anand kumar mishra_1211mt02_2012 batch.pdf

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Design, Simulation, Fabrication and Planning of Bio-

Inspired Quadruped Robot

A Thesis

Presented to

The Academic Faculty

by

Anand Kumar Mishra

In Partial Fulfillment

of the Requirements for the Degree of

Master of Technology

in

Mechatronics Engineering

Indian Institute of Technology Patna

[May 2014]

Copyright Anand Kumar 2014


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INDIAN INSTITUTE OF TECHNOLOGY PATNA

Evaluation Committee Approval

of a Thesis submitted by

ANAND KUMAR MISHRA

The thesis entitled Design, Simulation, Fabrication and Planning of Bio-Inspired Quadruped Robot has been read, found satisfactory and approved by

the following DPPC committee members.

Name: 1___________________,

Coordinator

School of Engineering/Basic Sciences Date: _________________

Name: 2 ___________________, Supervisor Date: _________________

Name: 3 ___________________, Co-Supervisor Date: _________________

Name: 4 ___________________, Member Date: _________________

Name: 5 ___________________, Member Date: _________________

Name: 6 ___________________, Member Date: _________________

Name: 7 ___________________, Member Date: _________________

Name: 8____________________, Member Date: _________________


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Dedicated

To

My beloved Master My father

mother Sapana Shipra and

Akanksha


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ACKNOWLEDGEMENTS

I would like to express my sincere gratitude to my thesis advisor Dr. Atul Thakur. Hehas given me excellent guidance and advice over the years here at IIT Patna. His

guidance helped me in all the time of research and writing this thesis.

Besides my advisor, I would like to thank the DPPC; Dr. Karali Patra, Dr.

Somnath Sarangi, Dr. Somnath Roy, Dr. M.K. Khan, Dr. Manabendra Pathak, Dr. S.S

Panda and Dr. Mayank Tiwari, for their encouragement, insightful comments, and

hard questions. I would like to convey my sincere thanks to all the faculty members in

the department of Mechanical and Electrical Engineering at IIT Patna.

My special thanks to the Center for Artificial Intelligence and Robotics,

DRDO for providing me an opportunity for internship and thereby enhancing my

skills and knowledge.

I would like to express my most sincere gratitude and deep regards to my

Co-guide Mr. Sartaj Singh, Sc E, Centre for Artificial Intelligence and Robotics, for

his guidance, monitoring and constant encouragement throughout the course of

project period.

I am very thankful to Mr. P. Murali Krishna, Sc E, Mr. Babu Jadhav, Sc D,

Mr. K Ramachandran, Sc C, Mr. Dharmendra Kumar Patel, Sc B at CAIR for their

valuable information and guidance through various stages, which helped me in

completing my internship project.

I also take this opportunity to express a deep sense of gratitude to Dr. Dipti

Deodhare, Sc G for granting me an opportunity to carry out the project at CAIR,

DRDO.

I thank my labmates Amrutesh and Delip and also I thank my friends

Sherbahadur, Nitin, Kapil and Amit for all the fun we have had in the last two years.

Last but not the least I would like to thank my family: my loving mother and

father, my sisters and Akanksha Tripathi who has always loved, supported, and

believed in me.

(Anand Kumar Mishra)


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Certificate

This is to certify that the thesis entitled DESIGN, SIMULATION, FABRICATION

AND PLANNING OF BIO-INSPIRED QUADRUPED ROBOT, submitted by

ANAND KUMAR MISHRA to Indian Institute of Technology Patna, is a record of

bonafide research work under my supervision and I consider it worthy of

consideration for the degree of Master of Technology of this Institute. This work or a

part has not been submitted to any university/institution for the award of

degree/diploma. The thesis is free from plagiarized material.

________________________________

________________________________

Supervisor Date: ______________


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Declaration

I certify that

a. The work contained in this thesis is original and has been done by me under the

general supervision of my supervisor/s.

b. The work has not been submitted to any other institute for degree or diploma.

c. I have followed the institute norms and guidelines and abide by the regulation as

given in the Ethical Code of Conduct of the institute.

d. Whenever I have used materials (data, theory and text) from other sources, I have

given due credit to them by citing them in the text of the thesis and giving their details

in the reference section.

e. The thesis document has been thoroughly checked to exclude plagiarism.

Signature of the Student

Roll No: 1211MT02


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TABLE OF CONTENTS

LIST OF FIGURES viii

LIST OF TABLES xii

LIST OF SYMBOLS xiii

LIST OF ABBREVIATIONS xiv

ABSTRACT

1. INTRODUCTION 1

1.1 Introduction to legged robots

1.1.1

Brief review of legged robots 2

1.1.2 Advantages of legged robots 3

1.1.3

Disadvantages of legged robots 3

1.1.4 Application of legged robots 4

1.2 Introduction to bio-inspired robotics 4

1.3

Introduction to quadruped robot 6

1.4 Objective 7

1.5

Organization of thesis 8

2. LITERATURE REVIEW

2.1 Overview 10

2.2

Snake robot 10

2.2.1 Active cord mechanism series 10

2.2.2 Amphibots 11

2.3 Legged robots 12

2.3.1

Scout 12

2.3.2 Takken-II 12

2.3.3 KOLT 13

2.3.4 Kenken-II 14

2.3.5 Big Dog 14

2.3.6 ELIRO-II 15

2.3.7

Shelley-RHex 16

2.3.8

Salamander 17


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3. DESIGN METHODOLOGY OF QUADRUPED ROBOT

3.1 Design description of legged robot 18

3.2 Design of alligator inspired robot 19

3.2.1

Biological inspiration 19

3.2.2 Robot design 21

3.3 Design description of mammalian inspired robot 26

4. KINEMATIC AND DYNAMIC ANALYSIS AND TRAJECTORY PLANNING

OF QUADRUPED ROBOT

4.1 Introduction 27

4.2 Kinematic modeling of alligator inspired robot 27

4.2.1 Frame assignment 27

4.2.2 D-H parameters 28

4.2.3 Forward kinematics 28

4.3 Jacobian: velocity analysis of alligator inspired robot 30

4.4 Trajectory planning for quadruped leg 30

4.4.1 Straight line trajectory of quadruped leg with via points 32

4.4.2

Cubic trajectory of quadruped leg with via points 33

4.5 Dynamic analysis of quadruped robot 34

4.6

Kinematic analysis of mammalian inspired robot 38

4.6.1

Frame assignment 38

4.6.2 D-H parameters 38

4.6.3 Forward kinematics 38

4.6.4 Inverse kinematics 40

4.7 Jacobian: velocity analysis of mammalian inspired robot 43

4.7.1 Linear and angular velocity from leg frame 43

4.7.2

Linear and angular velocity from body frame 44

4.8

Dynamic analysis of mammalian inspired quadruped robot 45

5. GAIT PLANNING AND STATIC STABILITY ANALYSIS OF QUADRUPED

ROBOT

5.1 Introduction 50

5.2 Gate synthesis 51

5.2.1 Crawl gait 52

5.2.2

Trot gait 54


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5.2.3

Bound gait 55

5.3 Stability analysis of quadruped robot 55

5.3.1 Introduction 55

5.3.2

Static stability margin and longitudinal stability margin

for crawl gait 56

5.3.3 Algorithm developed for SSM for crawl gait 58

6. SIMULATION OF QUADRUPED ROBOT

6.1 Introduction 60

6.2 Control architecture for simulation 62

6.3 Multibody simulation of alligator inspired robot 63

6.3.1 MBD simulation of leg 63

6.3.2 MBD simulation of whole body 64

6.4 MBD simulation of mammal inspired robot 67

6.4.1 Leg simulation 67

6.4.2 Dynamic leg simulation 69

6.4.3 Whole body simulation 70

6.5

Finite element analysis of quadruped robot 74

6.5.1 Leg simulation 75

6.5.2

Body simulation 75

6.6

Stability analysis of mammal inspired robot 76

7. FABRICATION AND ASSEMBLY OF QUADRUPED ROBOT

7.1 Fabrication of alligator inspired robot 77

7.2 Assembly of alligator inspired robot 79

7.3 Fabrication and assembly of mammalian inspired robot 81

7.4 Modular joint descriptions 81

7.4.1

Construction 81

7.4.2

Absolute encoder 83

8. CONTROL ARCHITECTURE AND EXPERIMENTAL STUDY

8.1 Control plan 84

8.2 Motion control of alligator inspired robot 86

8.2.1 Hardware descriptions for motion control 87

8.3 Motion control of mammalian inspired robot 89

8.3.1

Hardware descriptions for motor control 90


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8.3.2

Part descriptions and specifications 90

8.3.3 Software descriptions for motion control 93

8.4 Experimental study of alligator inspired robot 102

9. CONCLUSION AND FUTURE WORK

9.1 Conclusion 103

9.2 Future scope of work 104

References


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LIST OF FIGURES

Figure No. Page

Figure 1.1

(a) Sprit wheeled robot sticking on sandy surfaces (courtesy toNASA) (b)Big Dog robot is moving on sandy surfaces (courtesy

to Boston Dynamics) (c) Sketch of legged machine obtained

Rygg from the planar drawing in (Artobolevsky, 1964) (d)

Mechanical horse patented by U.S. Patent No. 491,927 dated

Feb. 14,1983 (e) The Adaptive Suspension Vehicle (ASV)

(photograph courtesy of Professor Waldron) (f) PV-II walking

robot (courtesy of Professor Hirose) 2

Figure 1.2 (a) Leg design of crocodiles and alligator (b) Leg design

mammalian 6

Figure 1.3

(a) Model of Robot in SolidWorks(b) Model of Robot in Pro/E 7

Figure 2.1 (a)Amphibious snake-like robot "ACM-R5"(courtesy to

Fukushima Robotics Lab, Japan) (b) Amphibot 1 snake robot

(courtesy to Bio robotics lab, EPFL) (c) Amphibot 2 snake robot

(courtesy to Bio robotics lab, EPFL) 12

Figure 2.3 Scout robot (courtesy to CIM lab, McGill University) 12

Figure 2.4

Takken II (courtesy to Professor Hiroshi Kimura and group) 13

Figure 2.5 KOLT robot (courtesy to bio-robotics lab Stanford and Ohio

University) 13

Figure 2.6 KenKen II (courtesy to bio-robotics lab Tohoku University) 14

Figure 2.7

BigDog (courtesy to Boston Dynamics) 15

Figure 2.8 ELIRO-II (courtesy to Kyungpook National University) 16

Figure 2.9

Shelley-RHex (courtesy DARA challenge project) 17

Figure 2.10

Salamander robot (courtesy to Bio robotics lab, EPFL) 17

Figure 3.1 Design approach 18

Figure 3.2 (a) Type of limb and segments of alligators leg (b) Anatomy of

pelvic limbs (c) Anatomy of pectoral limbs 19

Figure 3.3 Design inspiration 20

Figure 3.4 Scaled legged of alligator-inspired robot on body length 21

Figure 3.5

Designed CAD model in Pro/E 22


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Figure 3.6

Pro/E design alligator-inspired robot 23

Figure 3.7 Free body diagram 24

Figure 3.8 Selected motor 25

Figure 3.9

Quadruped robot 26

Figure 4.1 Frame assignment of the alligator-inspired robot 28

Figure 4.2 Velocity vector of neighbouring link 30

Figure 4.3

Trajectory planning with via point 31

Figure 4.4 Straight line trajectory 32

Figure 4.5 (a) Frame assignment on body (b) Frame assignment on leg 38

Figure 5.1 Quadruped gaits (a) Top view of a robot (b) Graph of leg

sequences (c)(h) sequences 51

Figure 5.2 Quadruped gait types 52

Figure 5.3 (a) Gait sequencing of crawl gait (b) Gait diagrams of crawl

gait (c) Successive gait pattern of a two-phase discontinuous

gait 53

Figure 5.4 Trot gait sequences (b): Gait diagram of trot gait sequences 54

Figure 5.5

(a) Bound gait sequences (b) Gait diagrams of bound gait

sequences 55

Figure 5.6

Support polygon and different static stability margin 56

Figure 5.7

Static stability margin 57

Figure 5.8 Quadruped in static mode all legs on ground 58

Figure 5.9 Geometric view of quadruped when it lifts its 1stleg 58

Figure 5.10Geometric view of quadruped when it lifts its 2ndleg 59

Figure 6.1 (a) Simplified CAD model of mammal (b) Simplified CAD

model of alligator (c) Defined joint and motion in Adams(d)

Plant generated by Adams(e) Simulink model of close loop

control for simulation 62

Figure 6.2 Control strategy for quadruped simulation 63

Figure 6.3 (a) CAD model of leg imported in Adams (b) Desired angular

position achieved (c) Torque required for robot leg 64

Figure 6.4 (a) CAD model of alligator-inspired robot imported in Adams

(b) Desired angular position achieved by Knee joint(c) Desired

angular position achieved by Hip joint(d) Distance travelled by


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the robot (e) Speed achieved (f) Angular velocity variation of

joint1 (g) Acceleration variation of the robot(h) Reaction force

from the ground(i) Power consumption required each motors 67

Figure 6.5

(a) CAD model of mammal-inspired leg imported in Adams (b)

Torque required for robot leg at joint 1 (c) Torque required for

robot leg at joint 2 (d) straight line trajectory of 3dof leg with

via point (e) For straight line trajectory of 3dof leg with via

point 69

Figure 6.6 (a) Model based control in joint space for dynamic analysis

quadruped robot (b) Torque control simulation results 70

Figure 6.7 (a) CAD model of mammal -inspired robot imported in Adams 71

Figure 6.8 (a) Crawl gait sequences (b) Angular position variation form

the each joint of legs (c) Velocity achieved in the crawl gait

implementation (d) Torque required in crawl gait

implementation by robot joints (e) Reaction forces from the

ground crawl gait implementation 72

Figure 6.9

(a) Velocity achieved in the trot gait implementation (b) Torque

required in trot gait implementation by robot joints (c) Reaction

forces from the ground crawl gait implementation 73

Figure 6.10

(a) Velocity achieved in the bound gait implementation (b)

required in bound gait implementation by robot joints 74

Figure 6.11(a) Maximum shear stress and von misses stress of leg FEA

simulations (b) Maximum shear stress and von misses stress of

whole body FEA simulations 75

Figure 6.12Static stability simulation of the robot 76

Figure 7.1

(a) Left-hand image is that of the targeted robot leg design

prototype developed in Pro/ENGINEER Wildfire 4.0 whereas

right-hand image is that of actual robot limb fabricated in 3D

Rapid Prototype Printer using ABSplusin ivory at about 1.6 kW

(RMS) (b) Part required for robot assembly; (i) Hons require for

motor coupling (ii) End of the leg part fabricate in 3D printer

(iii) Screws and nut required (iv) Front body part (v) Rear body


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part (vi) Leg of the robot (vii) Battery required (viii) Leg

coupling 79

Figure 7.2 (a) Assembled modular joint (b) Assembled modular joint

section model 83

Figure 8.1 The coordinate frame, BODY, used here for kinematic analysis

is the same as that used for standard analysis of any

vehicle/locomotion dynamics 85

Figure 8.2 Control priority level for robot 85

Figure 8.3 Flow chart communication for master, slave card and PC of

quadruped 86

Figure 8.4 (a) Proteus simulation of shield (b) Shield developed front view

(c) Shield back view (d) Arduino UNO 88

Figure 8.5 The algorithm to move the alligator forward is summed up as a

flowchart. The actual amount of actuation to be given and the

time delay for the different actuations involved was based on

gait diagram described earlier. This flowchart was generated

using Flow Breeze, a flowchart automation add-in for MS-Excel 89

Figure 8.6 Flow chart communication for master, slave card and PC of

quadruped 89

Figure 8.7

(a) Slave card (b) Motor 92

Figure 8.8 (a) PWM generation (b) Encoder testing (c) Servo loop based

motion control (d) Servo loop and trajectory based motion

control 101

Figure 8.9 (a) Single axis motion control hardware (b) Motion control

implemented 102

Figure 8.10

(a) Robot speed vs delay time (b) Robot speed vs Hip angle

amplitude 102

Figure 9.1 Current status of my research work 103


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LIST OF TABLES

Figure No. Page

Table 3.1 Alligatorslengths and masses 20

Table 3.2 Design specifications of modular body robot 22

Table 3.3 Modular robot servo motor specifications 25

Table 3.4 Design specification mammal-inspired robot 26

Table 4.1 D-H Parameters 28

Table 4.2 D-H Parameters of mammal leg 38

Table 7.1 Material specification 77

Table 7.2 Component required 77

Table 8.1 Requirement for single axis motion control 90


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LIST OF SYMBOLS Over all efficiency Twist angle

l Link length

d Link offset

Torque of joints or motors

Link rotation Leg position at the end Time for one point to next point for trajectory

Acceleration due to gravity

V Linear velocity of the links Linear velocity at center of links Angular velocity of joint Angular acceleration of jointF Inertia force

N Moment due to inertia

n Statics moment on the links

f Static force on each link

Angular velocity relative to links Angular acceleration relative to links Duty factor

Mass matrix

V Coriolis force matrix

G Gravitational force component matrix

Stride lengthR Stroke lengthn No. of legs

yaw movement Linear acceleration


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LIST OF ABBREVIATIONS

CAD Computer aided design

CAN Controller area network

COM Centre of massDOF Degree of freedom

FEA Finite element Analysis

LxWxH Length x Width x Height

PID Proportional integral derivative

PWM Pulse width modulation

MBD Multibody dynamics

SSM Static stability margin

PR Priority resister

D-H Denavit-Hartenberg

MSS Mechanical system simulation

PMMA Polymethy methacrylate

ABS Acrylonitrile butadiene styrene

LLC Low level control

MLC Medium level control

HLC High level control

CNA Contra lateral and non-adjacent

COG Center of gravity

SLSM Static longitudinal stability margin

CSP Conservative Support Polygon

SCLSM Crab Longitudinal Stability Margin


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ABSTRACT

This work reports design, simulation, fabrication, and planning of bio-inspired

quadruped robot. This dissertation deals with two types of bio-inspired quadruped

locomotion patterns, namely, mammalian and reptilian. Legged locomotion is one of

the most successful locomotion patterns found in the Nature. Quadruped walking in

many mammals and reptiles have made them very successful in surviving against

tough environments such as uneven terrains. Nature evolved legged locomotion over

half a billion years. It should be noted that the biological evolution favoured legged

locomotion instead of wheeled locomotion in spite of wheeled locomotion being

faster. This is because more than half of Earths landmass has highly rough terrain

and can be traversed by legged rather than wheeled locomotion. We thus take

inspiration from the Nature to develop legged robots that can traverse on rough

terrains and has advantage over wheeled robots.

We have developed alligator-inspired robot at the Mechatronics laboratory, IIT

Patna. The robot has four legs and each leg has two revolute joints representing the

hip (yaw) and knee (roll) respectively, which are actuated by servo motors, thereby

imparting eight degrees of freedom to the robot. The main contributions of this partof the thesis include following.

Design and modeling of the robot based on multidisciplinary design approach

incorporating CAD modeling, kinematic and dynamic modeling, multibody

simulation and finite element analysis of the robot. We used Pro Engineer for

CAD modeling, Adams, Nastran and Adams Flex for multibody and FEM

simulation.

Fabrication of the designed components of the robot using a CO2 laser cutting

machine and 3D printer. We developed a 3D leg design that has 2D components

to enable manufacturing on a laser cutting machine to reduce fabrication cycle

time.

Integration of electronics such as microcontroller, sensor, servomotors, drivers,

etc.


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Synthesis of crawl and trot gaits. We implemented the gaits in simulation

followed by on the physical robot. The maximum speed attained by the developed

robot is 0.51 BL/sec.

The Mammal-inspired robot known as Robotic muleis being developed at the

Center for Artificial Intelligence and Robotics, DRDO Bangalore where I was

working as an intern for seven months during my project work. This robot is expected

to carry heavy weapons and food over rocky terrains for the soldiers and civilian

purposes. Robotic mule has 4 legs and each leg has 3 degrees of freedom (one roll and

two pitch motions). Each motion is actuated by high torque DC motor with gear ratio

991 and the motor has an inbuilt encoder for positional feedback. The motion control

of the joints is based on forward feedback control. The load carrying capacity of the

robot is less than 10 kg. My contribution in this project includes the following:

Derivation of D-H parameters, frame assignment, kinematic and dynamic

analysis, simplified CAD modeling using SolidWorks.

Multibody dynamic simulation using Adams which helps to validate and optimize

the robot design and mechanism. I performed both kinematic and dynamic

simulation of the robot and implemented a proportional (P) controller.

Gait synthesis such as crawl, trot and bound gait. Algorithms were first

implemented in simulation followed by on actual robot.

Development and testing of static stability margin algorithm in the simulation.

Development of single axis motion control using dsPIC30F4011 series

microcontrollers.


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CHAPTER 1

INTRODUCTION

1.1. Introduction to legged robot

According to Raibert, only half of the earth's land mass is currently accessible by

wheeled or tracked vehicles, with a much larger fraction being accessible to legged

creatures. Legged robots often offer some advantage over wheeled robots [1]. For

example, wheeled or tracked vehicles are restricted by the roughness of the terrain

which they must traverse (see Figure 1.1(a), (b)).

Figure 1.1 (a) Sprit wheeled robot sticking on Figure 1.1 (b) Big Dog robot is moving on

sandy surfaces (courtesy to NASA) sandy surfaces (courtesy to Boston Dynamics)

Wheeled robots require a continuous path of support. On the other hand, legged

robots can traverse highly uneven terrains as they require point contacts between the

legs and the terrain. In addition, legs can serve as an active suspension system helping

to decouple terrain variations from body movements thus smoothing locomotion.

Some of the legged robot design challenges include incorporation of leg and

body compliance, multi-sensor integration, vibration resistance, dynamic and static

stability, onboard power supply. Control of legged robots also present a unique

challenge of gait planning for various terrain types. This is because of high

nonlinearity and discontinuous nature of the dynamics of the legged robots.


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1.1.1.Brief review of legged robots

Simple walking mechanisms were developed to study legged locomotion for toys that

move on limited type of flat terrains. Researchers started to study about the walking

mode of the legged creatures and recoded their motion. Afterwards, to study and

improve the walking mechanism the biological gaits and their mathematical

formulation were derived. Thus, stability measurements and gait generation

algorithms were developed based on exact locomotion patterns found in the Nature.

Improvements were later made to adapt to specific legged robots. In considering the

history of walking machines we can see from 18thcentury researchers have developed

many legged robot. Some of the examples are shown in Figure 1.1(c) to Figure 1.1 (f).

First robot legged mechanism was built around 1870 by Chebyshev in Figure 1.1 (c).

Similarly in 1893 mechanical horse was built shown in Figure 1.1 (d).

Due to their specific advantage over wheeled robot currently people are doing many

researches on the legged robot[2].

Figure1.1 (c) Design of legged machine obtained Figure 1.1 (d) Mechanical horse patented by Rygg

from the 2D drawing in (Artobolevsky, 1964) U.S. Patent No. 491,927 dated Feb. 14, 1893

Figure 1.1 (e) The Adaptive Suspension Vehicle (ASV) Figure 1.1(f) PV-II walking robots

(photograph courtesy of Professor Waldron) (photograph courtesy of Professor Hirose)


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1.1.2.Advantages of legged robots

There are several advantages of legged machine over the traditional tracked vehicles

and the advantages are explained below[3].

a.

MobilityMobility of a legged robot is more than a wheeled robot due to their Omni directional

nature. Legged robots can change the direction without any hindrance of the body and

only change in leg positions are required and wheeled robot have less maneuverability

than legged robots[2],[3].

b. Overcoming obstacles

A legged robot can overcome obstacles that are at a lower level than the maximum

ground clearance, just by stepping on them. On the other hand, a wheeled robot can

only overcome obstacles with heights of up to half of the wheel radius.

c. Active suspension

Active suspension is much better in legged robot due to natural property of

suspension however in wheeled robot a suspension is required. Active suspension

property come with the adjustment of leg position to maintain the body height same as

according to terrain nature.

d. Energy efficiency

Efficiency of heavy legged vehicle is better than the wheeled vehicle as suggested by

the Hutchinson in 1940 and it was proved by Bekker through the experiment, the

efficiency was much better on irregular terrain by legged vehicle over wheeled or

tracked vehicle.

e. Natural terrain

As Raibert suggested that only half of the land mass can be travelled by the wheeled

vehicle and wheeled vehicle is required expensive flat surfaces while legged vehicle

can go any type of surfaces such highly rugged, soft muddy etc.

1.1.3.Disadvantages of legged robots

Complex mechanisms are required to make robust legged vehicle.

Control is one of the challenging problems.

Gait planning for the highly rugged terrain is very difficult task.

Stability is one of the major issue in legged robotics.


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1.1.4.Application of legged robots

1.

Military applications

2.

Inspection of Nuclear Power Plants

3.

Land, Submarine and Planetary Exploration4. Forestry and Agricultural Tasks

5.

Forestry and Agricultural Tasks

6. Help for Disabled People

7. Study of Living Creatures

8. Civil Projects

9. Humanitarian De-mining

10.Support for AI Technique

1.2. Introduction to bio-inspired robotics

Legged locomotion is one of the most successful locomotion patterns found in the

Nature. Evidence of first locomotion among biological organisms is around 585

million years old. This means that it took the evolution process around 585 million

years to evolve various forms of walking gaits. Quadruped walking in many mammals

and reptiles have made them very successful in surviving against tough environments

such as uneven terrains. In comparison, humans invented wheel-based locomotion

around 4000 years ago. Nature evolved legged locomotion instead of wheels because

more than half of Earths landmass cannot be traversed by wheels, even today. It is

thus the imperative for the roboticist to learn the design and gait patterns from the

phylogenetic analysis of biological organisms and try to mimic them as closely as

possible to improve the performance of existing robots.

In this report, design and simulation of an alligator-inspired and mule inspired

robot have been accomplished. Robot exhibits a particular type of reptilian

locomotion and mammalian locomotion. Alligator locomotion is generally considered

as an intermediate step in the evolutionary paradigm of vertebrate locomotion [3], [4].

At one extreme, are the amphibians and lizards who are natural sprawlers. Their limbs

are held laterally to the body. At the other extreme, are the mammals and dinosaurs

exhibiting erect locomotion posture (ELP). Humans exhibit ELP too. In ELP, limbs

are held directly under the body. Reptilian locomotion posture of crocodiles and


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alligators is considered to be an intermediate locomotion posture between these two

extremes as a kind of transition from sprawl-to-erect [5].

Another interesting feature of alligator locomotion that has come to light is that

alligators still use sprawl to negotiate muddy lands at low speeds while high walk is

activated on drier lands at higher speeds. This transition between different gaits as a

function of speed is a general locomotion feature [6], [7], [8] .

Most reptiles can actually adapt to an amphibious habitat. Thus, imitating a reptile

can help in development of robots that can perform both terrestrial as well as aquatic

locomotion. But building robot designs inspired by biological counterparts can enable

us in imparting critical ethological functionality to robots. Moreover, it has been

studied that artificial intelligence can be developed more efficiently in bio-inspired

compliant designs[9], [10].

Success of biological designs lies in the optimal cooperative and coordinated

interplay among the following factors[11].

a.) Availability of optimal energy generation, storage and conversion mechanisms.

b.) Ability of memorising, storing, processing, internalising and passing information.

c.)

Complaint and robust structural features that can adapt to various environment.

This is what has inspired the fields of biomimetics, biokleptics and bio-inspiration.

However, exact mimicking of reptilian gait (biological gait in general) is plagued with

following challenges:-

a.) Mechanical complexity of nature is overwhelming. Fabrication of intricate

skeleton-muscular system, which gives enormous agility to animals, is very

difficult to replicate using existing manufacturing technology.

b.) Imitating self-replicating biological units like cells cannot be fabricated in

laboratory easily.

c.)

Energy generation and storage mechanism in biological systems are not

understood to an extent that it can be copied in robots.

Therefore, in the light of the above-mentioned motivations and challenges, many

researchers have proposed the use of biological inspiration instead of exact replication

of biological structures [12], [13], [14].

A lot of research has been done in the field of walking bio-inspired robots

mimicking biological counterparts. The bio-inspiration in case of mobile robots


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comes largely from tetra pods - both reptiles as well as mammals (See Figure 1.2 (a)

and (b)

Figure 1.2 (a): Leg design of crocodiles and alligators Figure 1.2 (b):.Leg design of mammalian

Note the ball-and-socket joint provided at the knee and hip about which rotatory

actuation takes place which results in locomotion. The approximate perpendicular

orientation of the coordinate frames attached to the hip and knee joints is the salient

feature of all members of the order Crocodilia. Note also the approximate parallel

orientation of the coordinate frames attached to the hip and knee joints. For walking

robots, both static and dynamic walking as well as both active and passive walking

has been extensively researched [15]. Interest in legged walking robots over

wheeled/tracked robots generated mainly because of

a.)

More efficient traversal of difficult terrains,b.)Nature is the best designer hence just bio-mimic the design handed over to us

by evolution,

c.)

More robust and durable if designed on the principles of compliant

mechanism, say by using flexible links, and

d.) More efficient motion planning can take place as a wider range of

manoeuvrability is made available.

1.3.

Introduction to quadruped robotIn this thesis, we are focusing on quadruped robots, which belong to the broader class

of legged robots as described earlier. In quadruped robots there are four legs, each leg

should have minimum two degrees of freedom. However, some quadruped robots

may have higher degree of freedom legs too. Quadruped robots can walk and run but

standing still it must be passively stable. The main challenge of quadruped robot is to

maintain stability by actively shifting body weight during the gait.


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The quadruped robots described in this thesis are inspired from two types of animals,

namely, mammals and reptiles. Mammalian type locomotion has an advantage that

they can move faster due to geometrical configuration of leg joints. Some examples of

mammalian locomotion based robot include ABIBO robotic dog, robotic cheetah etc.

Another advantage of mammalian type four-legged robots is an ease in gait transition.

Mammal inspired robot thus have a potential to serve as useful platform for research

in Human-robot interaction (see Figure 1.3 (a)). Reptile-inspired robots have

relatively slower speed but higher static stability (see Figure 1.3 (b)). Quadruped

robots can be used for civilian and military purpose to carry heavy loads.

Figure 1.3 (a) Model of Robot in SolidWorks Figure 1.3 (b) Model of Robot in Pro/E

1.4.

Objective

The thesis has been carried out partly at IIT Patna and CAIR, DRDO Laboratory. The

objectives of each part of the thesis are outlined below.

IIT Patna

Kinematics analysis of alligator-inspired quadruped robot.

CAD modeling of alligator-inspired quadruped using Pro\E based alligator

anatomy

Kinematic, dynamic modeling and trajectory planning

Derivation of gait sequences and simulation using Adams and Matlab.

Analysis of stability of alligator-inspired quadruped both static as well as dynamic.

Embedded control software for alligator-inspired quadruped.

Finite element analysis of alligator-inspired quadruped.

Complaint body design and simulation of alligator-inspired quadruped.

Development of alligator-inspired quadruped with complaint in the body.

Speed and stability analysis on actual setup.


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CAIR, DRDO Laboratory

Kinematics analysis of mammalian-inspired quadruped robot.

CAD modeling of mammalian-inspired quadruped using SolidWorks and

kinematics simulation with Adams and Matlab.

Dynamics analysis of mammalian-inspired quadruped robot with 3 DOFlegs.

Derivation of gait sequences and simulation using Adams and Matlab.

Analysis of stability of mammalian-inspired quadruped both static as well as

dynamic.

Design single axis motion control for mammalian-inspired quadruped

Embedded Control Software for mammalian-inspired quadruped

1.5. Organization of the report

The outline of the thesis is as follows.

Chapter 2 discusses literature review of the bio-inspired robot. A survey work of

snake robots, swimming robots and terrestrial locomotion based robot is briefly

described.

Chapter 3 discusses of the design methodology of the quadruped robot. Design of

quadruped robot describes CAD modeling based on imitation from biology, the

design leg ratio of robot is based on anatomy of actual alligators and torque

calculation and selection motors has been done.

Chapter 4discusses a kinematic, dynamic modeling of quadruped robot. The chapter

will explain the frame assignment, D-H parameters, forward kinematics analysis

velocity Jacobian analysis and dynamic analysis has been done. For robot motion

smooth the cubic and straight line trajectory has been derived.

Chapter 5reports a gait planning and stability analysis. Gait planning of quadruped is

based on mammalian-inspired and reptilian inspired robot. Graphical representation of

trot, crawl and bound has been shown and static stability margin analysis is done in

this chapter.

Chapter 6discusses multibody, FEA simulation of quadruped robot. Simulation of

alligator inspired robot and mammalian inspired robot is separately done.

Chapter 7 reports fabrication and assembly of alligator-inspired robot and modular

joint assembly of mammal-inspired robot.

Chapter 8discusses motion control and control architecture of the quadruped robot.

The chapter will elaborate the single axis motion controller which consist the


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hardware and software part both and 3 layer control architecture is used for alligator

inspired quadruped robot

Chapter 9 contains a summary of important conclusions and scope for future work in

the area of bio-inspired quadruped robots.


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CHAPTER 2

LITERATURE REVIEW

2.1.

OverviewThis chapter presents a review of the state of art in the area of bio-inspired robotics.

This review investigates the current methods of terrestrial locomotion based and

amphibious robots. It will cover the scope and application of these robots.

2.2. Snake robots

Implementing these advantages in a robot is a hard task but a close approximation is

quite possible. Snake inspired robots have come a long way since their inception. The

concept of serpentine motion and its advantages were recognized by Shigeo Hirosewho pioneered in this research. Since then many engineers conceptualized a lot of

ideas in making the snake robots. James Hopkins in 2009 developed a general

classification of these robots based on the material published till that date.

2.2.1.The Active Cord mechanism series:

ACM 3: This model was created in the initial stages of the snake robot research.

It consisted of 20 links with passive wheels actuated solely with the help of the

revolute joints between the links[16].

ACM-R3: The key difference between ACM 3 and ACM R3 is that the latter had

a scope to move in 3D. That is, the robot had consecutive passive wheels as well

as the revolute joints placed orthogonally. This model was significantly lighter

than ACM 3

ACM R4: R4 builds on R3 by replacing passive wheel with active ones. This

change enables the robot to traverse rough ground with relative ease[16], [17].

ACM R5: This is an amphibian design to increase the versatility of the robot. R5

uses paddles on the passive wheels to acquire anisotropic friction both on ground

and water. But the technology of the time could solve the problems that impeded

the realization of practical snake robots[18].


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Figure 2.1(a) Amphibious snake robot "ACM-R5"(courtesy to Fukushima Robotics Lab, Japan) [18]

grip onto the next robot. Thus the self sufficient modules form a chain and

accomplish tasks like climbing the stairs or crossing a ditch.

2.2.2.Amphibots:

i. Amphibot 1: This is a modular robot developed in the quest to find new robot

designs which could exhibit dextrose locomotion. Each link was made to be slightly

buoyant and the center of mass of each link was purposefully kept slightly lower than

the geometric centre of mass so that during idle conditions, the snake could float and

obtain vertical orientation[19].

Figure 2.1(b) Amphibot 1 snake robot (courtesy to Bio robotics lab, EPFL) [19]

ii. Amphibot 2: This is an advanced version of Amphibot 1. The design was

simplified and new powerful motors were equipped. An electronic suite was

introduced which could handle up to 127 segments theoretically. The robot used

removable wheel sets to achieve ground motion[20], [21].


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Figure 2.1(c) Amphibot 2 snake robot (courtesy to Bio robotics lab, EPFL) [20]

2.3. Legged robots

2.3.1. Scout

Martin Buehler in 1990s, at Ambulatory Robotics Lab (ARL) of McGill University

started developing the Scout robot series. In 1999 he presented, a quadruped robot

Scout II (Figure 2.3) which was dynamically stable and had a very simple mechanical

design. This robot had one active rotational joint at each leg located at the hip with the

help of which it was able to rotate the leg in the sagittal plane. The leg is divided into

two parts-upper and lower legs. These parts are connected by a spring to form a

compliant prismatic joint. It weighed around 27kg and has 0.55m x 0.48m x 0.27m

(LxWxH). After some year, Scout II, with a forward velocity of up to 1.3 m/s, was

able to perform a stable bounding gait[23], [24], [25].

Figure 2.3: Scout robot (courtesy to CIM lab, McGill University)[23]

2.3.2.Takken II

Hiroshi Kimura and colleagues had developed a quadruped robot Patrushand, later

Tekken series. These robots are a central pattern generators (CPG) based robot and

have joint reflexes. It is mainly used to study controllers which are biologically

inspired. In Figure 2.4, Tekken II is shown; it is a small quadruped robot having


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length of 0.3m length and weight of 4.3kg weight. Mechanical springs are adding

compliance to the joints whereas it is actuated by electric motors[26],[27].

Figure 2.4 Tekken II (courtesy to Professor Hiroshi Kimura and group)[27]

2.3.3.KOLT

Kenneth Waldron and his group at Stanford University in collaboration with Ohio

State University had developed the KOLT robot shown in Figure 2.5. The quadruped

robot has a weight of about 80kg and has the following dimensions: 1.75m x 0.6m x

0.8m (LxWxH). Robot has electric actuation with mechanical springs. In running

experiments, the robot was attached to a boom that permitted free motion in the plane

and it was found that the robot performed stable trotting with 1.1m/s on a treadmill

[28], [29], [30], [31].

Figure 2.5: KOLT robot (courtesy to bio-robotics lab Stanford and Ohio University)[29]


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2.3.4.KenKenII

In 1998, a hydraulic quadruped robot was developed by Sang-Ho Hyon with his

colleagues at Tohoku University (Japan). They had first built the monopod robot

KenKenI and later a biped version KenKenII (Figure 2.6), but an actual quadrupedrobot was never constructed. Nevertheless, they managed to achieve impressive

results[32], [32], [33].

Figure 2.6 KenKen II (courtesy to bio-robotics lab Tohoku University)[33]

2.3.5.Big Dog

Boston Dynamics Corporation was founded, as a spin-off from the MIT, in 1992 by

Marc Raibert and some of his colleagues. The initial company focus was on software

for human simulations, such as DI-Guy, which at that time was being used for

military applications. In 2005 however they presented the first version of their

quadruped robot called Big Dog (Figure 2.7).The main goal of the project was the

development of a mechanical mule with the following properties

Autonomous power

Capability of carrying heavy payloads

Outdoor operational

Having static and dynamic mobility

Fully integrated sensing for mobility

Able to jump over a 1m ditch, climb 45 (100%) slopes, run at 5m/s, and carry over

50kg payload.


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Figure 2.7 BigDog (courtesy to Boston Dynamics) [35]

The robot presented in 2005 (BigDog 2005) was 1m in length and 0.3m width, and

had a weight of about 90kg. It had four legs each having four DOF: hydraulic

cylinders are powered by three active rotational joints and one passive linear joint in

the foot based on a pneumatic spring[34], [35], [36].

2.3.6.ELIRO-II

Kyungpook National University came up with a robot gait built to incorporate

discontinuous twisting at the waist. Many natural walking gaits incorporate a central

DOF at the spine, which increases speed and stability, especially while turning. A

systematic approach was taken and following assumption were made that is, the robot

would be on flat terrain, parallel to the ground, with mass less legs, a uniform

mass of the body, and a single degree of freedom along the z-axis at the center as

the waist joint. From these set of assumptions, the kinematics was determined,

nothing especially that in a non rigid body an optimal hip position can be created.

Based on these kinematic observations some additional features were drawn, thestride increases drastically from a rigid body, maneuverability in unfavorable

situations was greatly improved and the general gait stability was improved. In gait

planning, ten time steps were used with the center of gravity shifted at varying

intervals; the bending angle for the center and the leg order were varied. Eventually

the conclusions from this were used in a quadrupedal robot with 3 DOF pantograph

legs called ELIRO-II. This robot achieved stable turning on flat ground and it is noted


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Figure 2.9 Shelley-RHex (courtesy DARA challenge project)[38]

2.3.8. Salamander

The salamanders robot is amphibious robot which can perform walking and

swimming gaits. It uses primary actuator for the center spine. It swims by body

undulation to create a wave for the propagation while in walking it uses terrestrial

gaits with the help of its leg. By using some assumptions, a robot was created with ten

actuators, four for the legs and six for the body. Using a central pattern generator

comprised of 16 to 32 oscillators as the gait basis. Relationships between each were

defined by matrices of weights and modeled in formulae representing the phase and

amplitude of any given oscillator as well as the positive signal representing the central

burst action. In creating this robot, it was shown to be consistent with the actual

salamanders movement in both walking and swimming. Ultimately it is noted that

the central pattern generator concepts used here would be very helpful in general

robotics, given that the dimensionality of a control problem may be reduced [39].

Figure 2.10: Salamander robot (courtesy to Bio robotics lab, EPFL) [39]


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CHAPTER 3

DESIGN METHODOLOGY OF QUADRUPED ROBOT

3.1.

Design descriptions of legged robotThe design and development of bio-inspired quadruped robot is based on the

multidisciplinary design approach. This approach focuses on CAD modeling,

kinematic and dynamic modeling, multibody simulation, finite element analysis of the

robot. This is concurrent engineering approach to do research for academic and R&D

for prototype modeling shown in Figure 3.1. This research helps to utilize the

concurrent engineering concepts in design and development of area of robotics

researches.In this approach we developed a CAD design based on alligator anatomy and

with the help of multibody dynamics (MBD) simulation we validated our design and

mechanism. For making MBD simulation more realistic the simulation environment

parameters are very close to the actual system such as material properties of robot

body, legs and track. Simulation is based on the kinematics and dynamics analysis,

trajectory planning and gait planningusing forward feedback control algorithms.

With MBD simulation we got the forces and torques at the joint and body of

robot that is further used in FEM analysis of the leg of the robot.

Figure 3.1: Design approach

Using FEM, we validated the design to determine whether the model can withstand

loading under different type of terrains. In addition, the concurrent multibody

simulation and FEM analysis helped us in optimizing the design. Next sections will

cover the design of alligator-inspired robot and mammal inspired robot.

CAD design

Fabrication

Control

Gait Planning

FEM analysis

and simulation

Dynamic simulation

Kinematic and

dynamic modelingDesign

optimization Robot


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3.2. Design of alligator-inspired robot

3.2.1.Biological inspiration

Alligator limbs are mainly categorized in two main parts, namely, pectoral and pelvic

limbs (see Figure 3.2(a)). Pectoral limb is front (anterior/Fore) leg and pelvic limb is

rear (posterior/hind) of legs of the alligators. Each leg of alligator has 3 DOF

movements and contains 3 segments, namely, proximal, middle and distal. Figure 3.2

(b, c) shows the anatomy of legs consisting pectoral limb depicting humerus, ulna,

and manus length and pelvic limb depicting femur, tibia and pes length of segments.

Figure 3.2 (a): Type of limb and segments of alligatorsleg

Figure 3.2 (b): Anatomy of pelvic limbs Figure 3.2 (c): Anatomy of pectoral limbs

We developed the equivalent design inspired by the alligator, however we have not

mimicked robot as actual alligators (see Figure 3.3) because of the leg design of

alligators are very complex and fabrication and material selection of a same structure

is very challenging so we developed simplified model of leg design. We developed


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the leg on the scaling factor of the body length, mass of the alligators. Researchers

have done the scaling analysis on the basis of these parameters, see Table 3.1

Figure 3.3: Design inspiration

We have developed the symmetrical legged design of our robot. Here pectoral limb

design and pelvic limb design is same whether it is not same as in alligators that is

basically categorized in hip limb and knee limb. Hip and knee limb lengths of robot

are 0.38thof the body length of the robot. The mass of the robot is 0.7kg and body

length of the robot is 0.26 m. Legged and body thickness of the robot is 3mm, (see

Figure 3.4)[40]..

Table 3.1: Alligators length and masses

Specimen No. =SN, Ulna length (m) = UL, Manus Length (m) =ML, Pelvic limb length =PVL

Femur length (m) =FL, Tibia length (m) =TBL, Pes length (m) = PSL, Mbody(Kg) =m, Length snout to

tail base (m) = STL, Tail length (m) =TL, Pectoral Limb length (m) =PL, Humerus length (m) =HL

SN STL TL PL HL UL ML PVL FL TBL PL M

12 0.27 0.33 0.104 0.038 0.028 0.037 0.131 0.04 0.037 0.052 0.52

15 0.29 0.33 0.104 0.042 0.028 0.035 0.135 0.044 0.039 0.05 0.58

11 0.29 0.35 0.109 0.042 0.031 0.04 0.14 0.044 0.037 0.054 0.67

13 0.31 0.38 0.119 0.044 0.033 0.041 0.156 0.049 0.042 0.061 0.75

14 0.32 0.38 0.122 0.044 0.033 0.04 0.152 0.048 0.041 0.054 0.86

8 0.47 0.55 0.167 0.068 0.047 0.062 0.219 0.075 0.06 0.087 3.20

6 0.51 0.56 0.148 0.072 0.055 0.061 0.233 0.078 0.022 0.096 3.50


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Figure 3.4: Scaled legged of alligator-inspired robot body length

3.2.2. Robot design

The alligator-inspired robotic platform has four legs to support the body and assist

in its locomotion. Each leg is a simple 2-link rigid body mechanism and has two

servos. One servo is provided for each hip and knee joints. Ankle joint has been

ignored because our focus is on studying the salient feature that distinguishes

mammalian gait from reptilian gait: orientation of rotating axes of hip and knee

with respect to each other. The hip servo provides hip-yaw and knee servo

provides knee roll. This is very different from mammalian arrangement. For

mammals, the hip servo and knee servo both provide pitching action. The purpose

of body in our platform at present is to contain the Electronic Control Circuit (ECC) as

well as impart passive roll stabilisation. Servos are housed outside the body in slots

created for each limb. This design is have modular structure where is body beaked

into two parts. Robot has given passive compliances (springs) which will move

the body in vertical direction and constraint into the horizontal direction and

developed robot with compliance in the body which will be help to the robot makemore energy efficient and it will help to robot for taking turn. CAD model and

design specification of robot is shown in the Figure 3.5 and Table 3.2.


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Figure 3.5: Designed CAD model in Pro/E

Table 3.2 Design specifications of modular body robot

A. CAD design of modular structure based alligator-inspired quadruped

robot

I designed alligator inspired robot using Pro\E software. CAD design contains the

all basic information of robot such as, joint type, screw, nut design, equivalent

motor design, leg design and body design of the robot Figure 3.6

S.

No.

Characteristics Value

1 Mrobot 700g

2 Mservo+ MArduino + Mbattery 300g

3 Mul, Mul - Mservo 15 g, 15 g

4 Mll, Mll - Mservo 15 g, 15 g

5 Width 100 mm

6 Length 260 mm

7 Limb length 100 mm

8 Distance from front hip joint to front of robot 40 mm

9 Distance from back hip joint to front of robot 40 mm

10 Centroid coordinate (50,130,-110)mm

11 Hip height from ground 100 mm

12 Maximum speed Vmax 0.133m/s

13 Speed in Body length per second, BL/s 0.51BL/s

14 Spring stiffness 3940 N/m

14 Gait Trot , crawl


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Figure 3.7: Free body diagram

(3.1)For torque at joint 1

Here only friction will come into the picture so the net torque at joint1 will be

(3.2)

(3.3)Net torque at joint 1 = (3.4) For torque at joint 2

Here only reaction from the ground will come into the picture so net torque at

joint will be

(3.5)

Net torque at joint 1 = (3.6) For flat surface , and And from MBD simulation in section 6.3.2 we are getting reaction forces =15 NFrom equation (3.2)


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For Torque at Joint 2

Here only reaction from the ground will come into the picture so net torque at

joint will be

From equation (3.6)

Here =20o At 90o

B.

Motor specification for modular robot

Figure 3.8 Selected motor

Table 3.3 Modular robot servo motor specification

Required Pulse 3-5 Volt Peak to Peak Square Wave

Operating Voltage 4.8-6.0 Volts

Operating Temperature Range -10 to +60 Degree C

Operating Speed (4.8V) 0.2sec/60 degrees at no load

Operating Speed (6.0V) 0.16sec/60 degrees at no load

Stall Torque (4.8V) 5.5 kg/cm

Stall Torque (6.0V) 7 kg/cm

Weight 41g

Dimensions 41x20x36mm

3.3. Design Description mammalian inspired robot

Quadruped robot is being developed in CAIR. Purpose of this robot is to carry the

heavy loads for civilians and military. According to proposed design robot can carry

the 10 kg load. Robot has 4 legs and each leg has 3 DOF freedom means total degree

of freedom of robot is 12. Each leg of quadruped has 10 kg weight and has 3 joint.


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Material used for structure is aluminum. The total weight of the robot is 58kg

approximately without consideration of power supply. Design of robot structure is

modular and flexible. No permanent joint (e.g. Welding or riveting) is used in

mechanical structure. Controller of the robot is kept into the universal joint and it has

used 12 slave controllers for 12 joints and all controllers are directly connected to

master controller. The design of robot was already developed by the team and I

contributed the simulation and control of part of the development of the robot which

is discussed in next section. CAD model of robot design and specification shown as

follows (see Figure 3.9 and Table 3.4)

Figure 3.9: Quadruped robot

Table 3.4 Design specification mammal-inspired robot

S.

No.

Characteristics Value

1 Mrobot 20kg

2 Mmotor+ Mextra 1.5 g

5 Width 360 mm

6 Length 720 mm

7 Leg, link 1 length 80 mm

8 Leg, link 2 length 400mm

9 Leg, link 3 length 400mm

10 Centroid coordinate (-360,-180,-720)mm

12 Maximum speed Vmax 4 m/s

13 Body length per second, BL/s 1.66 BL/s

14 Gait Trot , crawl, bound


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CHAPTER 4

KINEMATIC, DYNAMIC ANALYSIS AND

TRAJECTORY PLANNING OF QUADRUPED ROBOT

4.1. Introduction

The mechanism of walking robot is very complex due to many DOF. Kinematics and

dynamic modeling are requiring before simulation. Kinematics model describes joint

variables, leg position and velocities however dynamics model helps to determine the

torque and forces at the joint, body and ground. This chapter contains kinematic,

dynamic analysis, trajectory planning and Jacobian analysis of the quadruped robot.

Kinematic analysis is covered forward kinematics and inverse kinematics of robot. To

define the robot kinematics first we need to derive D-H parameters using geometrical

configurations of robot and for dynamic analysis and robot smooth motion, velocity

Jacobian and trajectory planning are required. In the following section kinematic and

dynamic modeling of alligator inspired robot and mammal inspired robot has been

discussed [42].

4.2. Kinematic modeling of alligator-inspired robot

In this section we discussed the kinematic modeling of robot. It consists of frame

assignment of leg and body, D-H parameters analysis and forward kinematics of

alligator inspired robot.

4.2.1.Frame assignment

Frame assignment of the robot gives the position and orientation in joint space and

Cartesian space because this is the arbitrary references and totally depends on the

observer reference frame. Global reference is used for body of quadruped and local

reference frame for leg and 3 frames we used for each joint according to D-H

convention (see Figure 4.1). Our convention is always considered the Z axis is in

vertical direction (outward to body) and joint motion.


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Figure 4.1 Frame assignment of the alligator-inspired robot

Proper color coding is done for representing each axis of frames, Red is used for z

axis, green for y axis and blue for the y axis. I have assumed the direction of each

frame is same due to reduce the extra calculation except body frame.

4.2.2.D-H parameters

DH parameters of quadruped robot are defined from geometrical configuration and

frame references[41]

Table 4.1: D-H Parameter

S.N Twist

angle Linklength Link offset Link length1 0 0 0

2 90 3 0 04.2.3.Forward kinematics

Forward kinematics analysis is done using Table 4.1 of the robot. Here we do the

transformation of leg from local 0th frame to 3th frame (see Figure 4.1). First

transformation for first link form 0th

frame to 1st

frame for joint 1


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(4.1)Similarly transformations form 1stframe to 2ndframe for joint 2.

(4.2)

Transformations form 2ndframe to 3rd frame for joint 3.

(4.3)

Final transformation from 0thframe to 3rdframe for quadruped leg from leg frame

(4.4) (4.5)

(4.6)Similarly the transformation for remaining three legs will be same because we have

taken the assumption frame assignment of all leg is same for reducing the calculation.

That means there is no need to calculate the transformation of the all legs.

(4.7) (4.8) (4.9)


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4.3. Jacobian: velocity analysis alligator-inspired robots

In this section we discussed the Jacobian matrix for all joints of each leg. Linear

velocity can describe by a point while angular velocity can be a body. Jacobian is

always associated with the angular velocity and describes the linear velocity. Weconsidered the 0th frame of robot leg is as a reference. Our calculation is done on

arbitrary links like {i}. Hence,is the linear velocity of the origin of link frame {i}and is the angular velocity of link frame {i}.The velocities of link i+1 will be thatof link i, plus whatever new velocity components were added by joint i+1 (see the

Figure 4.2).

Figure 4.2: Velocity vector of neighbouring link [41]

Angular and linear velocity can be written as (4.10) (4.11)After differentiation of equation 4.7, 4.8, and 4.9 we get the Jacobian matrix from 3th

frame w.r.t to 0thframe.

(4.12)4.4. Trajectory planning for quadruped leg

Leg movement describes by using trajectory planning of the robot in three

dimensional spaces. Here, trajectory refers to a time history of position, velocity and

acceleration for each degree of freedom. When we simulate legged of quadruped

without their trajectory planning. We found leg is moving randomly with sudden


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change in velocity in the Cartesian/Joint space. That creates vibration so our

requirement is to make robot motion smooth with our desired way point and for actual

robotics platform it should follow a particular trajectory which helps to make easier

the balancing of robot. For trajectory planning of leg is important for kinematics

based multibody simulation, here we are doing trajectory planning for legged

quadruped robot with and without via point. Quadruped has three DOF leg so robot is

moving in the Cartesian space in all 3 directions. This section discusses trajectory

plan with via point as follows.

Figure 4.3: Trajectory planning with via point

Assumptions for formulation of equations

We are considering one point between starting and end point of the robot motion.

Position and velocity at t=0, (see the Figure 4.4) , , (4.13) , , , , (4.14)

, , , , , ,

, , ) (4.15)


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, , 4.4.1.Straight line trajectory of quadruped leg with via point

Figure 4.4: Straight line trajectory

General equation for straight line is

-segment 1 t=0 to (4.16)

-- segment 1 t=to (4.17)

From eq. 4.13, 4.14, 4.15 put the value in eq. 4.17, 4.16. We get

, (4.18) , (4.19) , (4.20) (4.21) (4.22) , (4.23)


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4.4.2.Cubic trajectory of quadruped leg with via point

Segment 1 t=0 to

(4.24)

Segment 1 t=0 to (4.25)From eq. 4.13, 4.14, 4.15 put the value in eq. 4.24, 4.25. We get. We get each cubic

will be evaluated over an interval starting at t=0 and end t=

and i=1, 2

(4.26)

After solving the equation 4.26 we get

(4.27)

Put the value of eq. 4.27, 4.26 in 4.25, 4.24


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Similarly for y and z

4.5. Dynamic analysis of alligator-inspired leg

Robot dynamics describes the forces and moment relation between robot motion that

is specifically described as following

Robot location and its derivatives, velocity and acceleration.

Forces and torques applied at the robot joints.

Dimensional parameters of the robot leg such as link length, mass and inertia.

Forces and moments propagate through the kinematic chain from one leg to another,

and therefore dynamic coupling exists. For dynamic analysis there are two methods

one is Lagrangian methods and other is Newtons and Eulers method. Here my

analysis is based on Newtons Euler approach. For dynamic modeling quadrupedrobot, we have derived the torque of each joint.

Propagation of rotational and linear acceleration of leg (4.28) (4.29)


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Velocity about center of gravity of the link (4.30)

Value of angular and linear joint acceleration from eq. 4.28, 4.29For link0

(4.31)

(4.32)

For link 1, i= 0;

(4.33) (4.34)

For link 2, i= 1;

(4.35) (4.36)

Form equation 4.30 we can write the acceleration

For center of link 1, i=2;

(4.37)

For center of link 2, i=2;

K=


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(4.38)

Having computed the linear and angular accelerations of the mass center of each link,

we can apply the NewtonEuler equations to compute the inertial force and torque

acting at the center of mass of each link. Thus we have

(4.39) (4.40)Here inertia, m mass of the linkInertial force and torque for link 1

Put the value of

,

from eq. 4.37, 4.34

(4.41) (4.42)

Inertial force and torque for link 2

Put the value of , , from eq. 4.38, 4.36, (4.43) (4.44)

Net acting force and moment on link1

(4.45)

(4.46)


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Net acting force and moment on link2

(4.47) (4.48)After getting the forces and moments about all direction. We calculated get the torque

about each joint

(4.49)Torque about first joint

(4.50)

Torque about 2nd

joint

(4.51)

General dynamics equation is

(4.52) , M is mass matrix, V is centrifugal and Coriolis force matrix, G is gravityforce matrix.


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4.6. Kinematic analysis of mammalian-inspired robot

Kinematic modeling of mammalian inspired robot is same as reptilian inspired robot

only difference is mammalian have 3 DOF leg configurations so the analysis of the

mammal is more computational and complex than reptilian. This section discusses onD-H parameters, frame assignment, forward kinematics and inverse kinematics

4.6.1.Frame assignments

Frame convention is same as discussed in previous section and assign frame is

described as follows (see Figure 4.5 (a), (b))

Figure 4.5 (a): Frame assignment on body Figure 4.5 (b): Frame assignment on leg

4.6.2.D-H parameters

Table 4.2 D-H Parameter of mammal leg

1 0 0 0 2 +90 D 0 3 0

0

4 0 0 0are joints angles of the quadruped leg for joint 1 and joint 2 and joint 3 D,L1, L2are link lengths of the robot for joint 1 and joint 2 and joint 3.


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4.6.3.Forward kinematics

With the help of D-H parameters I calculated forward kinematics for leg and body of

the robot.

A.

Forward transformation of leg from local reference frameHere we do the transformation of leg from local 0 thframe to 4thframe.

Transformations are briefly described for 0thframe to 4thframe Appendix A, A.1 to

A.4. Final transformation is (4.53) , , , , (4.54)

Similarly the transformation for remaining three legs will be same because of

assumption for frame assignment of all leg is same as one which is reducing the

calculation.

B.

Generalized transformation from body frame to leg frame

There will be one rotation about y axis for transformation of body to leg frame and

three translations Px, Pyand Pz. Rotation from y axis will be same for each leg due to

assumption but the translation will be different for all legs. Magnitude of the

translation will be same for the legs only direction will be different. is rotationabout y axis and generalized transformation from body to leg frame that is

(4.55)

(4.56)


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=is a angle of rotation about y axis .this matrix will be same for all leg

transformation.=distance from the center of the body to leg frame in x direction

=distance from the center of the body to leg frame in y direction

=distance from the center of the body to leg frame in z direction,,is different for each leg then transformation of body frame to leg frame foreach leg describe briefly in Appendix A. General transformation is (4.57)4.6.4.Inverse kinematics

Inverse kinematics is used to find the joint angle at given desired position. It helps to

find the possible solution for desired point.

A. Inverse kinematics from leg frame

Inverse kinematics is to find the joint angle of the legs. Leg of quadruped has many

solutions for each angle. In the legged robot the all the solution may not be desirable.

So we need an inverse kinematic analysis of the robot. For getting solution from

inverse kinematic equation of the robot, there are many methods available like,

graphical methods, algebraic method and pseudo inverse method. Here I prefer the

algebraic method. From algebraic method we assume a new matrix of 4x4 thatsequal to 0thframe to 4thframe transformation.

(4.58)Multiply the inverse of 1sttransformation matrix in both side of the equation 4.53

(4.59)

Compare the value of both side of equation 4.49 we found the three equation independent

with (4.60) (4.61) (4.62)

After solving the equations 4.60, 4.61, 4.62 we can find the all joint angle of the leg 1


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(4.63) (4.64)

Take square of equation 4.64, 4.62and add them we found the third joint angle

(4.65) (4.66)

(4.67)Multiply with equation 4.62with 4.6and equation 4.64 with 4.67, we found the 2nd

joint angle

(4.68)Here we have two solutions for joint 3 and two solutions for joint 2. Inverse kinematics for

all leg of quadruped is same.

B.

Inverse Kinematics from body frame

In this case all the inverse kinematics solution for all leg should not be same. Here I

am going discuss inverse kinematics for only one leg (leg 1). Method of finding a

solution of leg joint is same as earlier discussed in above sections. Here I also

preferred the algebraic method. From algebraic method we assume a new matrix of

4x4 thats equal topthframe to 4thframe transformation.

(4.70)

Multiply the inverse of 1sttransformation matrix in both side of the equation 4.70

(4.71)Compare the value of both side of equation (4.71). we found the three equations

independent with r


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(4.72) (4.73) (4.74) (4.75)

Divide the equation 4.72 and 4.73. We get the first joint angle of the quadruped (4.76)Where b=

,

,

or

,

, ora= , , or , ,

b= , , or , , ora= , , or ,

,

Here we found the two solution of the joint 1 for 1stleg and take square of the 4.72

and 4.74 and add these equations.

(4.78) =S-d (4.79) (4.80)Take square of the equation 4.74 and 4.80 and add these equations it we get the joint

angle 3 (4.81)Multiply the equation 4.80 by P1 and equation 4.74 by P2then we get the third joint

angle

(4.82)


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From the body frame we got the 6 number of solution two solution for each joint angle. In

the 6 solution there may be chance occur the redundancy

4.7. Jacobian: velocity analysis mammalianinspired robot

This section discusses Jacobian matrix for all joints of each legs. Here we haveJacobians for leg and body frames.

4.7.1.Linear velocity and angular velocity form leg frame

From the equation 4.10 and 4.11

For link0

(4.83)

(4.84)

For link 1

(4.86) (4.87)

For link 2

(4.88) (4.89)

For link 3

(4.90) (4.91)

For end point of link3 and frame 4

There is no joint at the 4thframe then


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(4.92)

(4.93)

Jacobian for quadruped leg from 0th

frame to 4th

frame

(4.94) (4.95)

(4.96)

(4.97)4.7.2. Jacobian: linear velocity and angular velocity form body

frame

All the joint velocities are independent with the frame so all the joint velocity will be

same from the body frame and leg frame. Only difference comes when we take the

joint velocity form body frame one rotation matrix will be multiply withtransformation matrix the

(4.100)We know the joint velocity of 4th frame w.r.t to its own frame from equation 4.74 then

velocity from body frame is

(4.101)


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(4.102)

4.8.

Dynamic analysis mammalian inspired legs

In the dynamic analysis is same as the explained in section 4.5. Here we are writing

the direct equations. Putting all the values in equation 4.28 and 4.29 we get the

angular acceleration and linear acceleration of all links and joints

For link0

(4.103)

For link 1

(4.104)

For link 2

(4.105)

For link 3

(4.106)


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(4.107)

For end point of link3 and frame 4

There is no revolute joint at the 4thframe then (4.108)But linear velocity will be different due to the angular velocity of joint 3 at 4 thframe

is

(4.109)

After getting the accelerations on each joints then we derived the acceleration at

center of the links. From the equation 4.30 we get all the acceleration of center of

each links.

For center of link 1

(4.110)



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(4.111)


(4.112)

Dynamic force is derivation is based on Newton-Euler equation from equation 4.39,

4.40; we get the all force and moment from each link of the robot

Static force and moment calculation

All the static forces are known because we know force acting the end of the leg. But

we are not considering any inertial force and moment here. Here we are assuming the

force is acting on the leg contact is in all the direction of the Cartesian space that

is

,

,

and moment is zero.

Static force and moment for joint 4

(4.113)

Static force and moment for joint

(4.114)


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(4.115)


(4.116)

Now net force acting on the each link is

(4.117)

(4.118) (4.119)

Torque about first joint

(4.120)

Torque about 2nd

joint

(4.121)


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Torque about 3rd

joint

(4.122) +

+


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CHAPTER 5

GAIT PLANNING AND STATIC STABILITY ANALYSIS

5.1. Introduction

In order to make the mechanisms walk it is essential to perform a leg and body motion

sequencecalled gait.Since many years gait has been researched however, for a long

time the results functioned on surfaces with very favourable conditions: flat and level

terrain. The observation, comprehension and mathematical formulation of ordinary

natural gaits were the main focus on legged locomotion and it was found that many of

these motions are periodic in nature.

They categorized the motion into two way periodic and non periodic (free gaits). It

was ultimately found that the motion pattern of the quadruped robot is periodic in

nature. Another characteristic of this type of gaits is continuous gait, in which the

body moves with constant motion while all legs move simultaneously. For an uneven

terrain, mammals and insects generally use a special kind of continuous gait called

wave gait, at a low speed.

Many researchers have developed the mathematical formulation of continuous gait of

quadruped robots. Researchers had defined the duty factor, stroke length and phase

for legged of quadruped robots.In 1968 and 1989 (McGhee and Frank, 1968; Zhang

and Song, 1989) formulated a mathematical model so that they could describe the

sequence of leg and derive the model to perform crab and circular gaits, in case of flat

terrain conditions. They had also developed, in a specific uneven terrain, the

mathematical formulation for continuous gaits.

It was found that the mammal and insects change their gait pattern on sharp

irregular terrains, thus they defined it as a secure gait and it is characterized by the

sequential motion of legs and body[42].The body is pushed forward/backward with all

of the feet properly positioned on the ground and then leg is moved with all other

three legs and body remaining stationary, these gaits are called discontinuous gaits.

For causing intermittent body motion which is beneficiary to a real legged machine:

they are very easy to implement and they provide longitudinal stability margin which

is greater as compared to wave gaits. Also, they could achieve a faster velocity than

wave gaits.


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.

5.2. Gait synthesis

In this section only I will consider the standard gait sequence which nowadays people

are using for four legged robots. The dictionary meaning of gait is a method ofmoving on foot. In the field of legged locomotion, a gait is defined as a repetitive

pattern of foot placements (Todd, 1985). More precise definition given by Song and

Waldron (1989), as follows.

A gait is defined by the time and the location of the placing and lifting of each

foot, coordinated with the motion of the body in its six degrees of freedom, in

order to move the body from one place to another. McGhee and Frank were

focused on the mathematical formulation of gait sequences. These researchers focused

on finding the quadruped gaits to maintain static stability. For this study, McGhee

introduced a notation called the event sequence. An event is defined as a foot

placement or a foot lifting. Quadruped results for event sequence in only six event

sequences (see Figure 5.1 (b)) and illustrated in Figure 5.1 (c)(h). In this example,

with the movement of foot 4, the locomotion cycle starts. Leg numbers are indicated

in Figure 5.1 (a). For numbering the legs we use front to rear, we use even numbers

for right legs and odd numbers for left legs[2].

Tomovic (1961) defined, in case of creeping gait, that it is an n-legged robot and

every support pattern involves at least n1 contact points. Hence, gaits in Figure5.1

are creeping gaits. It has three feet in support. Creeping gaits may be either singular or

non-singular.

Figure 5.1: Quadruped gaits (a) top view of a robot (b) graph of leg sequences (c)(h) sequences[2]


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Based on existing research on animal locomotion, we can categorize the gaits into two

types, namely, periodic and non periodic (see the Figure 5.2).

Figure 5.2: Quadruped gait types

5.2.1.Crawl gaits

The crawl gait is defined as the quadruped animals lift their one leg at time and all

rest should be contact with the ground. This is most stable gait of the quadruped

robot. This is a low velocity gait of quadruped animals and it is known as the standard

gait. This is also called as the creeping gaits or the crawl gait. There is no universally

accepted definition of standard gaits but crawl and creeping gaits are synonyms for

quadrupeds. It is defined as when of an n-legged robot as a creeping gait and every

support pattern involves at least n1 contact points[43],[2].

In generating discontinuous-periodic gaits for quadrupeds, certain aspects should be

considered:

If one leg in its support phase reaches the rear limit of its workspace (kinematic

limit), this leg should change to the transfer phase to be placed at its front

kinematic limit.

The body is propelled forward with all legs on the ground. After a body motion,

at least one leg should stay in its rear kinematic limit to perform a transfer

phase into the next leg motion.

The leg that is contra lateral and non-adjacent (CNA) to the present transfer leg

should be placed at such a point that after the placement of the transferred leg,

the COG stays on the other side of the line connecting the CNA leg with the


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transfer leg (see Figure 5.4 (c)) In this way, it will be possible to lift another leg

while maintaining the machines stability.

The sequence of legs should be periodic; this will allow several locomotion

cycles to be joined to follow a path.

Graphical representation of gaits sequences has shown in the Figure 5.5(b) and here

we for crawl gait duty factor .75. Minimum value of duty factor for static stable gaits

is .75 for four legged robots

Figure 5.3 (a): Gait sequencing of crawl gait Figure 5.3 (b): Gait diagrams of crawl gait

Figure 5.3 (c): Successive gait pattern of a two-phase discontinuous gait[2]


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5.2.2. Trot Gait

The trot is a gait in which diagonally opposite pairs of feet are alternatively lifted,

swung forward, and again placed on the ground. Twice during each stride, the body is

ballistic and without support. In the case of some larger animals, this ballistic phase

amounts simply to the feet being dragged along the ground, nonetheless the feet are

not supporting the body during this phase of motion.Figure

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