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].

Before cleaning After cleaning Variable Mean SD Mean SD Temperature a [C] 22.9 1.5 22.3 1.0 Relative humidity a [%] 32 15 25 15 Air flow [L/s/Person] 26.3 13.7 26.9 9.6 Ventilation rate [1/h] 2.3 1.3 2.4 1.0 Particle mass concentration [µg/m3] 6.5 4.1 7.6 4.0 Airborne viable microbes [cfu/m3] Fungi (MEA)b 43 50 23 20 Fungi (DG18)c 27 36 22 20 Bacteria (THG)d 27 30 64 95 Viable microbial count f [cfu/cm2] Fungi (MEA)b 8 10 2 3 Fungi (DG18)c 17 40 2 2 Bacteria (THG)d 1200 3500 5 7 TVOC e concentration [µg/m3] 73 46 66 79 a CO2 [ppm] 480 29 470 40 Dust deposition f [g/m2] 8.8 6.6 1.7 1.2 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.

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 Image

Indoor Environmental Inspector Robot III [18] Solutions, Inc.

Indoor Environmental Deluxe [18] Solutions, Inc.

OmniBot MI-6000 [19] LLOYD‟S systems

MicroInspector MI-180 LLOYD‟S systems [20]

ANATROLLER ARI-10 Robotics Design Inc. [21]

ANATROLLER ARI-50 Robotics Design Inc. [22]

6

ANATROLLER ARI- Robotics Design Inc. 100 [23]

Multi-Purpose Robot Danduct Clean [24]

Hanlim Mechatronics Co., XPW-301 [25] Ltd.

Hanlim Mechatronics Co., XPW-501 [26] Ltd.

Table ‎2.2. Locomotion system and physical properties of sample DCRs

Locomotion Speed Dimensions [mm] Weight Robot‟s Name System [m/s] Length Width Height [Kg] Inspector Robot III 4W INA 177.80 177.80 76.20 3.63 Deluxe Tracked / 4W 0.381 460 285 153 17.2* OmniBot MI-6000 4W INA 440 380 310 29* MicroInspector MI-180 4W INA 180 180 80 2.3 ANATROLLER ARI-10 2W 0.91 177.8 177.8 127 5 ANATROLLER ARI-50 Tracked 0.18 279.4 89 ~ 127 127 5 ANATROLLER ARI-100 Tracked / 4W 0.18 292.1 179 ~ 216 127 8 Multi-Purpose Robot 4W INA 303 ~ 760 300 145 10 ~ 21 XPW-301 4W INA 360 200 210 INA XPW-501 6W INA 460 210 390 INA * The whole package weight (Package: robot, duct cleaning facilities, control unit and casing) INA: Information Not Available W: Wheels

7

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.

Table ‎2.3. Facilities and tools available on the sample DCRs

Robot Name ng Brush

Air Whip

Spray Tip

Air nuzzle

Rear Light

Rotati

FrontLight

Rear Camera

FrontCamera

Internal battery

ToolAdjustment Recording Capability Hand Held Controller Duct cleaning tools Inspector Robot III             Deluxe      ?  M     OmniBot MI-6000     ?     ?   MicroInspector MI-180   ?  ?        ANATROLLER ARI-10     ?   M     ANATROLLER ARI-50     ?   ?     ANATROLLER ARI-100     ? ?     ?  Multi-Purpose Robot     ?        XPW-301   *  *        XPW-501   *  *        : 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

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.

Table 2.4. Specifications of the climbing robots under review.

Model

technology(s)

-

Reference

Bio

Transitions

Hybrid action

Active Active DOFs

Structure type

Robot‟s Name

Mechanism typeMechanism

Workplace Geometry Workplace Adhesion

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 Q1 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]

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] Untitled SF L2, WH46 S EMW WL ‒ RA, OA S [52] Alicia3 SF L2, WH6 S VC WL ‒ RA, OA 5 PX [53] 1 The robot‟s quadruped structure performs like a biped. 2 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.

. 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. Legged locomotion is not as efficient as wheeled locomotion [55].

II. 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 g Adhesion system

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 xB S zB xB -θzB B xA zA {B} {B} T θzB {A} B xA a yB a h A -θyA S yA {A} F L A

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 B xB S1 max Δx2 B zB θ3 zB H Δz1 Δz3 S3 max zA θ S2 max 2 Δz2 θ3 zA

zB xA xA B A A 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:

√( ) ( ) ( 3.9)

21

, ( 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

z yB B B

zA yA

xA A

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 Name Cup‟s name and its application

These cups are suitable for lightweight lifting applications. Flat suction cup Inexistence of cleats makes them highly flexible.

Cleats increase rigidity of the cup and allow it to lift heavy without the cup "peeling" away from the object surface or Flat cups with causing deformation in it. These cups are suitable for cleats 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 compensate for varying stack heights. When vacuum is Single-Bellows applied, the accordion-style bellows cup contracts like a cup 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 This cup acts similar to Single-Bellows cup, but it has larger cup stork for its prismatic action under vacuum.

31

These cups are used in handling objects with flat or slightly Universal cup 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. They are not recommended for flat surfaces. This design is Deep cup capable of handling objects over corners and edges and it is excellent for handling porous objects such as golf balls, etc.

Due to their small dimensions, these cups are perfect in Ultra-Miniature handling extremely small objects (e.g. computer chips, cup wafers and electronics components).

Rigid design of these cups makes them ideal for porous UH Rigid Cup 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

Shore A UV Abrasion Oil, Hardness Temperature Weather Material name Wear Grease (Durometer) Range (°C) Aging Resistance Resistance +/-5 Resistance Nitrile (Buna-N) 40 – 60 -40 to +110 ●●●● ●●●● ●●● Neoprene (Chloroprene) 40 – 60 -40 to +110 ●●●● ●●●● ●●● Polyurethane (Anverflex) 30 – 65 -25 to +180 ●●●● ●●●● ●●● Silicone (Translucent clear) 40 – 60 -70 to +316 ●●● ●●●● ●●●● Vinyl 30 – 70 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:

∑ (‎3.20)

Solving equation (‎3.20) and substituting ∑ 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 Suction cup joint

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.

θ4 x4

x3 z3

y4 z5 x5

z4 y3 y5

d3

z2 y2 θ2

C y1 z0 x2 x1

y0 θ1 x0

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 π/2 0 0 θ1

2 -π/2 C 0 θ2

3 -π/2 0 d3 -π/2

4 -π/2 0 0 θ4 5 -π/2 0 0 0

[ ] ( 4.1)

40

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)

( )

[ ] ( ) ( 4.3)

As discussed in [5], is the inverse of 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)

M The rotation matrix and distance between origins of {M} and {N} defined in {M} ( PN) are equal to:

[ ] ( 4.7)

* + ( 4.8)

41

푃 푁푥 푁 yN ⬚푃 푁 푃 푁푦 푃 푁푧 푃 푀푥 푀 S ⬚푃 푀 푃 푀푦 2 {N} xN 푃 푀푧

yM φ d3

xM {M} S1

푃 푁푥 푁 ⬚푃 푁 푃 푁푦 푃 푁푧 푃 푀푥 푀 ⬚푃 푀 푃 푀푦 푃 푀푧

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 , which is previously defined in ( 4.3), into ( 4.16) yields to: 43

( ) ( ) ( ) ( 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 . Equating

PBx, PBy and PBz with corresponding components of 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. Solve ( 4.30) using desired position of cart B and calculate θ1.

II. 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

V. Use ( 4.9) and ( 4.10) to convert d3 and θ2 to S1 and S2.

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)

0 0 0 0 In ( 4.32), Px, Py and Pz are three components of P 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)

i i In these equations, ωi and vi represent angular and linear velocities of coordinate system {i},

respectively. Rotation matrix that maps coordinate system {i} to {i+1} is indicated by .

i Distance between origins of {i} and {i+1} that is defined in {i} is indicated by Pi+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 Ff Fb Ff

Mg LS LCM Mg Case 2

LCM LCM Ff Fb Ff Fl

Mg wS bCM Fr

Mg Fb Mg Case 3 h Case 4 h Case 5

LS ff

ff fb wS

Mg fb 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 퐹 퐹 α 3 퐹 퐹 퐹 Le y 퐹 퐹 α2 퐹 퐹 푦̅ 퐹 퐹 x

Mg

퐹 α4 푥̅

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 cross- section, 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 Duct-

Sweeper 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(E ) = C + n S e e e e 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.

dc hA1 (x , y ) y A1 A1 y

x x

hB4 hA2 h (xc ,0) B3 min(Ea) (xB3 , yB3)

Ea min(Ea) (xB1 , yB1)

Ea

hA3 y y hA4 hB1 x x

h (x , y ) B2 A3 A3 Figure ‎5.5. Two critical transitions of robot and the parameters used to define their constraints

57

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)

| | ( 5.18)

√

√( ( )) ( ( ) ( )) ( 5.19)

Constraints:

g1: g2: g3: g4: g5: ( ) g6: ( ) g7: ( ) g8: ( )

60

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.

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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 a (mm) (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 Height (mm) (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 lead- screw 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 Extra-

Limb 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 Duct-

Sweeper. 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

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Figure ‎5.14. Completed design of Duct-Sweeper

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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.

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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

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Figure ‎6.3. Scenes from Open Angle transition of the Duct-Sweeper

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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 Counter-

Mode 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.

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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.

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Figure ‎6.5. Passing through a turn with hollow space in between

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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 2 3 . n i 6

6 . t f 1

x

. n i 6

. t f 7 10 1 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.

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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 Counter-

Mode 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.

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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.

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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.

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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

T T claim two parametric vectors A = [AX, AY, AZ] and B = [BX, BY, BZ] 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.

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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 method method % 1: fmincon - trust-region-reflective % 2: fmincon - active-set % 3: fmincon - interior-point % 4: fmincon - sqp % 5: Genetic Algorithm method = 1; switch(method) case 1 fmincon_Algorithm = 'trust-region-reflective'; case 2 fmincon_Algorithm = 'active-set'; case 3 fmincon_Algorithm = 'interior-point'; case 4 fmincon_Algorithm = 'sqp'; end

%% 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; % Robot mass [Kg] g = 9.81; % Gravitational acceleration [m/s^2] P = 0.8; % Suction cup chamber pressure difference [bar] ws = 290; % Suction cups lateral distance [mm] h_min = 45; % Minimum height of robot cart [mm] h_max = 100; % Maximum height of robot cart [mm] Lc = 180; % Maximum length of robot cart [mm] F = 40; % Front portion of the cart [mm] Ca = 47; % Constant length of actuator [mm] Ce = 130; % Constant length of extra limb [mm] na = 2; % Actuator elongation Coefficient ne = 3; % Extra limb elongation Coefficient SFn = 2; % Normal loading safety factor SFt = 4; % tangential loading safety factor u = 1.0; % Coefficient of friction H = 350; % Working duct section [mm] offset = 30; % 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','iter- detailed','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

% Decode x Ls = x(1); as = x(2); ha1 = x(3); hb1 = x(4); Sa = 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; % g3: -Se; % g4: h_min - ha1; % g5: h_min - hb1; % g6: ha1 - h_max; % g7: hb1 - h_max; % g8: ds - Ls + offset; % g9: 2*F - min_Ea; % g10: Ea - max_Ea; % g11: max_Ea - max_Ee; % g12: -xC; % g13: 14 - dC; % g14: yB2 - max_Ea - h_max; % g15: min_Ea + 2*h_min - H; % g16: H - max_Ea - 2*h_min; % 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

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