Chapter 1. Robot and Robotics PP

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1 Chapter 1 Robot and Robotics PP

2 Modeling and Stability of Robotic Motions 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 with the variations in the neighboring environment

3 Mahesh A. Yeolekar 3 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.

4 Modeling and Stability of Robotic Motions 4 Input from Neighboring Environment Sensors Brain Effectors Fig 1.1 Synchronization between the components of robot 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. 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

Consequently, the working envelope of the robot is in a form of a rectangular box. Fig 1.2 Cartesian robots ii.

5 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 6 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.

It is useful to manufacturer of home appliances, electric appliances, auto parts, medical equipments. Fig 1.5 SCARA robots v.

6 Modeling and Stability of Robotic Motions 6 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.

Mahesh A. Yeolekar 7 Fig 1.6 Articulated robots vi. Parallel robots The robot which contains several computer controlled mechanism on a single platform is called parallel robot.

7 Parallel robots The mobile robot is a movable robotic system which can move from one place to other place within an environment.

7 Mahesh A. Yeolekar 7 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. II. Mobile robot Fig 1.7 Parallel robots 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 8 surrounding without onboard presence of human. It is used for military purposes. Fig 1.8 Unmanned Grounded Vehicle b.

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.

8 Modeling and Stability of Robotic Motions 8 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.

Mahesh A. Yeolekar 9 Fig 1.10 Autonomous Underwater Vehicle ii.

Wheeled robots The wheeled robots act on wheels which are fitted on the both side

This helps to move in any direction by changing the degree of rotation of its

Legged robots The legged robots movements are based on legs which placed on the

9 Mahesh A. Yeolekar 9 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 10 1.1.2 Types of Locomotion Fig 1.

In sense of mechanics, the degrees of freedom of system are the number of independent parameters which required for defining its configuration.

controllable degrees of freedom are the number of controller required to control the system. The locomotion of robot can be classified as follows: i.

10 Modeling and Stability of Robotic Motions Types of Locomotion Fig 1.12 Legged Robots 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.

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

11 Mahesh A. Yeolekar 11 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 12 arm is an example of redundant which has total six degrees of freedom, but seven controllers are required to control its motion. Fig 1.

12 Modeling and Stability of Robotic Motions 12 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

13 Mahesh A. Yeolekar 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 14 mapping from human activities to humanoid robot activities. Moreover, they are the best tool to study human intelligence.

14 Modeling and Stability of Robotic Motions 14 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:

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

they can raise the head and so they have a better ground vision with enhanced detection of remote hazards.

15 Mahesh A. Yeolekar 15 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

16 Modeling and Stability of Robotic Motions 16 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 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

17 Mahesh A. Yeolekar 17 Fig 1.18 Gait cycle of biped analogous to human gait cycle of gravity. The impact of swing foot with ground is complete the 1- cycle 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

18 Modeling and Stability of Robotic Motions 18 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,

19 Mahesh A. Yeolekar 19 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.

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