MODELING AND CONTROL OF BOUNCING MECHANISM FOR SPHERICAL MOBILE ROBOT
USING PSO-PID ALGORITHM
BY
MUHAMMAD AMIRUL BIN ABDULLAH
A thesis submitted in fulfillment of the requirement for the degree of Master of Science (Mechatronics Engineering)
Kulliyyah of Engineering
International Islamic University Malaysia
JULY 2018
ii
ABSTRACT
Mobile robots are widely used in a variety of nonindustrial applications, such as security surveillance, search and rescue, children education, and entertainment. Spherical mobile robots are much more robust compared to conventional mobile robots and exhibit number of advantages with respect to wheeled and legged mechanisms. Spherical mobile robot that can bounce/jump will produce excited phenomena that can be contributed to applications such as security surveillance, search and rescue. This is partly due to its manoeuvrability in uneven terrain and harmful environment. However, the dynamics of spherical robot with bouncing mechanism can be described by highly complex nonlinear equations, which is difficult to be dealt with. Many of the modeling approaches before have come out with mathematical equations which assumptions made that can restrict the actual performance of the nonlinear system. This study embarks on the design, development and control of a jumping spherical robot. The study was initiated with 3D modelling using modern tool, i.e. Solidwork. The steps continued with a systematic optimization technique where the material, diameter and number of spokes were optimized. Subsequently, the hardware of the robot was developed based on the optimized parameters. The open loop experimental performance analysis was conducted to observe its performance. It was observed that the developed robot is able to jump 94 mm which is 39.17% from its diameter. An empirical model was developed to quantify the maximum height attainable upon compressing the robot at a certain amount. From the data obtained, a jumping model for the designed spherical robot was derived and the model was further used for control simulation. In the simulation performance analysis, a closed loop positional control simulation was evaluated through classical control architecture namely P, PI, PD and PID. It was established that the PID controller works best in controlling the servo angle with the least steady-state error which is the performance criteria set. The capability of a metaheuristic optimisation technique i.e. Particle Swarm Optimisation (PSO) was further implemented in tuning the PID control gains to obtain better steady-state error results. Results show that PID PSO-optimised gains has produced a much better result which is having improvement of 99.86% in rise time and 99.16% in settling time compared to the classical PID controller.
iii
ا ةصلاخ ثحبل
رلما تاقيبطت في لثمتت ،ةيعانص يرغلا تاقيبطتلا نم يرثك في يربك لكشب ةلقنتلما تتاوبورلا مدختست ةبقا
ةردق يوركلا لكشلا تاذ ةلقنتلما تتاوبورلا كلتتم .ةيلستلاو لافطلاا ميلعت ،ذاقنلااو ثحبلا ،ةينملأا انها امك ةيديلقتلا لقنتلا تتاوبور عم ةنراقلمبا ةيلاع دومص م ةنراقلمبا دئاوفلا نم اددع ضرعت
تاوذ ع
نم ةيرثم رهاوظ جتنت فوس دادترلاا/زفقلا عيطتست تيلا ةيوركلا تتاوبورلا .تلاجعلا تاوذو لجرلأا تائيبلا في ةروانلما ىلع ةردقلا ببسب ،ذاقنلااو ثحبلا ،ةينملأا ةبقارلما تاقيبطتل فيضت نأ نكملما لما ةعونتم نم ةيوركلا تتاوبورلل دادترلاا اكيناكيم فلخ ةيكامنيدلا ،كلذ عم .سيراضتلا ةيوتسم يرغو
لبق .اهعم لماعتلا بعصلا نم تيلاو ،ديقعتلا ةديدش ةيطخ يرغلا تلاداعلما قيرط نع اهفصو نكملما له ًانكمم ناك تاضاترفا تكلتما ةيضيارلا اتهلاداعم عم ميمصتلا بيلاسا نم يرثك اهروهظ ءادلأا حدُحتَ نأ ا
.زفاق يورك توبورل ريوطتلاو مكحتلا ،ميمصتلا ىلع عرشت ةساردلا هذه .ةيطلخا يرغ ةمظنلأل يلعفلا ( ،ةثيدح ٍةادأ مادختسبإ داعبلأا يثلاث ٍميمصت عم تًأِدُتبِإ ةساردلا (Solidwork
.لاثلما ليبس ىلع
تي ثيح ةجهنمم ٍينستَ ةينقت عم كلذ دعب تاوطلخا عباتتت لا ،ةدالما لماوع ينستَ اهيف م
ددعو رطق
تاننسلما .
ءادلأ يبرخلما ليلحتلا .ةنسلمحا لماوعلا ىلع دامتعلابا توبورلا تادعم ريوطت متي كلذ دعب
ولعل زفقلا ىلع رداق ثدلمحا توبورلا اذه نأ ةظحلام تم دقل .ءادلأا ةنياعلم تم دق ةحوتفلما ةقللحا 94
مم
نىعبم 39.17%
رطق ةعس نم للاخ نم هزارحا نكملما ىصقلأا ولعلا باسلح بييرتج ميمصت ريوطت تم .ه
ممصلما يوركلا توبورلا نم ةزفاق ةخسن ميمصت تم ةلصلمحا تناايبلا نم .ينعم ردقل توبورلا ضيرعت مكحتلا مييقت تم ةاكالمحا ءادأ ليلتَ للاخ .كلذك مكحتلا ةاكامح في بركا لكشب ميمصتلا مدختساو لل يعضولما ةامسم ةيديلقت مكتَ نىب للاخ نم ةقلغلما ةقلح
(P, PI, PD, PID) نأ ظحول دق .
مكحتم PID وه اذهو ةدشب ةضفخنلما تابثلا تلااح ءاطخأ عم وفيرسلا ةيوازب مكحتلا في لضفلأأ
( يئزلجا داشتحلاا ينستَ لثم ايلعلا ةللادلا ينستَ ةينقت ةردق نإ .هطبض تم يذللا ءادلأا لماع PSO
)
دق ( مكحتم في تافعاضلما ةنزاولم قمعأ لكشب اهمادختسا تم PID
نم لضفأ جئاتن ىلع لوصحلل )
ةبسنب لضفأ جئاتن بركأ لكشب تجتنأ نسلمحا مكحتلما تافعاضم نأ تبثت جئاتنلا .تابثلا تلااح اهردق نستَ
99.86%
و ةعفترلما تارملل 99.16%
يديلقتلا مكحتلما عم ةنراقلمبا ةضفخنلما تارملل
نسلمحا يرغ
.
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APPROVAL PAGE
I certify that I have supervised and read this study and that in my opinion, it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a thesis for the degree of Master of Science (Mechatronics Engineering)
………..
Salmiah Bt. Ahmad Supervisor
………..
Siti Fauziah Bt. Toha @ Tohara Co-Supervisor
I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a thesis for the degree of Master of Science (Mechatronics Engineering)
………..
Internal Examiner
………..
External Examiner
This thesis was submitted to the Department of Mechatronics Engineering and is accepted as a fulfillment of the requirement for the degree of Master of Science (Mechatronics Engineering)
………..
Syamsul Bahrin Abdul Hamid Head, Department of
Mechatronics Engineering
This thesis was submitted to the Kulliyyah of Engineering and is accepted as a fulfillment of the requirement for the degree of Master of Science (Mechatronics Engineering)
………..
Erry Yulian Triblas Adesta Dean, Kulliyyah of Engineering
v
DECLARATION
I hereby declare that this thesis is the result of my own investigations, except where otherwise stated. I also declare that it has not been previously or concurrently submitted as a whole for any other degrees at IIUM or other institutions.
Muhammad Amirul Bin Abdullah
Signature ... Date ...
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COPYRIGHT PAGE
INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
DECLARATION OF COPYRIGHT AND AFFIRMATION OF FAIR USE OF UNPUBLISHED RESEARCH
MODELING AND CONTROL OF BOUNCING MECHANISM FOR SPHERICAL MOBILE ROBOT USING PSO-PID
ALGORITHM
I declare that the copyright holders of this thesis are jointly owned by the student and IIUM.
Copyright © 2018 Muhammad Amirul bin Abdullah and International Islamic University Malaysia.
All rights reserved.
No part of this unpublished research may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without prior written permission of the copyright holder except as provided below
1. Any material contained in or derived from this unpublished research may be used by others in their writing with due acknowledgement.
2. IIUM or its library will have the right to make and transmit copies (print or electronic) for institutional and academic purposes.
3. The IIUM library will have the right to make, store in a retrieved system and supply copies of this unpublished research if requested by other universities and research libraries.
By signing this form, I acknowledged that I have read and understand the IIUM Intellectual Property Right and Commercialization policy.
Affirmed by MUHAMMAD AMIRUL BIN ABDULLAH
……..……….. ………..
Signature Date
vii
ACKNOWLEDGEMENTS
Firstly, it is my utmost pleasure to dedicate this work to my dear parents and my family, who granted me the gift of their unwavering belief in my ability to accomplish this goal:
thank you for your support and patience.
I wish to express my appreciation and thanks to those who provided their time, effort and support for this project. To the members of my dissertation committee, thank you for sticking with me.
Finally, a special thanks to my supervisor Associate Professor Dr. Salmiah Ahmad and co-supervisor Associate Professor Dr. Siti Fauziah Toha @ Tohara for their continuous support, guidance and encouragement, and for that, I will be forever grateful. Not forgetting, the members of the Innovative Manufacturing, Mechatronics and Sports (iMAMS) Laboratory, UMP for making the end of my Master’s study a breeze.
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TABLE OF CONTENTS
Abstract ... ii
Approval Page ... iv
Declaration ... v
Copyright Page ... vi
Acknowledgements ... vii
Table of Contents ... viii
List of Tables ... x
List of Figures ... xi
CHAPTER ONE: INTRODUCTION ... 1
1.1 Research Background ... 1
1.2 Problem Statement And Its Significance ... 2
1.3 Research Scope ... 2
1.4 Research Objectives... 2
1.5 Research Methodology ... 3
1.6 Research Contributions ... 4
1.7 Thesis Organization ... 5
CHAPTER TWO: LITERATURE REVIEW ... 6
2.1 Introduction... 6
2.2 Spherical Mobile Robots ... 6
2.3 Existing Literature On Spherical Mobile Robots ... 7
2.4 Summary And Research Gap... 15
CHAPTER THREE: METHODOLOGY ... 16
3.1 Introduction... 16
3.2 3d Modelling Of Spherical Mobile Robot ... 17
3.3 Optimization Of Jumping Spherical Mobile Robot ... 17
3.3.1 Parameters For Mechanical Design Optimization ... 19
3.3.2 Simulation Setup ... 20
3.4 Hardware Fabrication ... 23
3.4.1 Compressive Deflection Mechanism Design ... 23
3.4.2 Experimental Setup ... 25
3.5 Controler Design And Optimization ... 26
CHAPTER FOUR: RESULTS AND DISCUSSION ... 29
4.1Introduction ... 29
4.23d Modelling Of Spherical Mobile Robot ... 29
4.3Mechanical Design Optimization Evaluation ... 32
4.4Hardware Fabrication ... 36
4.4.1 Mechanism Of Rolling And Jumping ... 38
4.4.2 Compressive Deflection Analysis ... 39
4.4.3 Empirical Model Of Compressive Deflection ... 40
4.5Classical Control Performance ... 42
ix
CHAPTER FIVE: CONCLUSION AND RECOMMENDATION ... 53
5.1Conclusion ... 53
5.2 Recommendation ... 53
REFERENCES ... 55
APPENDIX A: PUBLICATIONS ... 57
APPENDIX B: PATENT ... 57
x
LIST OF TABLES
Table 2.1 Characteristics of the various developed spherical robots for
rolling mechanism. (Chen, Chen, Yu, Lin, & Lin, 2012) 7 Table 4.1 Bill of material for the spherical mobile robot 32
Table 4.2 Optimized parameter 35
Table 4.3 Experimental measurement of compression deflection and
maximum jumping height 41
Table 4.4 Conventional PID tuning values 44
Table 4.5 Conventional PID Tuning Performances 44
Table 4.6 PID-PSO tuning values 50
Table 4.7 PID-PSO tuning performances 51
Table 4.8 Performances comparison between non-optimized PID gains with
PSO-PID 52
xi
LIST OF FIGURES
Figure 1.1 Flowchart of research methodology 4
Figure 2.1 OmniQiu by Chen et al. (2012) 8
Figure 2.2 BYQ-V by Qingxuan et al. (2009) 10
Figure 2.3 HIT by Ming et al. (2006) 11
Figure 2.4 SpheRobot by Pokhrel et el. (2013) 12
Figure 2.5 Pioneer of rolling spherical robots developed by Halme et al. (1996) 13 Figure 2.6 Spherical mobile robot with dual pendulum configuration by
Mahboubi et al. (2012) 13
Figure 2.7 Spherical mobile robot with quadraple pendulum by Mahboubi et al.
(2012) 14
Figure 3.1 3D base model of spherical mobile robot 17
Figure 3.2 Flowchart of optimization of bouncing spherical mobile robot 18 Figure 3.3 SimMechanics model of jumping spherical mobile robot 21 Figure 3.4 Simulink model of jumping spherical mobile robot 22 Figure 3.5 Corresponding SimMechanics model as Simulink submodel 22
Figure 3.6 Section view of the jumping mechanism 23
Figure 3.7 Jumping mechanism represented in slider-crank mechanism 24
Figure 3.8 Capture motion of the experiment 25
Figure 3.9 Control simulation model 26
Figure 4.1 3D model of spherical mobile robot 30
Figure 4.2 Exploded view of spherical mobile robot with annotations 31 Figure 4.3 Maximum bouncing height for different material of spokes versus
initial height 33
Figure 4.4 Maximum bouncing height for different number of spokes versus
initial height 34
xii
Figure 4.5 Maximum bouncing height for different diameter size of spokes
versus initial height 35
Figure 4.6 Front view of the fabricated spherical mobile robot 36 Figure 4.7 Side view of the fabricated spherical mobile robot 37 Figure 4.8 Electrical system of spherical mobile robot 37
Figure 4.9 Rolling motion of spherical mobile robot 38
Figure 4.10 Steering motion of spherical mobile robot 38 Figure 4.11 Jumping initiation of spherical mobile robot 39 Figure 4.12 Compressive deflection relationship with the servo angle 40 Figure 4.14 Empirical model of the compressive deflection and maximum
jumping height behavior 41
Figure 4.15 Overview of Simulink model to predict the spherical mobile robot
jump height 42
Figure 4.16 Servo motor control model 42
Figure 4.17 Forward kinematics model 43
Figure 4.18 Jump prediction model 43
Figure 4.19 Servo motor control response using PI controller 45 Figure 4.20 Servo motor control response using PD controller 45 Figure 4.21 Servo motor control response using PID controller 46 Figure 4.22 Servo motor control response comparison using P, PI, PD, and PID
controller 46
Figure 4.23 Convergence of the best controller gains Kp 47 Figure 4.24 Convergence of the best controller gains Ki 48 Figure 4.25 Convergence of the best controller gains Kd 48 Figure 4.26 Least mean-squared error at swarm size of 15 49 Figure 4.27 Servo motor control response using PSO-PID controller 51 Figure 4.28 Servo motor control response comparison using PID and PSO-PID
controller 52
1
CHAPTER ONE INTRODUCTION
1.1 RESEARCH BACKGROUND
In this day and age, mobile robots are extensively used in a variety of both industrial and nonindustrial applications. Mobile robots are often used where human intervention are undesirable i.e. hazardous environment and beyond human reach. Mobile robots may be broadly classed into land-based mobile robots, underwater vehicles and unmanned aerial vehicles that are used both for civilian and military purpose. According to the International Federation of Robotics, as of 2016, there are approximately 3,410 and 15,515 land based mobile robots are used in the manufacturing and non- manufacturing environments, respectively. The common types of land-based mobile robots are the wheeled and legged robots. Nonetheless, spherical robots have recently gained due attention due to its apparent advantages over the aforementioned conventional land-based mobile robots.
Spherical robots are more robust in changing its direction and navigating around obstacles as compared to wheeled robots. Furthermore, it does not fall over in the event it moves on uneven terrain, unlike wheeled and legged mechanism. The mechanism of motion for spherical robots may be demarcated into two namely rolling and bouncing/jumping. Most research conducted in the literature focusses on either pure rolling or pure bouncing. Limited number of research that has embarked on the integrating both mechanisms. This is inherently due to the highly complex nonlinear behaviour of such system. Most research on spherical robots in general delves into the development and design of the system but not on the control architecture of the system.
2
1.2 PROBLEM STATEMENT AND ITS SIGNIFICANCE
Spherical mobile robots may overcome the limitations of existing wheeled and legged based mobile robots in navigating around obstacles and traverse on uneven terrain.
However, owing to the highly complex nonlinear behaviour of spherical robots, the control of such system is non-trivial. Therefore, this study is significant in contributing to the body of knowledge by investigating the efficacy of the proposed control algorithm in performing a jumping motion. It is also worth to note that the design itself is novel in comparison to existing spherical mobile robots.
1.3 RESEARCH SCOPE
This study investigates the design and control of a jumping spherical mobile robot. The mechanical design of the robot is the highlight of this research. A simulation study is performed by examining the efficacy of the proposed controller i.e. Particle Swarm Optimised (PSO) based (Proportional-Integral-Derivative) PID as compared to classical PID control algorithm in achieving sound positional control of the servo motor.
1.4 RESEARCH OBJECTIVES
The study aimed to achieve the following objectives:
1. To perform 3D modelling and optimize the design of spherical mobile robot.
2. To fabricate of spherical mobile robot and conduct experimental performance analysis.
3. To design a PID-PSO controller and conduct simulation performance analysis
3 1.5 RESEARCH METHODOLOGY
In order to achieve the objectives of the research, the following procedures were employed. The flowchart of the process is provided in Figure 1.1.
1. Literature review
- Exhaustive review on existing literature on the design, modelling and control of spherical mobile robots.
2. Design and development of the spherical mobile robot
- Design and optimise the design of the robot via Solidworks.
Hardware realisation of the design is also conducted.
3. Data-driven modelling
- A data-driven/empirical model of the dynamic behaviour of the robot whilst jumping is identified via experimental works.
4. Performance analysis of the classical PID and PSO optimised PID on the fusion model.
- The performance of the PID tuned and PSO-PID tuned parameters on the model in controlling the servo motor angle that in turn controls the compressive deflection of the robot and predicting the maximum jump height of the robot upon launch.
4
Figure 1.1 Flowchart of research methodology
1.6 RESEARCH CONTRIBUTIONS
The contributions of the research can be underlined as the following:
1. A design and hardware development of the spherical mobile robot that jumps.
2. Empirical model of the dynamic jumping behaviour of the robot.
3. The employment of PSO in tuning the PID parameters to obtain desirable controller response.
Start
Literature review on existing design, modelling and control of spherical mobile robots
Design and optimization the design of the robot
Fabrication of the spherical mobile robot
Data-driven and empirical modelling whilst jumping
Performance analysis of classical PID and PSO- optimized PID tuned parameters on the model
End
5 1.7 THESIS ORGANIZATION
The thesis consists of five chapters and is organised as follows:
CHAPTER ONE: The overview of the research is briefly explained in this chapter. It begins with the introduction of the study and followed by the problem statement as well as the significance of the research. The objectives, the scope of research, the methodology as well as its contribution are also highlighted. The chapter concludes with the list of achievements of the present study.
CHAPTER TWO: Existing literature on the design and control of spherical robots are extensively reviewed in this chapter. Through the review, the gaps of the present research are identified.
CHAPTER THREE: This chapter elaborates on the mechanical design as well as the hardware integration of the system. The modelling, as well as the plant identification, are also presented
CHAPTER FOUR: This chapter evaluates the performance of the tuned controller parameters on the fusion model developed.
CHAPTER FIVE: Conclusions are drawn, and recommendations on future works are outlined in this chapter.
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CHAPTER TWO LITERATURE REVIEW
2.1 INTRODUCTION
In this chapter, an extensive literature survey is conducted by examining existing design of spherical robots, the modelling as well the control architecture employed on such land-based mobile robots. The gaps for the present study are also identified.
2.2 SPHERICAL MOBILE ROBOTS
A sphere is a unique shape where the set of all points in three-dimensional space lying the same distance – radius, for a given point – centre. It can freely rotate about any axis of rotation. In terms of robotics, a spherical structure can freely rotate in any direction, and stable at all positions.
The principle of mobility for a sphere is generally based on the movement of its centre of gravity (cog) inside the spherical shell. The further the cog is from the centre, the greater the driving force that can initiate rolling. The development of ball-shaped object began as early as 1889 in the form of a simple mechanical toy, but the first prototype and research built of a modern spherical robot only came into being in 1996 (Halme, Schonberg, & Wang, 1996). The different type of configuration for rolling spherical robots as well as its Inside Drive Unit (IDU) is tabulated in Table 1.
Conversely, to date limited literature that investigates spherical robots that bounce solely due to its deformable frame i.e. without the assistance of additional accessories that defies the definition of a sphere.
7
Table 2.1 Characteristics of the various developed spherical robots for rolling mechanism. (Chen, Chen, Yu, Lin, & Lin, 2012)
Robot Configuratio
n Single
wheel
Hamster car
Pendulum on rotating axis
Gimbal Single ball Driving
Mechanism
Direct- driving
Direct- driving
Direct- driving
Direct- driving
Direct- driving
DOF 2 2 2 2 2
Robot Configuratio
n Omni
wheels
Mass movement
Orthogonall y mounted flywheels
Flywheel on
pendulum
Parallelly mounted flywheels Driving
Mechanism
Direct-
driving Gravity Angular momentum
Direct- driving / Angular momentum
Angular momentum / Gravity
DOF 3 2 2 2 2
2.3 EXISTING LITERATURE ON SPHERICAL MOBILE ROBOTS
Research with regards to spherical mobile robots are often focussed either on the hardware development of the robots and/or to a certain extent, the control of such devices. Wei et al. (2013)built a single pendulum with dual extended wheels spherical robot (BYQ-X) that is able to perform conventional rolling motion in its folding mode and climbing when it is in its unfolding mode (Wei, Han-Xu, Qing-Xuan, Yan-Heng,
& Tao, 2013). ADAMS was used to simulate the performance of the folding and unfolding modes of the BYQ-X on uneven terrain. Experimental works were conducted
8
to validate the performance of the simulation study. However, it is worth to note that the control algorithm employed was not disclosed.
OmniQiu developed by the National Taiwan University is novel omnidirectional roll-based spherical robot (Chen, Chen, Yu, Lin, & Lin, 2012). Its driven ball is governed by two orthogonally-mounted rollers. The dynamics of the robot that is based on a simplified planar model is derived by means of the Lagrangian equation whilst the effects of the modelling parameters are simulated and evaluated. From the open loop simulation study it was discovered that the forward velocity of the robot is approximately proportional to the input voltage of the motors.
Figure 2.1 OmniQiu by Chen et al. (2012)
Jaminez et al. (2012) developed a spherical mobile robot dubbed as the Omnibola (Jaimez, Castillo, García, & Cabrera, 2012). The robot is designed to have a low cog to ensure exceptional stability. Furthermore, it is worth to note that it is driven by two wheels positioned on top that are always in contact with its shell. The Newton- Euler formulation is used in investigating the dynamics of the system. Matlab is used to simulate the dynamic effect of the system, and it was observed that the system is unstable at increased speed. Therefore, the authors employed a pure derivative (D) control architecture to attenuate the system. The closed-loop simulation study suggests
9
that the system that the D controller is apt in correcting the roll angle from straight to curved movement as well as compensating disturbances in a straight motion.
A barycentre offset based spherical robot, BHQ-3 was developed by Zhan et al.
(2012) (Cai, Zhan, & Xi, 2012). A number of kinematics analysis were performed by taking into consideration different scenarios, namely moving straight, turning, climbing an inclined slope as well as surmounting obstacle. A circular and linear trajectory simulations were also carried out by investigating the effect of noise towards trajectory error. The controllability of the system was also assessed, however, it is noteworthy to mention that the controller selection was not discussed.
Qingxuan et al. (2009) carried out a simulation and experimental study on an omni-directional rolling spherical robot that is equipped with a high-rate flywheel known as the BYQ-V (Qingxuan, Yili, Hanxu, Hongyu, & Hongyi, 2009). The dynamics of the system was derived by means of the Lagrangian by considering some simplification of the model as well as linearizing it. A proportional-derivative (PD) control architecture was utilised to regulate the velocity of the robot, whilst a Linear Quadratic Regulator (LQR) controller is used to control the pose of the robot. It was observed that the tuned parameters obtained via the simulation work produces acceptable results on the actual system. Nevertheless, the authors implied that the effectiveness of the control law rely on the ‘soundness’ of the model.
10
Figure 2.2 BYQ-V by Qingxuan et al. (2009)
HIT is a spherical robot that is governed by the flywheel on pendulum configuration that employs the decoupling of the turning and driving a head motion (Ming, Zongquan, Xinyi, & Weizhen, 2006). The dynamic model developed through the Lagrangian formulation adheres to the decoupled actual system. A Rayleigh dissipation function was introduced to simulate the effect of viscous damping that exist between the bearing and the turning motor of the actual system. Only the open loop simulation response of the system with respect to the aforementioned motions in terms of angular displacement as well as its angular velocity are examined.
11
Figure 2.3 HIT by Ming et al. (2006)
Alves and Dias (2003) investigated on the control of a four wheeled hamster car driven rolling spherical robot on a curvature path (Alves & Dias, 2003). The Newton- Euler equations of motion were employed in modelling the system. The proportional (P) controller tuned based on the modelling is used in the study and it was observed that the hardware’s response reasonably tracks the desired angle of inclination.
An analytical investigation was performed by Bhattacharya and Agrawal (2000) on a spherical rolling robot that is driven by two internally mounted motors (Bhattacharya & Agrawal, 2000). The model is based on nonholonomic constraints on its motion that is employed to the Newton-Euler representation of the Angular- Momentum Conservation. A first-order (state-space) robot dynamics model was derived from it. A number of feasibility simulations were carried out on the open-loop dynamics of the system.
SpheRobot was developed under the notion of the inverted pendulum principle (Pokhrel, Luitel, Das, & Ray, 2013). The Lagrangian was adopted in obtaining the dynamic model on the system. An open-loop assessment on the spinning and swinging angular displacement and angular velocity, respectively was performed. A simple
12
forward-reverse motion test was also employed in order to assess the stability of the robot under different terrain conditions.
Figure 2.4 SpheRobot by Pokhrel et el. (2013)
Bicchi et al. (1997) performed a simulation study of a three wheeled hamster car driven spherical robot (Bicchi, Balluchi, Prattichizzo, & Gorelli, 1997). A quasi-static kinematic model was fed in to the Langrangian formulation to derive the dynamics of the system. The controllability of the state-space model developed was also assessed and classical linear feedback controllers are proposed for further investigation on the closed-loop response of the model.
Amongst the pioneers of rolling spherical robots is Halme et al. (1996) (Halme et al., 1996). The IDU of the system is moved by a motor driven wheel. The Newton- Euler method was utilised for developing the dynamic model of the system. The study performed open-loop simulation of the dynamic model whilst proposing speed and distance rule based control architecture for their future work.
