Underactuated single wheeled mobile robot mimicking a human ridden unicycle 1

Research on single-wheeled robots is driven by several factors including 1 the inves-tigation of nonlinear and unstable dynamics [68]; 2 the emulation of human intelli-gence [71]; 3 the

Chapter 1

Introduction

In recent years, single-wheeled robots and single-wheeled vehicles have gained a lot of

attention Several companies have developed single-wheeled platforms and demonstrated

their functionality They were introduced to the market as either toys or modes of

personal transports Murata Girl (Fig 1.1), developed by Murata Manufacturing Co.,

Ltd., was marketed as a toy [6] Honda Motor Co., Ltd., on the other hand, developed

U3-X (Fig 1.2), a personal transporter [3]

Figure 1.1: Murata Girl

Figure 1.2: U3-X Personal Transporter

Before reaching this stage in the industrial world, single-wheeled robots have been in

existence in the academic research community for at least three decades In early 1980s,

several groups of researchers in Japan made an attempt to construct a single-wheeled

robot which, in our knowledge, is the first prototype of this class of robots As it was

reported in an article written in Japanese, their achievements remain unknown and

results inaccessible to non-Japanese-speaking research community In 1987, Arnoldus

Schoonwinkel developed a single-wheeled robot with a rotating turntable as part of his

Ph.D research in Stanford University [68] Schoonwinkel managed to balance that robot

longitudinally, i.e., in its forward-backward direction Nothing was reported about

mak-ing the robot balanced laterally However, Schoonwinkel’s work is a significant milestone

in this field of research as a wider research community, especially outside Japan, was

introduced to single-wheeled robots through that work Ever since Schoonwinkel’s

doc-torate thesis was published, interests in single-wheeled-robot research gained momentum

David W Vos and Andreas H von Flotow of Massachusetts Institute of Technology

in-vestigated exactly the same type of single-wheeled robot in 1990 [78], three years after

the publication of Schoonwinkel’s thesis

Research on single-wheeled robots is driven by several factors including (1) the

inves-tigation of nonlinear and unstable dynamics [68]; (2) the emulation of human

intelli-gence [71]; (3) the development of advanced mobile surveillance system [80] and (4) the

search for better means of transportation

Section 1.2 provides the background of single-wheeled robots including their historical

development, current state, classification and our view and evaluation of the trend of

single-wheeled robotic research Subsequently, some preliminaries are presented in

Sec-tion 1.3 and the motivaSec-tions of this research are explained in SecSec-tion 1.4 Finally, an

outline of this thesis is given in Section 1.5 for easy reference

Definition 1.1 [52] A wheeled mobile robot is defined as a robot capable of locomotion

on a surface solely through the actuation of wheel assemblies mounted on the robot and in

contact with the surface A wheel assembly is a device which provides or allows relative

motion between its mount and a surface on which it is intended to have a single point of

rolling contact

Wheeled mobile robots commonly have three or more wheels With three or more

wheels, a wheeled mobile robot maintains its static stability by keeping its center of

gravity inside its polygon of support However, most four-wheeled robots, have limited

manoeuvrability and require wheel suspension systems to ensure that the wheels are

always in contact with the ground [51] As for three-wheeled robots, their two drive

wheels must rotate at slightly different speeds in order to achieve accurate control of

turning [51]

Single-wheeled robots and two-wheeled robots avoid the problems encountered by the

multi-wheeled robots at the expense of static stability Two-wheeled configurations,

such as the Segway [9] and bicycle, are statically unstable in either longitudinal or

lateral direction Single-wheeled configuration, as found in unicycle, is statically unstable

in both longitudinal and lateral directions Apparently, single-wheeled configuration

seems to be at a disadvantage compared to its two-wheeled counterpart However, at

moderate to high speed, disturbance torque arising from uneven ground may make a

two-wheeled platform turned over [80] The distance between the two wheels, while

providing static stability, acts as a leverage to make small disturbance force result in

large disturbance torque On the other hand, single-wheeled configuration has minimum

disturbance torque because it only has one point contact with the ground Therefore,

disturbance force at the wheel is not magnified

Theoretical and experimental research in the field of wheeled mobile robotics has

progressed rapidly It benefits from the rapid development in related areas such as

artificial intelligence, sensing, actuation, control and computing In particular, for a

fully functional practical wheeled mobile robot, a systematic integration of all of these

areas is necessary [51] Below are some important theoretical and experimental results

on wheeled mobile robots reported in the literature

1 Kinematic formulation of wheeled mobile robots is reported in [13], [52] and [61]

Analysis of the internal dynamics of wheeled mobile robots is reported in [83]

2 Motion control of wheeled mobile robots has been achieved using various techniques

such as receding horizon control [32], self-organized fuzzy controller using an

evo-lutionary algorithm [46], fuzzy control with backstepping [35], combined

kinemat-ic/torque control [29], state-feedback linearization [23], sliding-mode control [82],

neural sliding-mode control [58], cross-coupling control [28], iterative learning

con-trol [42], computed torque concon-trol [62], neural concon-trol [22], neural concon-trol with

backstepping [26], virtual-vehicle approach [27], dynamic surface control [72] and

model-based adaptive approach [36]

3 Sensor development and navigation for wheeled mobile robots are reported in [16],

[33], [25], [77] and [24]

4 Actuator, computer and mechanism developments for wheeled mobile robots are

reported in [59], [14] and [41]

1.2.1.1 Monocycle Robot or Unicycle Robot

Several terminologies have been used to refer to a mobile robot that uses only one wheel

for locomotion These nomenclatures include single-wheeled robot, one-wheeled robot,

mono-wheeled robot, monocycle robot and unicycle robot While the first three terms are

self-explanatory and generally cause no confusion, monocycle robot and unicycle robot

must be used with care as they refer to two different groups of single-wheeled platforms

[19] Monocycle refers to a single-wheeled platform having all of its components enclosed

inside a wheel, giving it an appearance of a plain wheel from the outside Unicycle, on

the other hand, refers to a single-wheeled platform having an exposed chassis sitting on

the wheel’s shaft An example of monocycle is McLean Monocycle, created by Kerry

McLean [5] and shown in Fig 1.3, while U3-X personal transporter, shown in Fig 1.2,

is a unicycle.

Figure 1.3: McLean Monocycle

It is important to point out that several authors have used the term unicycle to describe

a two-wheeled platform especially two-wheeled inverted pendulum and differential-drive

mobile robots In order to remain consistent, definitions of monocycle and unicycle given

in [19] are adopted throughout this thesis

Figure 1.4: The Original Design of A Schoonwinkel’s Unicycle Robot

Figure 1.5: The First Successful Unicycle Robot Developed by Zaiquan Sheng and KazuoYamafuji

1.2.1.2 Early Development & Current State

The earliest published literature on single-wheeled mobile robots is the article by Ozaka,

Kano and Masubuchi [57], published in 1980 Two more articles were published around

that time, one [34] by Honma et al in 1984 and the other [81] by Yamafuji and Inoue

in 1986 However, all these articles were in Japanese and, hence, attracted little or no

attention from non-Japanese-speaking researchers The Ph.D thesis of Schoonwinkel

of Stanford University published in 1987 is the first recorded reference on this subject

written in English [68] In his work, Schoonwinkel developed a prototype of unicycle

robot with a turntable as its balancing mechanism This unicycle, shown in Fig 1.4,

was designed to mimic a young person in terms of masses and moments of inertia This

unicycle and its dynamic behaviour were studied by both simulations and experiments

Though simulations of both longitudinal and lateral motions were reported to be

success-ful, experimental results are shown for longitudinal motion only Since the publication of

this research, interest in single-wheeled mobile robots outside Japan gained momentum,

as evident from the work published by Vos and Flotow of Massachusetts Institute of

Technology who investigated exactly the same unicycle robot in 1990 [78], three years

after the publication of Schoonwinkel’s thesis In 1995, Sheng and Yamafuji of

Univer-sity Electro-Communication made the first claim of successfully balancing a unicycle

robot, the design of which follows that of Schoonwinkel with some modifications in the

turntable’s shape and the addition of a pair of closed-link mechanisms to imitate human

legs [70] Fig 1.5 shows the unicycle robot developed by Sheng and Yamafuji After

Sheng’s and Yamafuji’s success, the research on single-wheeled mobile robots spread into

several different directions as marked by two important events

The first event is the introduction of Gyrover by Brown and Xu of Carnegie Mellon

University in 1996 [39] As the first monocycle robot in the world, Gyrover paved the

way to generate more interest in research on monocycle robots This is evident by the

development of Gyrobots by Cavin et al of University of Florida in 2000 [20] and by

Saleh et al of National University of Singapore in 2004 [66], Reactobot by Joydeep et

al of Indian Institute of Technology Bombay in 2008 [53], GYROBO by Kim et al of

Chungnam National University in 2007 [44] and Mono-Wheel Robot by Cieslak et al of

AGH University of Science and Technology in 2011 [21]

The second event is the construction of Yamabico ICHIRO, a unicycle robot with a

rugby-ball-shaped wheel and a side-leaning head, by Nakajima et al of University of

Tsukuba in 1997 [54] The introduction of Yamabico ICHIRO paved the way to the

exploration in new stabilization mechanisms and the use of unconventional wheels In

the exploration of new mechanisms, lateral pendulum has been studied by Fujimoto

and Uchida of Yokohama National University in 2007 [30] and Xu, Mamun and Daud

of National University of Singapore in 2011 [79] In addition, reaction wheel has been

explored by Majima, Kasai and Kadohara of University of Tsukuba in 2006 [50], Ruan,

Hu and Wang of Beijing Institute of Technology in 2009 [63] and Lee, Han and Lee of

Pusan National University in 2011 [38] In the use of unconventional wheels, Ballbot, a

unicycle robot having a spherical wheel, was developed by Lauwers, Kantor and Hollis

of Carnegie Mellon University in 2006 [47], U3-X, a personal mobility vehicle with

omni-wheel, was developed by Honda Motor Co., Ltd in 2009 [3] and Volvot, a monocycle

robot having a spherical wheel, was developed by Ishikawa, Kitayoshi and Sugie of Osaka

University in 2011 [37]

The research and development on single-wheeled mobile robots are summarised in

the timeline shown in Fig 1.6 Based on this timeline, we identify six important

developments dividing the era from 1980 until 2013 into four periods

Firstly, the work by Ozaka, Kano and Masubuchi marked the beginning of Period

I when single-wheeled mobile robot research just started Period I lasted for about

seven years and during this period, Japan is the only country with active research on

single-wheeled mobile robots

Schoonwinkel’s work introduced single-wheeled mobile robots to research communities

across the continents and marked the beginning of Period II During this period, research

was mainly focused on unicycle robots with turntable mechanisms Period II ended when

the first successful attempt was reported by Sheng and Yamafuji between 1995 and 1997

Period III began when Brown and Xu introduced the Gyrover and Nakajima et al

introduced Yamabico ICHIRO Period III is marked by the active exploration in

mono-cycle robots, the development of several new stabilisation mechanisms and the use of

unconventional wheels Period III lasted until about 2008 when Murata Manufacturing

Co., Ltd unveiled Murata Girl [6] and opened the beginning of Period IV which still

lasts until this year In Period IV, more novel mechanisms such as air blower and

electro-magnet are introduced and there is a slight sign of increasing interest in single-wheeled

mobile robot research We believe that the publicity by the industrial companies such

as Murata Manufacturing Co., Ltd and Honda Motor Co., Ltd., to a certain extent,

contributes to this bright outlook

Figure 1.6: Timeline of Single-Wheeled-Mobile-Robot Development

1.2.2 General View and Evaluation

Looking in the retrospective from the year 2013, we find that, before 2007, a steady

interest in experimental research of single-wheeled robot had existed, but it remained

low A new idea emerged in every two or three years and it was from all over the

world (Japan, South Korea, U.S.A., Singapore, China, India, Poland) This trend is in

contrast to other types of robots, e.g humanoid robots, differential-drive robots, etc.,

which enjoy high interest in experimental research We notice that recently, there has

been a sign of increasing interest as evident from reporting of new research in almost

every year between 2007 and 2013 However, the number is still far below those for other

types of robots Some of the reasons behind the low but steady interest in experimental

work in single-wheeled mobile robots are summarised below

1 Huge challenge: To construct a working single-wheeled robots is a challenging

process which takes up a lot of effort, fund, time and trial-and-error process

Single-wheeled mobile robots are generally known to have very challenging properties

such as high static instability, strong nonlinearity, underactuation, non-minimum

phase and nonholonomy These properties set some theoretical limitations on

the aspects of stabilizability, controllability and performance of the systems [60],

[18] Experiments pose other additional challenges such as vibration and mass

imbalance Success is pretty sensitive to structural robustness and qualities of

actuators and sensors Therefore, it is not easy to even come up with the first

successful prototype In fact, several research groups had to build two or three

prototypes until they came up with the fully working one and the process easily

took up several years

2 Low commercialisation potential: No niche application has been identified so far

Personal transportation and surveillance are two potential applications However,

when it comes to commercialization, profitability becomes the most important

concern Static instability of single-wheeled robots makes the use of high precision

inertial sensor a more profound necessity than it is in other forms of mobile robots

High precision inertial sensor and other advanced technologies are essential for

single-wheeled platforms just to meet the minimum requirement of stabilization

Robots with three or more wheels and humanoids do not suffer from such

prob-lem These necessary advanced technologies cost money Hence, without some

unique advantage and elegance, single-wheeled robots will remain commercially

non-competitive

3 Low entertainment value: The resemblance of humanoid robots to human and some

biomimetic robots to animals easily gains a lot of attraction and popularity

espe-cially in conferences and exhibitions Compared to those robots, single-wheeled

robots may not easily attract the crowd’s attention, although external modification

can certainly be done to improve it, as in the case of Murata Girl

4 High academic value: Being a good candidate for complex and challenging systems

to be controlled, a single-wheeled mobile robot carries enormous academic value

Should a prototype of single-wheeled mobile robot be made to work successfully

with a certain controller, it would be of much value for academic research and give

some recognition to the pioneers, as in the case of Schoonwinkel’s unicycle and

Gyrover This may be the reason that despite the low interest in experimental

research of single-wheeled mobile robots, this field has not encountered a natural

death yet

Mobile Robots

A lot of designs and mechanisms for single-wheeled mobile robots have been proposed

in the literature These various single-wheeled mobile robots can be classified based

on four criteria namely wheel shapes, platform types, driving mechanisms and steering

mechanisms Based on the wheel shapes, single-wheeled mobile robots can be divided

into (1) conventional-single-wheeled robots and (2) innovative-single-wheeled robots

Following the classification of single-wheeled vehicles based on Cardini’s article [19],

based on the platform types, single-wheeled mobile robots consist of (1) monocycle

robots and (2) unicycle robots Based on how driving thrust is generated, single-wheeled

mobile robots can be either (1) swinging-pendulum driven or (2) electric-motor driven

Based on the mechanisms implemented for steering and navigation, there are at least

six different mechanisms including (1) high-speed rotating gyroscope; (2) turntable; (3)

reaction wheel; (4) lateral pendulum; (5) air blower and (6) electromagnet

1.2.3.1 Conventional Wheel vs Innovative Wheel

Conventional wheel constitutes classic pneumatic wheels commonly found in bicycles

Conventional wheel is statically unstable in the lateral direction and designed to only

move in the longitudinal direction when actuated Therefore, all single-wheeled mobile

robots with conventional wheels installed are statically unstable in the lateral direction

and have their motions constrained by nonholonomic kinematic constraints

Innovative wheel constitutes all wheels other than conventional wheels Innovative

wheel can be rugby-ball-shaped, spherical, omni-directional and so on The use of

in-novative wheel eliminates or reduces the drawbacks of conventional wheel (static lateral

instability and nonholonomy) However, it also brings new challenges such as big size

and high mechanism complexity Currently, there are three innovative wheels which

have been implemented in single-wheeled mobile robots

1 Rugby-ball-shaped wheel: This innovative wheel was introduced by Nakajima et

al [54] for their unicycle robot, Yamabico ICHIRO Due to its wide shape and large

curvature, this wheel is statically stable in the lateral direction The interesting

fact about this wheel is that it is not reflected in the mathematical model of the

robot dynamics

2 Omni-wheel: Omni-wheel is capable of moving directly in the lateral direction

Thus, the advantage that it provides is the elimination of nonholonomy

Omni-wheel has been existent for some time, but its implementation in single-Omni-wheeled

mobile robot is rather new It is demonstrated in U3-X which utilizes HOT Wheel,

an advanced version of omni-wheel made by Honda Motor Co., Ltd [3]

3 Spherical wheel: As its name suggests, spherical wheel has the shape of a sphere

It is holonomic and its implementation has been reported in Volvot, a monocycle

robot made by Ishikawa, Kitayoshi and Sugie [37], and Ballbot, a unicycle robot

made by Lauwers, Kantor and Hollis [47]

Figure 1.7: Yamabico ICHIRO, Its Rugby-Ball-Shaped Wheel Helps in Lateral Balancing

Figure 1.8: Volvot

Figure 1.9: Ballbot, Its Ability to Move in Any Direction Is Attributed to Its SphericalWheel

1.2.3.2 Monocycle vs Unicycle

Monocycle is a single-wheeled platform having its chassis contained inside the wheel

Monocycle is statically stable in longitudinal direction because its chassis hangs on the

wheel shaft instead of sitting on it in an inverted position Monocycle as a vehicle was

much explored in late 1800s and early 1900s [19] However, due to its control difficulty

especially at low speeds, it has not been adapted as a daily vehicle Despite the fact, a

fully working monocycle vehicle has been developed by McLean, a freelance machinist,

since 1970 [5] A single-wheeled mobile robot with monocycle type of platform was first

created by Brown and Xu in 1996

Different from monocycle, a unicycle is a single-wheeled platform with an exterior

chassis sitting on the wheel’s shaft in an inverted position The chassis arrangement

makes unicycle statically unstable in both longitudinal and lateral directions Unicycle is

more common than monocycle as a personal transport and an entertainment equipment

in circus The adoption of unicycle type of platform in a robotic system was first done

by Ozaka, Kano and Masubuchi [57]

The two different platform types affect single-wheeled mobile robots in terms of

dy-namics and potential applications

The dynamics of monocycle robots is unstable only in one dimension, while that of

unicycle robots is unstable in two dimensions Therefore, unicycle robots are naturally

more challenging to control than monocycle robots since control objective must take into

account one more unstable degree of freedom Monocycle robots have not been reported

in the literature to have specific control difficulty

The type of platform used in single-wheeled mobile robots can be a deciding factor for

their potential applications Due to the nature of the enclosed chassis design, monocycle

robots are especially suitable to operate in harsh and wet environments [80] With

transparent covers and vision systems, monocycle robots can be good candidates for

surveillance [80] The open platform design of unicycle robots makes it possible to install

various tools such as robotic manipulators and renders them naturally as candidates for

personal transport of the future In addition, unicycle robots can be used as control

benchmark problems in control education

The contrasts between monocycle and unicycle platforms can be seen in McLean

Mono-cycle and U3-X shown in Figs 1.3 and 1.2 respectively

1.2.3.3 Driving Mechanisms

Single-wheeled mobile platforms can also be classified according to the means by which

driving thrust is generated Most, if not all, of single-wheeled mobile robots are relatively

small in size and, therefore, electric motors are suitable as the actuator of choice Since

most electric motors provide small torques and high speed, usually, mechanical

trans-mission systems such as gearheads, timing belts and pulleys, and chains and sprockets

are used to properly adjust the torques and speeds to the required levels Monocycle

robots driven by electric motors include Gyrobot, shown in Fig 1.10 [66], GYROBO [44]

and Mono-Wheel Robot [21] All unicycle robots are driven by electric motors and this

includes Lee’s unicycle robot, shown in Fig 1.11 [38]

Figure 1.10: Gyrobot, a Monocycle Robot Driven by Electric Motor

Figure 1.11: Unicycle Robot Developed by Lee et al at Pusan National University

Swinging pendulum is another way of generating the required thrust in single-wheeled

mobile robots This mechanism was first introduced by Brown and Xu in Gyrover, shown

in Fig 1.12 [39] In this mechanism, the installed electric motor is not used to drive the

wheel directly Instead, it is used to swing the pendulum forward (backward) in order

to create mass imbalance which, in turn, drives the robot forward (backward) So far,

this mechanism has been applied to monocycle robots only This is due to the structural

construction of the monocycle robots where the chassis is enclosed in the wheel and

can be used as a pendulum In unicycle robots, the swinging pendulum does not have

any clear advantage over the electric motor and, given the potential complexity of its

implementation, it has not been implemented in unicycle robots so far

Figure 1.12: Gyrover, The First Monocycle Robot

1.2.3.4 Steering Mechanisms

Steering mechanism is the means by which a single-wheeled mobile robot maintains its

balance and steer itself to follow a designated path on Cartesian x-y plane Many

dif-ferent steering mechanisms have been suggested in the literature including turntable,

high-speed rotating gyroscope, reaction wheel, lateral pendulum, air blower and

electro-magnet

Turntable is the oldest steering mechanism which was first introduced by Schoonwinkel

[68] The unique characteristic of turntable is its capability of direct control over the

yaw motion of a single-wheeled mobile robot Placement of actuator on the chassis does

not affect the system’s centre of gravity greatly because turntable is mounted on top of

the chassis with its axis pointing upward Turntable was also used successfully by Sheng

and Yamafuji for steering their version of unicycle robot [71]

High-speed rotating gyroscope uses the concept of gyroscopic precession in order to

control the roll and yaw motions of a single-wheeled mobile robot It rotates continuously

at high speed and control is achieved by changing the orientation of its rotational axis.

A drawback of this method is high energy consumption, which, in turn, necessitates the

use of vacuum chamber [80] Most single-wheeled mobile robots which apply high-speed

rotating gyroscope are of monocycle type

Reaction wheel is a classic mechanism which has been used in orientation control of

ships and space vehicles [67] Reaction wheel has been implemented successfully in both

monocycle robots [53] and unicycle robots [6], [63], [50], [38] Reaction wheel exerts

direct control over the roll motion and, due to its cylindrical shape, does not shift the

centre of gravity of the whole system during the balancing process

Figure 1.13: Reactobot, a Monocycle Robot Controlled by Reaction Wheel

Application of lateral pendulum for balancing was first mentioned by Schoonwinkel as

part of the complete mechanism for emulating a human riding a unicycle [68] Working

principle of stabilisation by lateral pendulum is based on the application of reaction

torque Lateral pendulum is not symmetric with respect to its rotational axis, so, during

the balancing process, it greatly affects the centre of gravity of the system and, thus,

makes the balancing process much more challenging Yamabico ICHIRO and Cieslak’s

Mono-Wheel Robot are the only single-wheeled mobile robots which have successfully

applied the lateral pendulum mechanism [54], [21] However, in Yamabico ICHIRO, the

success is partially attributed to the use of a rugby-ball-shaped wheel, which helps in the

lateral balancing There is currently no claim on successful implementation of lateral

pendulum on unicycle robot with conventional wheel Therefore, this represents a gap

in the research which is worth to be studied and filled

Figure 1.14: Mono-Wheel Robot, a Monocycle Robot Applying Lateral Pendulum forControl

Figure 1.15: Mono-Wheel Robot Developed by Yasutaka Fujimoto and Shuhei Uchida

All of the steering mechanisms presented so far essentially consist of a solid cylindrical

body which is put at different configuration A completely different concept for steering

is the use of air flow which can be realised by adding a blower Air blower has been used

in monocycle vehicle by McLean [5] and in unicycle robot by Kim et al in their robot

named CNU Blower, shown in Fig 1.16 [48] For implementation of such mechanism,

at least two air blowers are needed in order to provide air flow sideways The two air

blowers are securely placed on the chassis and, therefore, they do not represent separate

rigid bodies in the mathematical modelling This results in simpler mathematical model

compared to robots equipped with other mechanisms However, the big size of the

air blower represents a drawback in that some clearance must be assured in order to

accommodate it In addition, because it depends on the presence of air, this mechanism

will not work in outer space environment

Figure 1.16: CNU Blower, The First Unicycle Robot Making Use of Air Flow for bilisation and Control

Sta-A novel steering mechanism based on electromagnet was proposed by Ruan et al in

2012 [65] This mechanism is still at its infancy and, hence, it has not been

experimen-tally proven to work on single-wheeled mobile robot

1.2.3.5 Classification of Current Single-Wheeled Mobile Robots

With the four criteria, we classify the currently available single-wheeled mobile robots

in a top-down fashion based on the wheel shapes and platform types For single-wheeled

mobile robots with conventional wheels, further division is performed based on driving

mechanisms and steering mechanisms For single-wheeled mobile robots with innovative

wheels, further division is carried out based on the specific wheel shapes This

classifi-cation is summarised in Fig 1.17 where at the lowest level are the groups to which the

current single-wheeled mobile robots are classified

Single-Wheeled Mobile Robots

• Group A: Gyrover [80], [15], Cavin’s Gyrobot [20]

• Group B: Reactobot [53]

• Group C: Zhu’s Gyrobot [66], [86], GYROBO [44], [45]

• Group D: Cieslak’s Mono-Wheel Robot [21]

• Group E: Schoonwinkel’s unicycle robot [68], Vos’ unicycle robot [78], Sheng’s

unicycle robot [70]

• Group F: Murata Girl [6], Majima’s unicycle robot [50], Lee’s unicycle robot [38],

Ruan’s unicycle robot [63], [64]

• Group G: Fujimoto’s Mono-Wheel Robot [30], ALP Cycle [79]

• Group H: CNU Blower [48]

• Group I: Ruan’s unicycle robot [65].

In this section, we summarise some basic preliminary definitions which are useful for

understanding the subsequent chapters

Definition 1.2 [43] Consider a time-invariant system described by

where x is the state vector The equilibrium points of system 1.1 are the real roots of the

equation

f (x) = 0

Definition 1.3 [43] The equilibrium point x = 0 of ˙x = f (x), where f : D → Rn is a

locally Lipschitz map from a domain D ⊂ Rn into Rn, is

• stable if, for each  > 0, there is δ = δ() > 0 such that

||x(0)|| < δ → ||x(t)|| < , ∀t ≥ 0,

• unstable if it is not stable,

• asymptotically stable if it is stable and δ can be chosen such that

||x(0)|| < δ → lim

t→∞x(t) = 0

Definition 1.4 [31] Consider a mechanical system described by

¨

q = f (q, ˙q, u)

where q is the vector of generalised coordinates, f (·) is the vector field representing the

dynamics and u is a vector of external generalised inputs Suppose that some constraints

restrict the motion of the system If the constraints satisfy the complete integrability

property,that is, if they can be written in the form

h(q, t) = 0

Then, they are called holonomic If the constraints can not be expressed in that fashion,

then they are called nonholonomic

Definition 1.5 [31] Consider the affine mechanical system described by

¨

q = f (q, ˙q) + G(q)u (1.2)

where q is the state vector of linearly independent generalised coordinates, f (·) is the

vector field that captures the dynamics of the system, ˙q is the generalised velocity vector,

G is the input matrix and u is a vector of generalised inputs System 1.2 is said to be

underactuated if the external generalised inputs are not able to command instantaneous

accelerations in all directions in the configuration space Formally stated, this occurs if

rank(G) < dim(q), where the dimension of q is usually defined as the number of degrees

of freedom of system 1.2

Definition 1.6 [43] A system is said to be minimum phase if its zero dynamics has an

asymptotically stable equilibrium point in the domain of interest Otherwise, it is said

to be non-minimum phase [55] A linear system is said to be non-minimum phase of its

transfer function has zeros in the right half-plane Otherwise, it is said to be minimum

phase The step response of a linear non-minimum-phase system is characterised by an

initial reversal in direction

Although the concept of lateral pendulum for stabilisation and control of unicycle robot

was first mentioned by Schoonwinkel in 1987, only two groups of Japanese researchers

had attempted to investigate this particular robot before our research commenced

Naka-jima et al derived a simple dynamic model for this robot and developed a prototype

named Yamabico ICHIRO equipped with a rubgy-ball-shaped wheel [54] Although

Yamabico ICHIRO is a successfully working prototype, it owes its success to its unique

wheel shape In separate research, Fujimoto and Uchida also derived a simple

dy-namic model for this robot and attempted to construct a prototype with a conventional

wheel [30] However, up to this year, there is no report of successful implementation from

them It is apparent that lateral-pendulum unicycle robot represents a niche of

single-wheeled mobile robots which is still open for investigation especially in the aspects of

compelete dynamic modeling, control design for posture balancing, manoeuvring, path

following and position control, and experimental verification

In view of the research state of lateral-pendulum unicycle robot, the objective of the

research presented in this thesis is, therefore, to investigate the dynamics and control

of lateral-pendulum unicycle robot from both theoretical and experimental points of

view Theoretical investigation covers the construction of complete dynamic model,

dynamic and static analyses, design of feedback control schemes and control-performance

evaluation based on numerical simulations Experimental investigation covers the design

and construction of a prototype as a research platform for concept verification and

implementation of the designed control schemes

This research carries the following significance

1 From a theoretical point of view, this study fills the knowledge gap in the study of

single-wheeled robots and partially contributes to the knowledge base of

human-ridden unicycle system as envisioned by Schoonwinkel in the early days of

single-wheeled-robotics research

2 From a practical point of view, the experimental study in this research shows

the feasibility of a lateral pendulum for unicycle stabilisation and control which,

although having been hypothesised before, has not been successfully realised in

practice

3 From a pedagogical point of view, the developed prototype of lateral-pendulum

unicycle robot has the potential to become a new benchmark for the study of

complex system where nonlinearity, nonholonomy, underactuation, 2-D instability

and non-minimum phase appear together

The central object of study in this thesis is the unicycle robot which is stabilised and

controlled by a lateral pendulum Its conceptual design is shown in Fig 1.18

Figure 1.18: Conceptual Design of ALP Cycle

The unicycle robot was initially named Pendulum-Balanced Autonomous Unicycle

(PBAU), but its name was later changed to Automatic Lateral-Pendulum Unicycle (ALP

Cycle) to reflect the fact that the pendulum functions not only as a balancer, but also

as a steering mechanism during manoeuvring and path following

The proposed robot consists of three links or bodies, namely wheel, chassis and

pendu-lum, which are connected in series by two rotary joints The wheel is directly actuated

by an electric motor, rigidly attached to the lower part of the chassis The chassis is

a platform where all electronic and electromechanical components are securely placed

The pendulum is directly actuated by another electric motor, rigidly attached to the

upper part of the chassis Since the prototype is our first attempt at constructing ALP

Cycle, we kept the conceptual design to be as simple as possible by avoiding the use of

mechanical transmission mechanisms like chain and belt In this way, practical

compli-cations due to component complexity are avoided

Prior to the development of ALP Cycle, we developed a prototype of a single-wheeled

in-verted pendulum during which significant experiences in robot development were gained

We built three prototypes with each prototype being the improvement over the earlier

one The latest two of these prototypes are shown in Figs 1.19 and 1.20

We encountered a lot of practical problems with the first prototype of single-wheeled

inverted pendulum including the followings

1 Poor mechanical design: Due to budget constraints, the prototype was constructed

in the department’s workshop The construction was done in a hurry and we

discovered that the structure was prone to vibration, especially the pendulum

Drilling different parts manually introduced misalignment in the assembly We

adopted brute force assembly to overcome the misalignment issue which caused a

large mismatch in assembly

2 Poor actuators, sensors and controller board: The first prototype used low cost

actuators, sensors and controller board [7] The DC motors used as actuators were

found to have backlash of 80, which were too large and too difficult to deal with

The sensors and controller board were also found to be unsuitable due to their

insufficient memory, inability to be programmed and low sampling rate, despite

their user friendly interface

The second prototype was an improvement over the first one with controller board,

actuator and sensors from Renesas Electronics Corporation [8], Maxon Motor [4] and

SparkFun Electronics [10] respectively Posture balancing was successfully achieved with

this prototype, but vibration was still found to be too much This is especially

obvi-ous during long-term experiments Hence, improvement on mechanical structure was

necessary Besides structural problem, the motor amplifier used was of one-quadrant

operation Therefore, jerky motion was observed especially during directional change

Figure 1.19: Single-Wheeled Inverted Pendulum Version II

For the third prototype, we used aluminium sheet with thickness of at least 3 mm to

make the structure stiff and not prone to vibration The fabrication was done using CNC

machines to minimise alignment and dimensional errors Four-quadrant motor amplifier

is used in replacement of one-quadrant amplifier This prototype works well and since

then, it has been used for tests of some newly designed controllers in another separate

research project [84]

(a) Front View (b) Side View

Figure 1.20: Single-Wheeled Inverted Pendulum Version III

This preliminary work, though only loosely related to ALP Cycle, highlights several

considerations in the design and construction of a robotic prototype In our case, the

following conclusions, based on the previously completed work, serve as guidelines and

reminders during the design of ALP Cycle:

1 Mechanical structure: In the design of robot mechanical structure, it is desired

to have stiff, robust and vibration-free structure This can be achieved by using

metal sheet with medium thickness The previous work shows that at least 3 mm

thickness must be provided for a robot of such size in order for the structure to be

stiff, robust and free of unwanted vibration

2 Actuators: In the selection process of electric motor and gearhead, we have to bear

in mind that since our ALP Cycle prototype involves harmonic motion, zero

gear-head backlash is needed For the motor amplifier, four-quadrant motor amplifier is

a must because during the stabilization of ALP Cycle, harmonic repetitive motion

is often encountered

3 Sensors: Inertial measurement unit must have minimum noise whenever possible so

that filters are not needed An alternative to this is to choose inertial measurement

unit with built-in filter In addition, response linearity and measurement range

must also be given serious attention during the selection of inertial measurement

unit Encoder with high count per turn is necessary for good accuracy

4 Controller board : Controller board must have high sampling rate and must be able

to be interfaced at ease with actuators and sensors

5 Project management : The budget available for this research project is

unfortu-nately very limited and therefore, we have to provide some trade-off during our

selections of components Besides, since it is very costly for us if a component is

found out to be unsuitable or breaks down, more time should be spent on design

evaluation before fabrication, purchasings and experiments kicked in

The remaining content of this thesis is organised into six chapters, in which all key

works on ALP Cycle development and investigation including (1) design, analysis and

fabrication of the structure; (2) design of actuation, sensing and power systems; (3)

processor system; (4) dynamic modelling and analysis and (5) control design, simulation

and implementation are presented in detail

In Chapter 2, ALP Cycle’s complete dynamic model is constructed and its

character-istics analysed Euler-Lagrange formulation is adopted to derive the dynamic model

The dynamic model is then linearised and simplified into a form which is reasonable for

control design Characteristics of the robot dynamics are evaluated by numerical

sim-ulation and issues of posture balancing and manoeuvring are discussed in detail The

conditions important for balancing stability check and manoeuvring are derived

Chapter 3 focuses on the design and fabrication of ALP Cycle’s mechanical structure

in detail Basic design concerns including component placement and material selection

were addressed Next, SolidWorks 3-D modelling software was chosen as the platform

where 3-D model of the conceptual design was developed With the 3-D model, the

problems of placement of centre of gravity and trade-off between mass and structural

robustness were looked into and solved

In Chapter 4, the design of ALP Cycle’s actuation, sensing and power systems is

presented The selection processes of actuation-system components including gear trains,

electric motors, motor amplifiers and bearings are outlined Then, some experiments for

characterising the actuation system are described The sensors used include encoders and

inertial sensors Selection criteria and characteristics of these components are discussed

in detail Their responses were characterised experimentally Finally, speed-observation

algorithms and extended Kalman filters were designed and implemented to get good

sensor measurements.

Chapter 5 details the processor system of ALP Cycle Firstly, selection of

proces-sor system is presented based on requirements dictated by the actuation and sensing

systems Next, the interfacing of the processor system with the actuation and sensing

systems is elaborated in detail Finally, the software system comprising of

hardware-interfacing algorithms, user-interface algorithms, filter algorithms and control algorithms

is developed using C programming language

In Chapter 6, ALP Cycle’s control tasks are identified and control schemes are

de-signed for posture balancing and manoeuvring Firstly, we identify two control tasks

namely (1) posture balancing and (2) manoeuvring Next, we design a control scheme

to achieve stabilisation in posture balancing and evaluate its performance by numerical

simulations For manoeuvring, we propose two control schemes and design two

con-trollers to achieve asymptotic path following, the performances of which are evaluated

by numerical simulations Finally, implementation of posture-balancing control scheme

using the developed prototype is presented and the result is discussed in detail

Finally, Chapter 7 concludes the thesis with summary, academic contributions and

recommendations for future research

Chapter 2

Dynamic Modelling &

Characteristics Identification

This chapter presents the development of ALP Cycle’s complete dynamic model and

the identification of its characteristics Such dynamic model is useful for (1)

numerical-simulation study; (2) control design and (3) evaluation of the robot’s characteristics

In Section 2.1, dynamic modelling by Euler-Lagrange formulation is described step by

step Subsequently, the resulting model is validated in Section 2.2 by comparison with

the dynamic models of two well-studied robots in the literature namely Single-Wheeled

Inverted Pendulum (SWIP) and Acrobot Due to the complexity and size of the dynamic

model, pseudolinearisation with respect to the equilibrium state representing the ALP

Cycle’s upright posture is carried out in Section 2.3 Using the pseudolinearised dynamic

model, the ALP Cycle’s static and dynamic characteristics are evaluated by analyses and

numerical simulations in Section 2.4 Finally, some concluding remarks are summarised

in Section 2.5