Chapter 1
Robot and Robotics
PP. 01-19
Modeling and Stability of Robotic Motions
1.1
Introduction
A Czech writer, Karel Capek, had first time used word ‘ROBOT’ in his
fictional automata 1921 R.U.R (Rossum’s Universal Robots) which
means ‘forced labor’. In this play robot looks like human but it does
not have human feelings and its work efficiency doubles than the
human. However, robot does not have any standard definition. But it
can be considered as ‘a mechanical machine made to perform one or
more tasks repetitively, with precision’. The concept of robot has been
existing since ancient period. It is depicted in “Vedas”, the ancient
scripture of Hinduism. There are many reasonable images of robots
such as dancing and singing artificial birds like the living ones, clocks
which has moving figures and many astronomical replicas which
represents the motion of the planets.
The “Dama”, “Vyala” and
“Kata”, unmanned machines for the war, were described in an ancient
book “Yoga Vasistha”. The Kata was similar to a present tank for
defending army, Dama was used to tame of course the enemy, Vyala
was cruel like snack or tiger. The basic characteristics of robot which
make it different from other mechanical machines are as follows:
i.
it function by itself
ii.
it is responsive about the neighboring environment
iii.
it
can
adjust
environment
with
the
variations
in
the
neighboring
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iv.
it is task oriented
v.
it has capability to use various methods to finish a task.
The robot can have the following components:
i.
Effectors: The parts of robot which really do the work are
known as effectors like hands, legs, torso, arms etc.
ii.
Sensors: The parts of robot which perform like senses and
collect the information about its neighboring environment
(like obstacles, light, heat etc.) are known as sensors.
iii.
Brain: The part of robot which has instructions in the form
of algorithms to control the system of robot is known as
brain.
The synchronization between three components is required for
finishing the particular task. In the first step of synchronization, the
sensor takes information from the neighboring environment and sends
it to the brain. On basis of this information, brain takes the decision of
action as per the installed algorithm and effectors do the action as
shown in Fig 1.1.
Modeling and Stability of Robotic Motions
Input from
Neighboring Environment
Sensors
Brain
Effectors
Fig 1.1 Synchronization between the components of robot
1.1.1
Classification of robot
There are various types of robots available, each produced for different
purposes and for different platforms. They can be developed for the
purpose
of
domestic
assists,
industrial
employs,
investigations,
entertainment etc. This family of robots can be classified by several
different methods which based on their applications, kinematics
structure, shape of workspace, operating method, type of controller,
type of technology, arm configuration, type of locomotion etc. Using
the method based on locomotion, robots can be classified into two
basic classes: (I) Stationary robot, and (II) Mobile robot.
I.
4
Stationary robot
The stationary robot is not really motionless, but its motions are
restricted to a small boundary. It includes robotics arms which can be
moves around the global axis. The industrial robots are the examples
Mahesh A. Yeolekar 5
of stationary robots. The stationary robots can be further classified
into the following subclasses:
i.
Cartesian robots The Cartesian robots move linear rather than
rotating in three perpendicular axes which means, they can
move left-right, in-out, up-down. Consequently, the working
envelope of the robot is in a form of a rectangular box.
Fig 1.2 Cartesian robots
ii.
Cylindrical robots The Cylindrical robots move linear in two axes
while rotate in one axis.
Generally, such robots can move
linearly in Y and Z axes and rotate along Z axis as shown in Fig
1.3. So, the working envelope of such robot is in a form of a
cylindrical box.
Fig 1.3 Cylindrical robots
iii.
Spherical
robots
The
robots
which
require
the
spherical
coordinates system to describe their motions are called the
Modeling and Stability of Robotic Motions
spherical robots. As a result, the working envelop is in a form of
sphere as shown in Fig 1.4.
Fig 1.4 Spherical robots
iv.
SCARA robots The Selective Compliance Assembly Robot Arm
(SCARA) is rigid in the Z-axis and flexible in the XY-plane. This
type of structure gives more flexibility than the Cartesian robot.
It is useful to manufacturer of home appliances, electric
appliances, auto parts, medical equipments.
Fig 1.5 SCARA robots
v.
Articulated robots An articulated uses rotary joints to access its
workspace. The rotary joints permit the robots to turn back and
forth between different work areas. Generally, they are arranged
in a sequence, so that one joint assists another joint further in
sequence which raises the momentum of work.
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Fig 1.6 Articulated robots
vi.
Parallel robots The robot which contains several computer
controlled mechanism on a single platform is called parallel
robot. This mechanism is good in sense of rigidity, stability and
precision to control large loads.
Fig 1.7 Parallel robots
II.
Mobile robot
The mobile robot is a movable robotic system which can move from
one place to other place within an environment. The autonomous
guided vehicles, humanoid robots are the examples of mobile robots.
The
mobile
robot
can
be
further
classified into
the
following
subclasses:
i. Environment based classification
a. Unmanned Ground Vehicle (UGV) The unmanned ground vehicle
works
on
the
ground
and
can
sense
and
interact
with
Modeling and Stability of Robotic Motions
surrounding without onboard presence of human. It is used for
military purposes.
Fig 1.8 Unmanned Grounded Vehicle
b. Unmanned Aerial Vehicle (UAV) The unmanned aerial vehicle is a
vehicle which can fly without human operator in it. It can fly
autonomously or be controlled remotely. It is also known as
drone. It is used in military operations, civil operations, police
and non-military securities.
Fig 1.9 Unmanned Arial Vehicle
c. Autonomous
Underwater
Vehicle(AUV)
The
autonomous
underwater vehicle is one which can travel without any human
operator. It is also known as submarine. It is used in underwater
research.
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Fig 1.10 Autonomous Underwater Vehicle
ii. Device based classification
a. Wheeled robots The wheeled robots act on wheels which are
fitted on the both side of body. This helps to move in any
direction by changing the degree of rotation of its wheels without
additional steering control.
Fig 1.11 Wheeled Robots
b. Legged robots The legged robots movements are based on legs
which placed on the lower part of the rigid body. The one-leg
jumping robot (pogo stick robot), biped robot (humanoid robot),
quadruped robot, hexapod robot are the legged robot. The
legged robots are more efficient than the wheeled robot in the
ruff surrounding.
Modeling and Stability of Robotic Motions
Fig 1.12 Legged Robots
1.1.2
Types of Locomotion
The types of locomotion of robot depend on the relationship between
the total and controllable degrees of freedom. In sense of mechanics,
the degrees of freedom of system are the number of independent
parameters which required for defining its configuration. In robotics
system, it has two types of degrees of freedom: first, total degrees of
freedom are the number of independent parameters which completely
described system and second, the controllable degrees of freedom are
the number of controller required to control the system. The
locomotion of robot can be classified as follows:
i. Holonomic locomotion: If the number of controllable degrees of
freedom is equal to the number of total degrees of freedom, then it
is called holonomic locomotion. The locomotion of robot which built
on Omni-wheels is an example of holonomic locomotion. It has total
degrees of freedom is three because it can move freely in any
direction and same number of controller are required to control it,
so the controllable degrees of freedom is three.
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Fig 1.13 Holonomic Robot with Omni-wheels
ii. Non-holonomic locomotion: If the number of controllable degrees of
freedom is less than the number of total degrees of freedom, then it
is called non-holonomic locomotion. The car-type locomotion is the
simplest example of non-holonomic locomotion for which total
degrees of freedom are three, two for position axis and one for
orientation while controllable degrees of freedom is two, one for
acceleration and one for steering.
Fig 1.14 Non-holonomic car-type Robot
iii. Redundant Locomotion: If the number of controllable degrees of
freedom is greater than the number of total degrees of freedom,
then it is called redundant locomotion. The locomotion of a robotic
Modeling and Stability of Robotic Motions
arm is an example of redundant which has total six degrees of
freedom, but seven controllers are required to control its motion.
Fig 1.15 Redundant robot
In this thesis, we study about two legged (biped) UGV mobile robot
with non-holonomic locomotion. The study of robot is called the
robotics. It includes robot design, construction, application and
operation. The following are the reasons which inspired to study robot:

It reduces the human effort.

It can work in hazardous environment where human can’t
work.

It can work tirelessly for long period of time.

It works accurately more than humans.
Before the study of robot, the three laws of robotics must be kept in
the mind, also known as Asimov’s Laws which are given below:
1. robot may not injure a human being or, through inaction, allows
a human being to come to harm
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2. A robot must obey any orders given to it by human being,
except where such orders would conflict with the First Law
3. A robot must protect its own existence as long as such
protection does not conflict with the First or Second Law.
Considering these three laws, we start our journey of robotics. In the
next section, we will discuss about humanoid robots in details.
1.2 Humanoid Robot
Humanoid robot is a growing and challenging research field due to the
ability of humanoid robot to do the work like human with better
precision. They are being built for our homes and offices, for medical
professions, for space research, for military applications and many
more.
The humans created their neighboring environments which suited to
the human body like stairs, handles of doors, gears etc. As a result,
the robot with structure analogous human body can get the benefits of
these human-based environments. The humanoid robot is a robot
which is structurally similar to the human body and possesses a sense
like human. It has two legs, a torso, two arms and a head. If the
humanoid
robot
is
capable
to
recognize
and
produce
speech,
understand the body language, develop the self learning capability,
able to communicate with humans, then there can exist a one-to-one
Modeling and Stability of Robotic Motions
mapping from human activities to humanoid robot activities. Moreover,
they are the best tool to study human intelligence.
In Vedas, the humanoid robot is called “Yantrapurusha”, that means
man-machine which is described in the ancient book “Bhagaya-vastu”.
They were made of wood but completely covered by skin like human.
The system bolts, springs, iron rods were gave the motions to the
robot. They can play music, served things to guests etc.
Fig 1.16 Humanoid robot
The research issues of humanoid robots are bipedal locomotion,
audio-visual sensitivity, adaptive control, robot-human communication,
self-learning etc. In the next, we will describe the bipedal locomotion
in details.
1.3 Bipedal Locomotion
The bipedal locomotion is distinguishing feature of the humans. This
locomotion is more suitable in the hazardous situation than the
locomotion of other legged robots due to the following reasons:
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
to make the synchronization between two legs is easier than the
synchronization between four, six or more legs.

they can easily climb stairs, run on the ground

two hands of the humanoid robot are free during the walking
and so they can be used for other jobs like lifting, holding.

they can raise the head and so they have a better ground vision
with enhanced detection of remote hazards.
(a) Walking
(b) Running
(c) Climbing
Fig 1.17 Bipedal locomotion
Because of these advantages, we have decided to work on the bipedal
locomotion of humanoid robot.
1.4 Objectives
The objectives of our research are:
1. Study of the dynamics of humanoid robots.
2. Study of gait locomotion.
3. Build the stable walking patterns for passive dynamic biped
robot
Modeling and Stability of Robotic Motions
The objectives are explained in detail in the following paragraph.
1. Study of dynamics of humanoid robots
To understand the mobility of humanoid robot, many aspects like
inertia, gravity etc should be taken into account. Due these aspects,
the dynamics modeling of humanoid robot becomes a complex
problem which needs a complex analysis and high computation time.
This model calculates positions and velocities of arms and contains
physical constraints with consideration of gravity and inertial effects
for controlling the system. These constrains make a nonlinear model.
Commonly, the recursive methods are used to solve such dynamics
problem.
2. Study of gait locomotion
The gait locomotion is a study of walking pattern of the humanoid
robot. The dictionary meaning of ‘gait’ is “A particular manner of
moving on foot”. So the “gait locomotion” is an appropriate word for
the study of human walking.
The walking of biped is inspired by the human walking, so the gait
cycle of biped is analogous to human gait cycle as shown in the Fig
1.18. We considered here the passive dynamic biped robot which
makes a waking motion only under the gravity and other external
forces are absent. That means, the swing foot falls down due the effect
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Fig 1.18 Gait cycle of biped analogous to human gait cycle
of gravity. The impact of swing foot with ground is complete the 1cycle of gait and in the next cycle swing leg become will become the
stance leg and stance leg will become the swing leg. For the symmetric
gait the pattern will be repeated with the same initial value in each
cycle. The objective of study of gait locomotion is finding symmetric
gait for the passive walking of biped.
3. Build the stable walking patterns for passive dynamic biped
robot
The final objective behind the study of biped is generating a symmetric
gait which is stable. It means that find a walking pattern which gives
the stable walk to biped. Basically, the system of biped robot is
discontinuous system as it is hybrid of two events: swing phase and
impact phase. So, it is challenging task to find a stable walk for such
discontinuous system. The stable walking pattern of biped means that
the small disturbances in walking do not affect the walking pattern.
The magnitude of allowable disturbance shows the robustness of
Modeling and Stability of Robotic Motions
biped. The parameters likes slope angle of ramp, the height of robot
and weight of robot are also affect the stability of walk. Our objective
is finding the suitable values of parameters which give the maximum
robustness to walking of biped.
Considering these objectives, the flow of thesis explains in the
following section.
1.5 Outline of Thesis
This thesis is divided into three chapters.
Chapter 1 is preliminary.
Chapter 2 contains the detail study of double inverted pendulum
which can be considered as a pre-robotic problem. It describes
mathematical modeling of the double inverted pendulum and the pole
placement method to control it. In this chapter, we discussed about
many key issues related to the control of the double inverted
pendulum, such as stabilization, non-linear and robust problems etc.
The objective of this work is to keep steady the double inverted
pendulum in an Up-Up unstable equilibrium point. In the pole
placement control method, poles will be placed at the desired position
by computing gain matrix of the system.
Chapter 3 discusses about the mathematical modeling and stability
analysis of a passive dynamic simple biped robot when it walks on the
ramp. The mathematical modeling contains two basic equations: first,
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motions equation which can be described by the ordinary differential
equations and second, impact equation which can be expressed by the
transaction mapping. The stability analysis is studied into in three
levels:

first, local stability which explained that how much disturbance
can be allowed to a stable cyclic motion,

second,
global
stability
which
discussed
about
the
initial
conditions which give the stable symmetric gait,

third, the stability due to the values of parameters like slope of a
ramp, mass and length of robot.
List of papers published/ presented follows the last chapter. The
thesis ends with Bibliography.