City College of New York
And
Graduate Center of City University of New York
I5501 Introduction to ROBOTICS
Homework #1
1. What is the rotation matrix for a rotation of 30 about the OZ axis,
followed by a rotation of 60 about the OX axis, followed by a
rot
Yaw-Pitch-Roll Representation
Compare LHS and RHS of Equation A, we have:
sin nx cos ny 0
a tan 2(ny , nx )
cos nx sin n y cos
nz sin
a tan 2(nz , cos nz sin ny )
sin s x cos s y cos
sin ax cos a y sin
a tan 2(sin ax cos a y , sin sx cos s y )
Th
Preliminary
Coordinate Transformation
Reference coordinate frame
OXYZ
Body-attached frame Ouvw
z
P
Point represented in OXYZ:
Pxyz [ px , p y , pz ]
Pxyz px i x p y jy pz k z
T
Point represented in Ouvw:
Puvw pu i u pv jv pwk w
Two frames coincide =>
y
Introduction to ROBOTICS
Robot Kinematics II
Dr. Jizhong Xiao
Department of Electrical Engineering
City College of New York
[email protected]
The City College of New York
1
Outline
Review
Manipulator Specifications
Precision, Repeatability
Homogeneo
Quiz 1
How to get the resultant rotation matrix for YPR?
T Rz , Ry , Rx,
C
S
0
0
S
C
0
0
0 0 C
0 0 0
1 0 S
0 1 0
Z
X
0
1
S
0
0
0
0
1
0 C
0 0
1 0
0 C
0 S
0 0
0
S
C
0
0
0
0
1
The City College of New York
Y
12
Quiz 2
Geometric Interpretation?
R33
T
Introduction to ROBOTICS
Kinematics of Robot Manipulator
Dr. Jizhong Xiao
Department of Electrical Engineering
City College of New York
[email protected]
The City College of New York
1
Outline
Review
Robot Manipulators
Robot Configuration
Robot Spec
Example II: PUMA 260
1.
2.
3.
2
Z1
3
O1
Establish base frame
Establish joint axis Zi
4.
1
Number the joints
Locate origin, (intersect.
of Zi & Zi-1) OR (intersect
of common normal & Zi )
X1
Z2 Z6
5.
Y1
O2
Y3
Z
Z4
O3
X 2 5 6 Y6
Y2
5
O6
Z0
Y5
X 3 Y4
t
O5
X5
Single Camera Omni-stereo vision
POV-ray
Simulation
The City College of New York
81
3D SLAM Research
Simultaneous Localization and Mapping in 3D space
Multi Volume Occupation Grid (MVOG)
The City College of New York
82
3D SLAM Research
Simultaneous Loc
Autonomous UGVs
The City College of New York
41
The Honda Humanoid (1997)
The City College of New York
42
Humanoid
The City College of New York
43
Robot Applications
Manufacture Industry
Assembling
Automation
Biotechnology
Micro/Nano manipulation
Sa
Robot Applications
Entertainment Industry
The City College of New York
61
Robot Applications
Entertainment Robots
Sony-Qrio
The City College of New York
62
Personal Robot?
http:/www.personalrobots.com
Just as the personal computer is used for automated
Robot History
Shakey (Stanford Research
Institute)
the first mobile robot to be
operated using AI
techniques
Simple tasks to solve:
To recognize an object
using vision
Find its way to the object
Perform some action on the
object (for example, to pus
Example 4
Find the rotation matrix for the following
operations:
Rotation about OY axis
Rotation about OW axis
Rotation about OU axis
Answer .
R Rot ( y, ) I 3 Rot ( w, ) Rot (u , )
0
C 0 S C S 0 1 0
0 1 0 S C 0 0 C S
- S 0 C 0
0
1 0 S C
CC SS CSC
Introduction to ROBOTICS
Introduction and Syllabus
Dr. Jizhong Xiao
Department of Electrical Engineering
The City College of New York
[email protected]
The City College of New York
1
Outline
Introduction
What is a Robot?
Why use Robots?
Robot Histor