Introduction To Robotics

cuckootrainMechanics

Oct 31, 2013 (3 years and 7 months ago)

101 views

MECH572

Introduction To Robotics

Fall 2004

Dept. Of Mechanical Engineering

Course Topics


Introduction


Mathematical Background


Rigid
-
Body Mechanics


Robotic Kinematics


Robotic Dynamics

Text
:

Angeles, J
., 2002,
Fundamentals of Robotic Mechanical Systems,
Theory, Methods and Algorithms,

2
nd

Edition, Springer
-
Verlag, New
York


References:


Craig, J
., 1989.,
Introduction to Robotics. Mechanics and Control
,
2
nd

Edition, Addison
-
Wesley Publishing Company, Reading MA


Paul, R. P
., 1981,
Robot Manipulators. Mathematics, Programming
and Control
, The MIT Press, Cambridge, MA


Asada, H
. and
Stoline, J
-
J.E
. 1986,
Robot Analysis and Control
,
John Wiley and Sons, Inc, New York.


Lung
-
Wen Tsai
, 1999 Robot Analysis,
John Wiley & Sons



Marking Scheme
:




Course Assignments 10%



Midterm Exam 30%



Final Exam 60%




Introduction

Basic

Definitions
:


Robot



Any automated machine programmed to perform specific mechanical
functions in the manner of a man


Robotics



the science dealing with design, construction and operation of robots


Main Research Areas of Robotics



Mechanical Manipulation, Computer
Vision and Artificial Intelligence

(AI)

History
:


1923:

“Robot” entered into English Vocabulary


1950s:

Computer
-
based control appeared


1960/70s:

Academic research started


1980/90s:

Research and education advanced



Applications in manufacture, space, underwater, military, etc.


2000s:

Medical, personal assistance/domestic, entertainment, …


Introduction

Scope of the Course



Robotic Mechanical Systems


Definition of
System:


A group or combination of interrelated, interdependent, or interacting
elements forming a collective entity.




Introduction

Application example


Mars exploration (NASA Viking Mission, 1975)

Introduction

CANADARM 1

Major Specification
:

DOF: 6

Length: 15.2 m

Weight: 410 Kg

Max Payload: 266,000 Kg


Introduction

Canadarm 1 installed on US space Shuttle

Introduction

Canadarm1 viewed from the window of space shuttle

Introduction

Canadarm Mission Example: Hubble Space Telescope Repair (Dec 1993)

Introduction

Canadarm Mission Example: Construction of international space station (April
2001)

Introduction

International Space Station

Introduction

Mobile Servicing System (MSS)

MSS Base System
(MBS)

Special Purpose Dexterous
Manipulator (SPDM)

Space Station Remote
Manipulator System (SSRMS)

Introduction

Canadarm2


SSRMS

Major Specification:

DOF: 7

Length: 17.6 m

Weight: 1800 Kg

Max Payload: 100,000 Kg

On orbit since April
2001

Introduction

MSS Base System (MBS)



Moving base for
Canadarm2


Dimension


5.7m x
4.5m x 2.9m


Weight


1,450 Kg


Mass handling
capability


20,900 Kg

On orbit since June
2002

Introduction

Special Purpose Dexterous Manipulator (SPDM)

Major specifications:

Height: 3.5m;

Arm length: 3m;

Weight: 1660kg;

DOF: 7/arm, 1/body;

Max load: 600kg per arm;
Max arm speed: 7 cm/s
(unloaded)

To be sent to orbit

Introduction

Canadarm1/2 Handshake

Payload Handover

Introduction

Two arms; each has 4 DOFs. One arm
is 1.5m long with 1kg load

capacity and the other is 0.5 long with
2 kg load capacity.

Mars exploration 2003


Opportunity & Spirit Rovers


Introduction

Example of Medical Robots


Zeus Robotic system

Introduction


Example of Robot Hands


Hand developed by DLR


Major specifications:

Size: human hand; Weight: 1.8kg; DOF: 3/finger; Max load: 11N per finger;

Each finger has 4 joints, 3 motors, and 25 sensors.

Introduction

Height: 1.2m; Weight: 43kg; DOF: 5/arm, 6/leg, 2/hand;

Max load: 0.5kg per hand; Operation time: 15min; Max speed: 0.5 m/s

Humanoid Robot built by HONDA

Introduction


Example of Industrial Robots


Industrial robots performing spot welding in an automobile assembly line.

Introduction


Classification of Robot


Serial


Parallel


Robot Hand (Tree Type Manipulators)


Walking Machines


Rolling Robot (Rovers)


Basic Topology of kinematic Chains


Chain


Tree


Necklace


Introduction

Serial manipulators


a, b, e

Parallel manipulators


g, h, j

Tree manipulators


c, d

Walk machines


f, I


(i)

(j)

Introduction


Manipulator Components


Link, Joint, End
-
Effector


Type of Joint (Kinematic pairs)


Revolute (R), Prismatic (P), Cylindrical (C), Helical (H), Planar (E),
Spherical (S)

Mathematical Background


Vector Space


A set of vectors that follow certain algebraic rules




Mathematical Background


Vector Space (cont'd)







Example


Linear system of equations/column space









Ax

=
b

Linear combination of columns of
A

b:

b

lies in the column space of
A

Mathematical Background

Example


Column Space

Mathematical Background


Example


Null Space

Bx
' =
0

x
' lies in the null space of
B

X

Y

Z

null space of
B

Mathematical Background


Linear Transformation


the concept





Useful Linear Transformation in 3
-
D Euclidean Space

Projection
-

P

Reflection
-

R

Rotation
-

Q

L

takes on different forms



Mathematical Background


Linear Transformation


Projection







1



Identity matrix


Property


p

n

P'

Mathematical Background


Linear Transformation


Reflection




Property



Application




orthogonal decomposition

n

p

p"

Mathematical background


Linear Independence/Basis of vector space






Recall


the concept of
Linear Independence



c
1
v
1

+ c
2
v
2

+ … + c
n
v
n



0 unless c
1

= c
2

= … c
n

= 0



v
1
,
v
2
, …
v
n

is linearly independent


Example:


i
,
j
,
k


unit vectors along directions of X, Y Z axes is a base in 3
-
D
space

Mathematical background


Matrix representation of linear transformation



Mathematical background


Example



i

j

k

Mathematical background


Eigenvalues/Eigenvectors


Mapping a vector into multiple of itself


Characteristic equation



Cayley
-
Hamilton Theorem



Mathematical background


Cross
-
Product Matrix













V



Skew
-
Symmetric


Mathematical background


Cross
-
Product Matrix


General property














Mathematical Background


Concept of Rotation




main property


preserve distance




orthogonal




One eigenvalue is 1


physical meaning: mapping rotation
axis to itself



p

P'

e

Mathematical Background


Matrix Representation of Rotation


Rotation axis:


Rotation angle:


From geometry:


1
st

term:



2
nd

term:

Mathematical Background


Special case




Alternative forms of rotation Matrix


Taylor Expansion:

Mathematical Background


Rotation Matrix


Alternative form from Taylor Expansion



Canonical Form


Euler Angle

-

Roll

-
Pitch

-

Yaw