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,2nd Edition,Springer-Verlag,New
York
References,
Craig,J.,1989.,Introduction to Robotics,Mechanics and Control,
2nd 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
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?
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?
?
?
?
?
?
?
?
?
?
0
0
0
642
945
101
c
c
c
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
c1v1 + c2v2 + … + c nvn ? 0 unless c1 = c2 = … c n = 0
v1,v2,… vn 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,
1st term,
2nd 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
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,2nd Edition,Springer-Verlag,New
York
References,
Craig,J.,1989.,Introduction to Robotics,Mechanics and Control,
2nd 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
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
?
?
?
?
?
0
0
0
642
945
101
c
c
c
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
c1v1 + c2v2 + … + c nvn ? 0 unless c1 = c2 = … c n = 0
v1,v2,… vn 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,
1st term,
2nd 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
