid can be calculated using equation used to
evaluate center of distinct areas by considering equal area for all suction cups:
51
∑
∑
∑
∑
̅
̅
→
̅
→
̅
∑
(4.55)
∑
(4.56)
A definition of the problem and forces are illustrated in Figure 4.4. Substituting n = 4, x3 = x4
= 0, x1 = x2 = LS, y2 = y4 = 0 and y1 = y3 = wS into equations (4.55) and (4.56) yields to values
of
̅ and ̅. Load exerted to the system introduces a shear at each joint. Considering
equivalent distribution, corresponding force at each joint can be calculated by dividing load to
number of joints. These forces are named as
to
and are illustrated with green color in
Figure 4.4.
(4.57)
α1
𝐹
α3
𝐹
𝐹
𝐹
𝑦̅
𝐹
𝐹
Le
y
𝐹
α2
𝐹
𝐹
𝐹
𝐹
x
Mg
𝑥̅
𝐹
α4
Figure ‎4.4. Coordinate system, geometric properties and forces for case 6
Forces due to torsion, named as
to
and indicated by purple color in Figure 4.4, are
calculated as follows [67].
(4.58)
∑
where
̅ . The distance ri is measured from joint (suction cup) number i to
centroid and defined as:
52
√
(4.59)
Substituting (‎4.59) into (‎4.58) yields to:
(
)
(‎4.60)
√
Finally, the force supported by cup i evaluated by calculating the resultant of
and
. Due
to the symmetrical geometry α1 = α2 and α3=α4, thus:
√
√
(
(
)
)
(
(4.61)
)
(4.62)
The force generated by the suction cup is calculated by multiplying gage pressure of its
chamber with its area. Since the cup model that is selected in ‎3.5.3.1, has a circular crosssection, required diameter of the cup for normal and tangential loads is calculated as:
√
(4.63)
√
(4.64)
In these equations dS defines diameter of suction cup in millimeters. Fn and Ft represent
normal and tangential forces in newton, respectively. Factor of safety for normal and
tangential loadings are defined by SFn and SFt, respectively. The amount of gauge pressure in
bars is represented by P. To find appropriate suction cup size, maximum normal and
tangential forces must be implemented into equations (4.63) and (4.64). Studying equations
(4.50), (4.51) and (4.52) prove that, among cases 1 to 3, case 2 requires maximum normal
force. Since the size of the cups are defined based on maximum forces, only equation (4.51) is
considered in driving the equation for the size of the cups. Furthermore, the only difference
53
(
between (4.61) and (4.62) is the
) term which is presented in (4.62).
Since LCM, aS and LS are all larger than 0 and aS is considered to be larger than LS, the force
calculated in equation (4.61) always has greater values than force calculated in (4.62).
Considering maximum forces, equations (4.63) and (4.64) are combined to form a single
equation to define the diameter of suction cups:
√
((
)
(
) (
)
)
(
(4.65)
√
√
(
)
)
Equation (4.65) defines diameter required for each one of the cups employed in DuctSweeper by considering all severe conditions of this robot. Note that, in this equation, all
dimensions are considered to be in millimeters, mass is defined in kilogram; gravitational
acceleration (g) is in m/s2 and gauge pressure is in bars.
54
Chapter 5
Design optimization and prototype design
Duct-Sweeper is designed to survive from any unexpected duct condition; but it only can
climb using its wheeled locomotion system in specific range of duct sizes. In this chapter, an
optimization problem is formulated to find the optimum geometrical parameters of the robot
for specific range of duct sizes. To show effectiveness of the approach, the results of
optimization problem are used in the prototype design of Duct-Sweeper. This prototype could
be used as design guideline for various versions of Duct-Sweeper for different duct sizes.
5.1 Definition of parameters used in optimization
Since parameters assigned to the carts of the robot are covered in Figure 3.2, there only
remains defining parameters related to its waist. As discussed in section 3.2, waist of the
robot consists of two electromechanical actuators and an Extra-Limb. Parameters assigned to
each one of these parts are covered in what follows.
Figure 5.1 shows parameters assigned to an electromechanical actuator. In this figure, Sa
represents stroke of the actuator, na is stroke multiplier which is 2 for the case of single step
non-telescopic actuator, Ca is a constant related to mechanical design and Ea is the elongation
of the actuator.
max(Ea) = Ca + naSa
min(Ea) = Ca + Sa
Figure ‎5.1. Parameters assigned to linear electromechanical actuator
As mentioned in section 3.2, two serial revolute joints of the waist are actuated by two EWGs.
EWG designs introduce a new challenge in design of the robot. Since the output shaft of the
55
worm-gear gearbox is perpendicular to its input shaft, most manufactures use a design pattern,
similar to Figure 5.2, to produce EWGs. A design pattern, illustrated in Figure 5.3, is
proposed to locate Extra-Limb and DC-motors in the middle of two linear actuators. Locating
Extra-Limb in the middle of two actuators produces desired kinematic behavior. On the other
hand, since two EWGs are the heaviest parts of the robot, locating them in the middle of each
cart reduces torsions along xA and xB axes.
Figure ‎5.2. Common design of EWGs
Worm-gear gearbox
DC motor
Waist-Arc
Linear actuators
connection points
Extra-Limb
connection point
Figure ‎5.3. Sample design to locate Extra-Limb in the middle of two linear actuators
Waist-Arc adds two constant values to minimum length of Extra-Limb. On the other hand,
Extra-Limb must not prevent complete extraction of linear actuators. This means that
maximum elongation of Extra-Limb divided by its minimum elongation must be larger than
maximum elongation of linear actuators divide by their minimum elongation. To fulfill this
condition, Extra-Limb is designed by a telescopic linear mechanism. The proposed telescopic
design of Extra-Limb and its parameters are illustrated in Figure 5.4. In this figure, Se
represents the stroke of the Extra-Limb, Ce is constant related to mechanical design (this
constant also includes lengths added due to presence of Waist-Arc), ne is stroke multiplier
56
which is 3 for the case of single step telescopic mechanism and Ee is the elongation of the
Extra-Limb.
min(Ee) = Ce + Se
Se
max(Ee) = Ce + neSe
Figure ‎5.4. Parameters assigned to Extra-Limb
Other parameters that must be clarified prior to formulating optimization problem are related
to robot transitions. As mentioned in section 3.2, Open Angle and Right Angle Transitions
introduce two of the three severe conditions for the waist of the robot. These transitions not
only introduce constraints on stroke of the actuators, but also may cause collision of actuators
with substrate surface. Figure 5.5 illustrates these transitions, parameters assigned to actuators
and new parameters and variables that are used in defining optimization constraints.
hA1
y
dc
(xA1 , yA1) y
x
x
hB4
hA2
hB3
(xc ,0)
min(Ea)
(xB3 , yB3)
Ea
min(Ea)
(xB1 , yB1)
Ea
hA3
y
hA4
hB1
y
x
hB2
(xA3 , yA3)
Figure ‎5.5. Two critical transitions of robot and the parameters used to define their constraints
57
x
5.2 Optimization formulations
Design variables and constant values must be defined before formulating optimization
problem. To do so, all the parameters assigned to geometry of the robot are considered. Points
that are considered to select appropriate design variables are presented in what follows.
Although a and L are two key parameters of the robot, their values are functions of LS, aS and
dS. The length of the linear actuators and extra limb are defined by six variables. Four of these
six variables (Ca, na, Ce and ne) depend on design, manufacturing methods and material
properties; make it impossible to assign any arbitrary value to them. The strokes of the extra
limb and actuators depend on each other, thus only one of them can serve as design variable.
Since adhesion system leveling mechanism of each cart works independently, each cart may
have different h in different phases of each transition, as suggested in Figure 5.5. It is desired
to get advantage of this flexibility to have larger feasible region. Width of the robot, w,
depends on wS and dS. Since wS only affects motions of the robot in 3D space, the design may
get advantage of this flexibility to provide required space for actuators and other facilities
need to be mounted on each cart. Although Right Angle Transition will not be problematic
due to various configurations that robot can get prior to this transition as mentioned in
section 3.2, the geometry of the robot must at least provide feasibility of one configuration.
To reduce number of design variables, this configuration and its constraints are defined using
limiting values and other design variables. Considering the above discussions, parameters LS,
aS, dS, hA1, hB1 and Sa are independent parameters that perfectly describe the geometry of the
robot. Thus, they are good choices to be the design variables of the problem.
The objective of optimization is selected to be Sa itself. Minimizing Sa decreases torque
required to actuate two serial revolute joints and consequently reduces the size and weight of
EWG. Reducing Sa also reduces the weight of the waist. These reductions in weight increases
the reliability of the robot. But on the other hand, since constraints of the optimization are
nonlinear functions of Sa and other design variables, it is impossible to assign any arbitrary
58
value to Sa or exclude it from other design variables. Thus, selecting Sa both as design
variable an cost function is a fair decision.
The optimization formulation is presented in what follows.
Design variables:
LS, aS, dS, hA1, hB1 and Sa
Constant values:

M: Mas of the robot (Kg)

g: Gravitational acceleration (m/s2)

P: absolute value of suction cup chamber‟s gauge pressure (bar)

wS: Lateral distance of suction cups (along yA and yB axes) (mm)

min(h): Minimum possible value of h (mm)

max(h): Maximum possible value of h (mm)

LRC: Maximum length of each cart (mm)

F: Length of the front portion of each cart (mm)

Ca: Constant length of each actuator (mm)

Ce: Constant length of Extra-Limb (mm)

na: Actuator stroke multiplier

ne: Extra-Limb stroke multiplier

ra: Actuator radius

SFn: Safety factor for suction cups normal loadings

SFt: Safety factor for suction cups tangential loadings

μ: Coefficient of friction between suction cups and substrate surface

min(H): Minimum height of the duct which the robot is expected to work in

max(H): Maximum height of the duct which the robot is expected to work in

offset: The offset distance between two suction cups of each module
Dependent variables:
(
(
)
(5.1)
)
5.2)
(
(
)
)
(5.3)
(5.4)
59
(
)
(5.5)
(
√
)
(5.6)
((
)
(
) (
(
)
)
(5.7)
√
√
(
)
)
(5.8)
(5.9)
(5.10)
(5.11)
(5.12)
(5.13)
(
√(
))
(
)
(5.14)
(5.15)
(5.16)
(5.17)
|
√
√(
(
))
|
(
Constraints:
g1:
g2:
g3:
g4:
g5:
( )
g6:
( )
g7:
( )
g8:
( )
60
( )
(5.18)
( ))
(5.19)
g9:
g10:
(
)
g11:
(
)
g12:
(
)
(
)
g13:
g14:
(
g15:
g16:
(
g17:
( )
)
( )
)
(
( )
( )
)
( )
Cost function:
In this formulation, constraints g1 to g8 are related to the feasibility of the geometries. Constraint g9 is
used to provide an offset distance between two suction cups of each adhesion module. This distance is
used to place wheels of the wheeled locomotion system. Constraints g10 and g11 are related to the
feasibility of the electromechanical actuators. Constraint g12 is used to ensure that Extra-Limb
provides necessary stroke for electromechanical actuators. The minimum distance between waist
mechanism and duct corner in Open Angle transition is restricted by g14. Constraint g13 guarantees
feasibility of this distance. The condition required for Right Angle transition is defined by g15. Finally,
g16 and g17 define the constraints related to the Parallel Plane transition.
5.3 Applying optimization to prototype design
The following subsections discuss different steps of applying proposed optimization problem
to calculate geometric parameters of prototype.
5.3.1 Evaluating constant values
Prior to applying the method, constant values defined in section 5.2 must be clarified. These
values are related to four distinct areas: geometries of the duct which the robot is desired to
work in, robot‟s weight, actuators and linear motion components and adhesion system. Each
one of these subjects is discussed in what follows.
61
5.3.1.1 Duct geometries
R.E.E Electric Appliances Company [68], in Reetech Air Duct Standards catalogue [69],
presents standard rectangular air duct sizes. Table 1.1 shows the standards of rectangular air
ducts based on what is presented in [69]. In this table, common duct sizes are indicated by
blue color.
Table 5.1. Standard rectangular air duct sizes presented in [69]
b
(mm)
a (mm)
100
150
200
250
300
400
500
600
800
1000
1200
150
200
250
300
400
500
600
800
1000
1200
1400
1600
1800
2000
Table 5.2 presents regular sizes of rectangular air ducts as proposed by The Engineering
Toolbox [70]. In this table, preferred, acceptable and not-common sizes are indicated by
green, yellow and red respectively.
Commercially available DCRs, discussed in section 2.1, have width and height no more than
400 millimeters and length no more than 460 millimeters. Also the average of the length,
width and height of the robots are about 350, 210 and 200 millimeters respectively.
Considering duct geometries and available prototypes, robot is desired to work inside ducts
with height ranging from 350 to 500 millimeters.
62
Table 5.2. Regular rectangular air duct sizes based on Engineering Toolbox suggestion [71]
Width
(mm)
Height (mm)
100
150
200
250
300
400
500
600
800
1000
1200
200
250
300
400
500
600
800
1000
1200
1400
1600
1800
2000
5.3.1.2 Constants related to adhesion system
As mentioned in section 3.5.3.4, onboard miniature vacuum pumps are chosen to produce
required vacuum. Surveying products of different miniature vacuum pump manufacturing
firms (e.g. TCS Micro Ltd., Parker, Dynaflo, Schwarzer Precision, Smart Products Inc. and
ALLDOO) proves that it is possible to generate vacuum up to 1000 mbar with dimensions no
more than 125000 mm3 and weight less than 100 grams. By taking into account miscellaneous
effects that alter pump‟s performance, vacuum level for optimization is selected to be 800
mbar.
Safety factors for normal and tangential forces, exerted to suction cups, are selected to be 2
and 4, respectively. These values are recommended by most of the firms and technicians in
suction cup industries. By investigating cup materials, covered in section 3.5.3.2, and duct
materials, covered in section 3.5.1, the coefficient of friction between cups and substrate
surface is taken to be 1 [72].
5.3.1.3 Constants related to actuators, linear motion components and robot’s weight
Due to respectively large elongation of the waist mechanism, it is expected that the length of
the carts is dominated by the length of the rotary motors responsible for actuating two serial
63
revolute joints of the waist. Surveying different available EWGs shows that each cart needs at
least 180 mm length with front portion less than 40 mm. minimum height of the cart, min(h),
is dominated by the size of EWG, size of suction cups and size of motors used to actuate
wheels and it is chosen to be no less than 45 mm. The maximum height of the cart, max(h), is
constrained by elongation of waist in specific transitions and duct geometries and chosen to
be no more than 100 mm. By taking into account the size of actuators used in wheeled
locomotion system and adhesion system leveling mechanism, the distance between two
adhesion modules, wS, is taken to be 300 millimeters.
Using an electric motor to rotate a screw of a Lead-Screw or Ball-Screw mechanism is the
most common practice in electromechanical actuator design. Ca is affected by methods used
to connect motor to the screw and size of the nut. Ca is taken to be 47 millimeters after
surveying different available design samples and actuators power ratings.
To reduce the prototyping time, available linear guides on the market considered to provide
linear motion of the Extra-Limb. After surveying products from different miniature linear
guide manufacturing companies and different designs of Waist-Arc, Ce is decided to be 127
millimeters.
Due to its lightweight, strength, formability and reachability, main material for the robot
structure is chosen to be Aluminum alloy numbered 5052 – H38. Considering density of the
aluminum and power rating of the actuators, the total mass of the robot is expected to be no
more than 5 kilograms.
5.3.2 Solving optimization problem
Since generating a new optimization method is far beyond the scope of this thesis, available
methods are used to solve this problem. To do so, two different optimization algorithms
available in MATLAB toolboxes are considered: gradient based methods to find minimum of
a nonlinear constrained problem (also known as nonlinear programing) and finding a
64
minimum for a nonlinear constrained function using genetic algorithm. Function “fmincon” is
the MATLAB function which is responsible for solving nonlinear programing problems. This
function uses one of four different algorithms to solve nonlinear programming problems.
These algorithms are: Trust Region Reflective, Active Set, Interior Point and Sequential
Quadratic Programming (SQP). SQP solves nonlinearly constrained optimization problems by
solving quadratic sub-problems and it can be used both in line search and trust-region
frameworks. SQP methods are appropriate both for small or large problems and they show
their strength when solving problems with significant nonlinearities [73]. Fortunately, both
gradient based algorithms and genetic algorithm can successfully solve this problem.
Figure 5.6 shows the approach of these 5 algorithms to find the optimal solution. The
optimum design variables computed by these five algorithms are tabulated in Table 5.3.
Figure ‎5.6. Different algorithms approach to find minimum value for cost function
65
Investigating gradient based methods shows that the ability of Trust Region Reflective,
Active Set and Interior Point algorithms to find a feasible solution for this problem is highly
affected by their initial conditions. Selection of several initial points (starting points) shows
that choosing inappropriate starting point for these algorithms prevents them from finding a
feasible solution.
Table ‎5.3. Design variables computed by different algorithms
Applied method
LS
aS
hA1
hB1
Sa
Trust Region Reflective
82.9331
112.9148
47.0059
100.0000
190.9374
Active Set
82.9331
112.9148
47.0059
100.0000
190.9374
Interior Point
82.9331
112.9148
47.0059
100.0000
190.9374
SQP
82.9331
112.9148
47.0059
100.0000
190.9374
Genetic Algorithm
82.9422
112.9289
47.0047
99.9861
190.9532
5.4 Prototype design
Mechanical design of the robot is divided into a number of sub-assemblies. Each one of these
assemblies is described in the following sections. These design patterns plus proposed
optimization problem could be used to create different robots for different duct geometries.
5.4.1 Cart design
Isometric simple view of the cart is illustrated in Figure 5.7. Cart‟s main structure carries
wheeled locomotion system components (motors, wheels, omnidirectional-wheel and support
bearings), EWG (which actuates one of two serial revolute joints of the waist), Waist-Arc
support bearings, a number of adhesion system leveling mechanism parts (motors, lead
screws, support bearings and cylindrical joint supports) and a 2DOF actuated yaw-tilt
mechanism used for camera adjustment. Electronic boards and batteries, which are not
illustrated in this figure, are going to be mounted in the open area available atop of wheeled
66
locomotion DC-motors. Trimetric exploded view of prototype cart is illustrated in Figure 5.8
to give more insight about the design.
Figure ‎5.7. Isometric view of the designed cart
Figure ‎5.8. Trimetric exploded view of the cart
5.4.2 Adhesion module design
Adhesion module contains vacuum pump, directional valve, suction cups and parts of
adhesion system leveling mechanism (Spherical and cylindrical joints plus the nut of the leadscrew mechanism). Isometric and trimetric exploded views of adhesion module are illustrated
67
in Figure 5.9. Four of these modules, two on each cart, provide required adhesion for robot.
Directional valve is not illustrated in these figures.
Figure ‎5.9. Isometric and trimetric exploded views of the adhesion module
5.4.3 Waist design
Mechanical design of the waist, excluding linear actuators, is illustrated in Figure 5.10. Due
to their force and bending moment ratings, four miniature linear guides are used in ExtraLimb design (two for each portion of the telescopic guide). Exploded Isometric view of the
waist, Figure 5.11, shows different components of each module and their connections.
Figure ‎5.10. Mechanical design of waist, excluding linear actuators
68
Figure ‎5.11. Isometric exploded view of the waist, excluding linear actuators
Figure 5.12 shows linear electromechanical actuator that is used in the waist of DuctSweeper. Exploded view of the actuator is illustrated in Figure 5.13 to give insight about
different parts used in its design.
Figure ‎5.12. Linear electromechanical actuator which is used to actuate waist of the robot
69
Figure ‎5.13. Exploded view of the linear electromechanical actuator
5.4.4 Overall robot assembly
Figure 5.14 illustrates completed assembly of Duct-Sweeper in its fully retracted state. The
specifications of robot are listed in what follows.

Minimum length of the robot when all the wheels of the robot have contact with
substrate plane: 569.83 millimeters

Maximum length of the robot when all the wheels of the robot have contact with
substrate plane: 749.11 millimeters

Minimum height of the robot when all the wheels of the robot have contact with
substrate plane: 161.13 millimeters

Maximum height of the robot when all the suction cups have contact with substrate
plane and adhesion system leveling mechanisms are full extracted: 207.59 millimeters

Total weight of the robot (Excluding duct cleaning facilities, batteries and electronic
boards): 4670 grams
70
Figure ‎5.14. Completed design of Duct-Sweeper
71
Chapter 6
Path planning
This chapter focuses both on details about different transitions of the robot and use of these
transitions in order to pass different duct conditions. First, main transitions of the robot and
number of their deviations are discussed. Then, these transitions are used to pass the robot
through different paths of an arbitrary duct construction.
6.1 Transition schemes
Sample motions of each cart in Parallel Plane, Right Angle, Open Angle and number of other
transition are illustrated in Figure 6.1 to Figure 6.5. In all of these figures, a green triangle
beside each cart is used to illustrate activated adhesion of corresponding cart. Blue and
magenta lines are used to indicate motion path of carts A and B, respectively. The sequences
of steps are illustrated from left to right and from top to bottom. All these images are
produced by SolidWorks software using the designed prototype. To validate the design,
during each transition, collision between different parts of the robot with each other and with
duct surface are checked with corresponding tools that are available in SolidWorks.
One of the main transitions of the robot is Parallel Plane transition which is illustrated in
Figure 6.1. The following list presents details regarding each step of this transition.
1. Both carts are located on the source plane and are ready to start transition.
2. Cart A activates its adhesion system, and after achieving a secure adhesion, cart B
inactivates its adhesion (if it is already active). Then, cart A starts relocating cart B on
destination plane which is parallel to source plane.
3. Cart B activates its adhesion system and achieves a secure adhesion. Then, cart A
inactivates its adhesion system. Finally cart B relocates cart A on destination plane.
4. If the robot tends to fall due to gravitational forces, cart A activates its adhesion and
both carts keep their adhesions active until the next move of the robot.
72
The next main transitions of the robot are Right Angle and Open Angle transitions that are
illustrated in Figure 6.2 and Figure 6.3, respectively. The following list presents details
regarding each step of these transitions.
Figure 6.1. Scenes from Parallel Plane transition of the Duct-Sweeper
1. Both carts, that are located on the source plane, get close to the corner between source
and destination planes.
2. Cart A activates its adhesion system. Then cart B inactivates its adhesion (if it is
already active) to allow cart A start relocating it on destination plane.
3. If there is enough space for cart A left on destination plane, cart B activates its
adhesion and relocates cart A on the destination plane and goes directly to step 6.
Otherwise following steps are considered.
4. Cart B activates its adhesion system and moves cart A, which has inactivated its
adhesion, on the source plane toward destination plane.
5. Cart B inactivates its adhesion after the activation of cart A‟s adhesion. Then cart A
moves cart B away from source plane on the destination plane. And the process
repeats from step 3.
73
6. If robot tends to fall due to gravitational forces, cart A activates its adhesion and both
carts keep their adhesions active until the next move of the robot.
Figure ‎6.2. Scenes from Right Angle transition of the Duct-Sweeper
74
Figure ‎6.3. Scenes from Open Angle transition of the Duct-Sweeper
75
Thus far, three main transitions of the robot are covered. In what follows, the numbers of
other transitions that are derived from these main transitions are discussed. The following list
presents descriptions of different terms that are used in defining the state of the robot.

On-Plane: both carts are located on the same plane

Counter-Mode: the carts are pushed toward opposite planes via waist in order to
generate counter force on substrates and allow robot climb a vertical path using its
wheeled locomotion system.
Figure ‎6.4 illustrates a transition of the robot that transforms robot from On-Plane to CounterMode state.
Figure ‎6.4. Scenes from On-Plane to Counter-Mode transition of the Duct-Sweeper
The following list presents details regarding each step of the On-Plane to Counter-Mode
transition. This transition is composed of a number of steps that have formed Parallel Plane
transition.
1. Both carts are located on the source plane and are ready to start transition.
2. Cart B activates its adhesion system and after achieving a secure adhesion cart A
inactivates its adhesion (if it is already active). Then, cart B starts relocating cart A on
destination plane, which is parallel to source plane.
3. Both cart A and cart B activate their adhesions to secure the robot in its place.
76
4. Finally, both cart A and cart B lower their wheels on corresponding planes. Then
waist produces required force to keep the robots from falling. Finally, both carts
deactivate their adhesions and get ready to climb the duct with their wheeled
locomotion system.
The fourth DOF of the waist, which is rotation about zA axis, is required both for passing
through turns and during inchworm motion of the robot. Figure 6.5 Shows robot transition
from a turn with a hollow space in between. The following list presents details regarding each
step for passing a turn.
1. Both carts are located on the source plane.
2. Cart A activates its adhesion system and relocates cart B atop of itself.
After
adjustment of the zero moment point (ZMP) of the system inside the support convex
polygon of wheeled system of cart A, cart A inactivates its adhesion.
3. Cart A moves on the duct surface via its wheeled locomotion system until it gets
close to the turn. Then, it starts adjusting robot in an appropriate orientation to start
transition.
4. Once again cart A activates its adhesion and relocates cart B on the other side of the
turn. Then cart B activates its adhesion system.
5. Cart A inactivates its adhesion and cart B relocates cart A atop of itself. Then it
adjusts ZMP of the system to be located on its wheeled locomotion convex support
polygon.
6. Cart B moves forward to empty required space to land cart A.
7. Finally, cart B activates its adhesion and locates cart A on the duct surface.
77
Figure ‎6.5. Passing through a turn with hollow space in between
78
6.2 Transition combinations
To demonstrate the capability of the robot in passing through any duct condition, the duct
construction, illustrated in Figure 6.6, is considered. In this figure, each duct branch is
illustrated with olive green triangle and different paths between these branches are indicated
with different colors. Specifically, orange color is used to define common transitions of
different paths. The symbols and arrows used to define different transitions are defined in
Table 6.1.
1ft. 6in. x 1ft. 6in.
12in. x 12in.
4
1ft. 6in. x 1ft. 6in.
1
3
1ft. 6in. x 1ft. 6in.
2
6
7
10
1ft. 6in. x 1ft. 6in.
11
8
5
9
Figure ‎6.6. Passing through different conditions by combining basic transitions
Table ‎6.1. Definition of symbols used in Figure ‎6.6
Symbol
Definition
Moving with wheeled locomotion system both in horizontal and vertical ducts.
Note that, robot must be in Counter-Mode state before climbing vertical paths
via wheeled locomotion system.
79
Moving with inchworm motion profile. Robot can pass both vertical and
horizontal paths with inchworm motion. This motion type also provides
capability of moving on curved surfaces for the robot.
Both Right Angle and Open Angle transitions are indicated with this symbol.
Parallel Plane transition
This symbol represents On-Plane to Counter-Mode transition.
This symbol represents Counter-Mode to On-Plane transition.
As an example, consider the paths between duct branches #1 and #4. One of these paths is
indicated by green color while the other possible path is represented by blue color. Based on
the information presented in Figure 6.6, details about each of these paths are as follow:
Blue path: 1) robot uses its wheels to get close branch #2. 2) in order to pass the gap, it
performs an Open Angle transition, followed by a Parallel Plane and another Open Angle
transitions. 3) it continues its motion to get close to branch #3. 4) robot performs a Parallel
Plane transition to relocate itself on the upper plane of the duct. 5) to get into vertical duct, it
performs an Open Angle transition. 6) now the robot is in vertical duct; In order to climb the
duct with the wheels it performs an On-Plane to Counter-Mode transition. 7) robot climbs
vertical duct and curved portion until it reaches the horizontal duct. 8) it performs a CounterMode to On-Plane transition and continuous its motion to reach branch #4.
Green path: 1) robot performs a Parallel Plane transition to relocate itself on upper plane of
the duct. 2) robot moves like an inchworm until it reaches branch #3. 3) it performs an Open
Angle transition to relocate itself on vertical plane. 4) robot continuous its inchworm motion
80
until it reaches horizontal plane. 5) finally, it performs a Parallel Plane transition and uses its
wheels to finish the path.
81
Chapter 7
Conclusions and future works
The primary goal that motivated this thesis was proposing a robot to clean different air ducts
with different orientations. Towards this goal, available DCRs are reviewed to find out their
current capabilities, facilities and limitations. Since both moving in horizontal ducts and
climbing in vertical ducts are desired, most of the successful climbing robots, introduced in
the literature, are surveyed in order to select appropriate structure for the robot. These
reviews showed that a biped structure provides maximum dexterity with minimum number of
active DOF. In order to improve performance and speed of the biped structure, a hybrid
wheeled-legged structure is proposed to serve as the main structure of Duct-Sweeper.
After studying different conditions that robot may encounter in air ducts, number of required
active DOF of the robot‟s waist is selected to be 4. Furthermore, these studies are used to
define minimum workspace requirements of the waist. In order to increase payload capacity
of the waist and consequently decreasing the weight of the robot, a fully parallel waist
mechanism is desired to be employed in Duct-Sweeper. Unfortunately, many efforts taken to
find an appropriate parallel structure, which satisfies the number of DOFs and workspace
requirements of the waist of Duct-Sweeper, remained inconclusive. Authors have also
developed a novel parallel robot structure, but its singularity problems have remained
unsolved and prevent its usage as waist of Duct-Sweeper. Thus, a hybrid serial parallel
mechanism is proposed to serve as the waist of Duct-Sweeper.
Different materials used in duct construction and different adhesion systems are investigated
in order to find a reliable adhesion system. As a result of these studies, adhesion system based
on pressure difference, implemented by miniature vacuum pumps, directional valves and
suction cups, is selected to provide required adhesion for Duct-Sweeper. To further increase
the reliability of the system, different suction cup designs and materials are reviewed. Suction
82
cup model is chosen to be flat cup with cleats and its material is chosen to be Nitrile,
Neoprene or Polyurethane. Torsions and bending moments dramatically reduce performance
of suction cups. Grübler-Kutzbach mobility criterion is used to find minimum number of cups
required to provide stability of the robot without tolerating any torsion or bending moment.
Although this criterion proved that at least three cups are required, In order to increase the
reliability of the adhesion system, four suction cups are selected to be mounted on each cart.
A mechanism with 1 active and 6 passive DOFs is designed to adjust the heights of the
suction cups and consequently adjust the height of the robot. Each one of these mechanisms is
responsible for adjusting the height of two suction cups; therefore there are two mechanisms
employed in each cart. Independent actions of two mechanism of each cart compensate the
lateral effect which may be present in air ducts. Six passive DOFs of the mechanism allow
corresponding 2 suction cups passively adapt themselves with substrate surface.
Kinematic analysis of the robot is presented in chapter 4. In order to simplify this analysis,
parallel portion of the waist is modeled with an equivalent serial linkage; then, DH approach
is used to solve forward and inverse kinematics of the robot.
Considering worst case scenarios of adhesion system, a formula that defines the size of the
suction cups required based on the geometry and weight of the robot is proposed.
An optimization problem is defined in order to find optimal robot geometry for specific range
of duct sizes. Proposed optimization formulation takes into account constraints imposed by
different robot transitions, duct geometries and robot parts. The result of the proposed
optimization is used in prototype design of Duct-Sweeper. Different assemblies of the
prototype and their potential to serve as design patterns for other generations of the robot are
also discussed.
Finally, details of robot transitions are covered to indicate the ability of the robot in passing
different duct conditions with proposed structure. Also, as an example, usage of main
transitions of the robot in passing through a sample duct construction is discussed.
83
7.1 Future work
Although this thesis completely covers conceptual design of mechanical parts of the robot,
optimization and prototype design, control structure and electronic circuits of the robot are
not covered. The next step of the authors will be the design of electronic circuits and control
strategies to build real physical prototype of Duct-Sweeper.
84
Appendix‎A
Prove for mathematical declaration
In section ‎4.1.3.1, it is claimed that: if two out of three components of nonzero vectors cross
product are equal to zero, the third component will be zero as well. In order to prove this
claim two parametric vectors A = [AX, AY, AZ]T and B = [BX, BY, BZ]T are considered. The cross
product of these two vectors is equal to:
(
)̂
(
)̂
(
)̂
(A.1)
Consider A and B are defined in a way that make x and y components of A×B equal to zero.
Equating x component of the resultant vector to zero and solve to find AY yields to:
(A.2)
Substituting AY obtained from A.2 into z component of A.1 yields to:
(A.3)
The result obtained in A.3 is equal to y component of A×B. since y component of A×B is already
assumed to be equal to zero, z component of A×B is equal to zero. This finishes the proof of
declaration.
85
Appendix‎B
Robot geometry optimization code
The MATLAB code provided to solve robot geometry optimization problem consists of three
subroutines: “main_program”, “constraints” and “costfcn”. The “main_program” is the core
subroutine that calls optimization algorithm. This algorithm minimizes output value of
“costfcn” while satisfies constraints defined in “constraints” subroutine. The corresponding
code of each subroutine is presented in what follows.
main_program
%-------------------------------------------------------------------------%
Duct-Sweeper geometry optimization
%
%
Author: Siamak Ghorbani Faal
%
Sharif University of Technology - International Campus
%
2011
%-------------------------------------------------------------------------%% Initializations
clc; clear all; close all;
%% Choose optimization
%
1: fmincon
%
2: fmincon
%
3: fmincon
%
4: fmincon
%
5: Genetic
method = 1;
method method
- trust-region-reflective
- active-set
- interior-point
- sqp
Algorithm
switch(method)
case 1
fmincon_Algorithm
case 2
fmincon_Algorithm
case 3
fmincon_Algorithm
case 4
fmincon_Algorithm
end
= 'trust-region-reflective';
= 'active-set';
= 'interior-point';
= 'sqp';
%%
Declare global variables (Constant variables)
global M
global g
global P
global ws
global h_min
global h_max
global Lc
global F
global Ca
global Ce
global na
global ne
global u
global SFn
global SFt
global H
86
global offset
M = 5.0;
g = 9.81;
P = 0.8;
ws = 290;
h_min = 45;
h_max = 100;
Lc = 180;
F = 40;
Ca = 47;
Ce = 130;
na = 2;
ne = 3;
SFn = 2;
SFt = 4;
u = 1.0;
H = 350;
offset = 30;
%%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
Robot mass [Kg]
Gravitational acceleration [m/s^2]
Suction cup chamber pressure difference [bar]
Suction cups lateral distance [mm]
Minimum height of robot cart [mm]
Maximum height of robot cart [mm]
Maximum length of robot cart [mm]
Front portion of the cart [mm]
Constant length of actuator [mm]
Constant length of extra limb [mm]
Actuator elongation Coefficient
Extra limb elongation Coefficient
Normal loading safety factor
tangential loading safety factor
Coefficient of friction
Working duct section [mm]
Offset distance between suction cups [mm]
Start optimization
lb = [10 10 h_min h_min 10];
ub = [1000 1000 h_max h_max 1000];
disp('Selected Algorithm:')
if(method == 5)
disp('Genetic Algorithm')
options =
gaoptimset('CreationFcn',@gacreationlinearfeasible,'CrossoverFcn',@crossoverarithmetic
,'CrossoverFraction',0.1,'Display','iter','PopulationSize',1000,'PopulationType','doub
leVector','PlotFcns',@gaplotbestf );
[x,fval,exitflag] = ga(@costfcn,5,[],[],[],[],lb,ub,@constraints,options);
else
disp(fmincon_Algorithm)
%x0 = [82.5 110 51 51 250];
x0 = [100 90 50 50 150];
options = optimset('Algorithm',fmincon_Algorithm,'Display','iterdetailed','MaxFunEvals',1e6,'MaxIter',100,'PlotFcns',@optimplotfval,'AlwaysHonorConstr
aints','bounds');
[x,fval,exitflag,output,lambda,grad,hessian] =
fmincon(@costfcn,x0,[],[],[],[],lb,ub,@constraints,options);
end
%% Display Robot
h = figure();
test_equation(x)
%% Decode x
Ls = x(1);
as = x(2);
ha1 = x(3);
hb1 = x(4);
Sa = x(5);
%% Calculate dependent parameters
%-------------------------------------------------------------------------%
Variables depended to actuator
min_Ea = Ca+Sa;
max_Ea = Ca+na*Sa;
Lcm = max_Ea/2;
%-------------------------------------------------------------------------%
Variables depended to suction cups
ds_temp = sqrt( (SFn*M*g/(2*P))*max([(1+Lcm/Ls),((h_min+Lcm)/Ls),((h_min+Lcm)/ws)]) );
ds = 3.57*max([ds_temp, sqrt( (SFt*M*g/(4*P*u))*sqrt( (4*(Lcm+as)^2 + ws^2)/(Ls^2 +
ws^2) ) )]);
L = Ls+ds;
a = as+(ds/2);
%-------------------------------------------------------------------------%
Variables depended to extra limb
Se = min_Ea - Ce;
87
max_Ee = Ce + ne*Se;
%-------------------------------------------------------------------------%
Variables depended to open-angle-transition
xA1 = a-L;
yA1 = ha1;
xB1 = hb1;
yB1 = -a-sqrt(min_Ea^2 - (h_max-h_min)^2);
Line_m = (yB1 - yA1)/(xB1-xA1);
Line_b = -Line_m*xA1 + yA1;
xC = -Line_b/Line_m;
dC = abs(-Line_b/sqrt(Line_m^2 + 1));
Ea = sqrt( (xB1-xA1)^2 + (yB1-yA1)^2 );
Results = [ds max_Ea Ea xC dC];
%%
Show results
disp('=====================================================================');
disp('
Ls
as
ha1
hb1
Sa');
disp(x);
if(exitflag > 0)
disp(' -> Results are valid');
else
disp(' X) Results are invalid');
end
disp('---------------------------------------------------------------------');
disp('
ds
max_Ea
Ea
xC
dC');
disp(Results);
costfcn
function [ f ] = costfcn( x )
%-------------------------------------------------------------------------%
Cost function for Duct-Sweeper geometry optimization
%
%
Author: Siamak Ghorbani Faal
%
Sharif University of Technology - International Campus
%
2011
%
%
Input: Design variables (x)
%
Output: Cost value evaluated at x
%-------------------------------------------------------------------------f = x(5);
end
constraints
function [ cons, cons_eq ] = constraints( x )
%-------------------------------------------------------------------------%
Constraints function for Duct-Sweeper geometry optimization
%
%
Author: Siamak Ghorbani Faal
%
Sharif University of Technology - International Campus
%
2011
%
%
Input: Design variables (x)
%
Output: Equality (cons_eq) and Inequality (cons) constraints vectors
%
Optimization seeks the minimum cost function while it satisfies
%
following equations:
%
%
cons_eq(i) = 0
i = 1:length(cons_eq)
%
cons(i) <= 0
i = 1:length(cons)
%-------------------------------------------------------------------------%==========================================================================
88
%
Ls
as
ha1
hb1
Sa
Decode x
= x(1);
= x(2);
= x(3);
= x(4);
= x(5);
%==========================================================================
%
Declare global variables
global M
global g
global P
global ws
global h_min
global h_max
global Lc
global F
global Ca
global Ce
global na
global ne
global u
global SFn
global SFt
global H
global offset
%==========================================================================
%
Calculate dependant variables
%-------------------------------------------------------------------------%
Variables depended to actuator
min_Ea = Ca+Sa;
max_Ea = Ca+na*Sa;
Lcm = max_Ea/2;
%-------------------------------------------------------------------------%
Variables depended to suction cups
ds_temp = sqrt( (SFn*M*g/(2*P))*max([(1+Lcm/Ls),((h_min+Lcm)/Ls),((h_min+Lcm)/ws)]) );
ds = 3.57*max([ds_temp, sqrt( (SFt*M*g/(4*P*u))*sqrt( (4*(Lcm+as)^2 + ws^2)/(Ls^2 +
ws^2) ) )]);
L = Ls+ds;
a = as+(ds/2);
%-------------------------------------------------------------------------%
Variables depended to extra limb
Se = min_Ea - Ce;
max_Ee = Ce + ne*Se;
%-------------------------------------------------------------------------%
Variables depended to open-angle-transition
xA1 = a-L;
yA1 = ha1;
xB1 = hb1;
yB1 = -a-sqrt(min_Ea^2 - (h_max-h_min)^2);
Line_m = (yB1 - yA1)/(xB1-xA1);
Line_b = -Line_m*xA1 + yA1;
xC = -Line_b/Line_m;
dC = abs(-Line_b/sqrt(Line_m^2 + 1));
Ea = sqrt( (xB1-xA1)^2 + (yB1-yA1)^2 );
%-------------------------------------------------------------------------%
Variables depended to right-angle-transition
T = Lc-F;
yB2 = T+a+sqrt(min_Ea^2 - (h_max-h_min)^2) + Lc/10;
if(isreal(yB2)==0)
yB2 = 10^5;
end
%==========================================================================
%
Define constraints
CONS = [
Ls-Lc;
% g1:
-as;
% g2:
89
-Sa;
-Se;
h_min - ha1;
h_min - hb1;
ha1 - h_max;
hb1 - h_max;
ds - Ls + offset;
2*F - min_Ea;
Ea - max_Ea;
max_Ea - max_Ee;
-xC;
14 - dC;
yB2 - max_Ea - h_max;
min_Ea + 2*h_min - H;
H - max_Ea - 2*h_min;
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
g3:
g4:
g5:
g6:
g7:
g8:
g9:
g10:
g11:
g12:
g13:
g14:
g15:
g16:
g17:
];
cons_eq = [];
%-------------------------------------------------------------------------%
Correct constraints
for i=1:length(CONS)
if( CONS(i)==Inf || isnan(CONS(i)) || isreal(CONS(i))==0)
cons(i,1) = 1e+15;
else
cons(i,1) = CONS(i);
end
end
%==========================================================================
end
90
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