HW 3: Twists and Screws
Due: 10/02/12
1
Homogeneous matrices and screws
Consider the rigid body transformation shown in the gure below. The rotation is /2 around the
y -axis.
xb
za
zb
yb
2
xa
ya
2
4
Figure 1: Change of coordinates and screws.
(a) Compute
1a. (10 points) For the manipulator shown, nd the twist coordinates 5,- and 95¢(0) using the
product of exponentials approach. Use the base and tool frames shown.
b. (10 points) Find" eéia" for 53 and 55.
>< we. le-equ
2a. (15 points) Show how you would
EE 125 Fall 2014
Professor: Ruzena Bajcsy
GSIs: Robert Matthew
Austin Buchan
Aaron Bestick
Preamble
All slides in this course have benefited
from previous lectures prepared by
Vincent Duindam, Edgar Lobaton, Ram
Vasudevan ,notes from Zexiang Li and
Yuanqi
Lecture 4
Velocities and twists
Ruzena Bajcsy
EE125 Fall 2013
What is a velocity?
Rotational Velocity
Rotational Velocity
Rotational velocity of a point
Rotational velocity for a point
Rigid Body velocity
Rigid Body velocity
Rigid Body velocity of a point
Discussion 2: Rigid Body Motion and
Homogeneous Coordinates
Robert MATTHEW
GSI EECS
1
Administrivia
Let me know asap if you do not have access to BSpace.
Homework 1 will be due in via Bspace. If you do not have
access to Bspace by Friday 11:59pm you will
Discussion 8: Jacobians and Inverse
Kinematics
MLS: Chapter 2.4, 3.4, 3.2
Robert MATTHEW
GSI EECS
1
Administrativa
Homework due Friday
Midterm 2 18th November
2
Soda 310, Soda 405
Inverse Kinematics,Velocities, Jacobians and simple Dynamics
Piazza Questio
EE C125/EE 215A/BIOE C125: Introduction to Robotics
Description
This course is an introduction to the kinematics, dynamics and control of robot manipulators, as
well as robotic vision, sensing and the programming of robots. We'll begin with the forward an
Discussion 6: Velocities & Adjoints
MLS: Chapter 2.4
Robert MATTHEW
GSI EECS
1
Administrivia
Project Proposals: October 17th
2
Groups of 2/3 people
Talk to your Lab GSI to discuss projects before the proposal
Include milestones, team specialties, Gantt ch
Discussion 7: Velocities & Jacobians
MLS: Chapter 2.4, 3.4
Robert MATTHEW
GSI EECS
1
Velocities: The story so far
2
Velocities: The story so far
Two notations for velocity: spatial and body .
3
Velocities: The story so far
Two notations for velocity: spat
Discussion 1: Intro & Rotations
Robert MATTHEW
GSI EECS
Robotics
Course Robots
GSIs
AARON BESTICK
AUSTIN BUCHAN
My Research: Human Modeling
My Research: Assistive Devices
My Research: Assistive Devices
My Research: Assistive Devices
Administrivia
Course R
Discussion 4: Twists and Review
Robert MATTHEW
GSI EECS
1
Administrivia
Midterm 1: October 7th in class
Homework 2: Due Friday 26th September (11:59pm)
2
Last Time
( ) =
( ) =
()
()
3
=
=
=
= ()
Twist Notation
Absolute
Relative
( ) =
Rigid Body transformation
Lecture 1
Ruzena Bajcsy
EE 125 Fall 2013
Outline
Introduction to vector and matrix algebra
Coordinates and Frames
Rigid body transformations
Properties of Rotation transformation.
This is covered in the text Chapter 2, section 1.
Lecture 8
Jacobean and Differential Inverse
Kinematics
Velocity of the end effector
Twist of the end effector and Spatial
jakobean
Structure of Spatial Jakobean
Structure of Spatial jakobean
Every body has a Jakobean
Spatial Jakobean
Properties of Jakobea
EE/BIOE C125 Problem Set 1
Assigned 9/2/05; Due 9/13/05
Late homework policy: Homework and labs are due in lecture on the due date. Late homework will
only be accepted before the solutions are handed out, usually 1 or 2 lectures after the assignment is
du
NumPy/SciPy Notes
Aaron Bestick
September 15, 2013
1
What is NumPy/SciPy?
NumPy and SciPy are libraries which, together, provide MATLAB-like functionality in Python. NumPy provides a
multidimensional array datatype and some basic linear algebra functional
Homework 2: Forward Kinematics and Twists
Part 3 needed in lab section the week of 9/15
Parts 1-3 Due 9/26
September 13, 2014
Problem-sets are due in before 11:59 pm on the day they are due via BSpace. Feel free to use a computer to
help you with this pro
Homework 4: Dynamics
Due Friday, 14th November, 11:59 pm
October 31, 2014
Problems:
1. Simple Dynamics Problems
Write the equations of motion for the following systems using both Newtons equations of motion and
the Euler-Lagrange equations and show that t
Introduction to Robotics EE125
Homework 5
DUE: 2014 December 5th
Name:
SID:
There are four questions worth 20 marks and a bonus question worth 10 marks. You have
two weeks to complete this homework. Please plan accordingly.
Calculators allowed, though use
Homework 1: Rotations and Transformations
Due: Fri, 9/12
Set: September 9, 2014
Problem-sets are due in before 11:59 pm on the day they are due via BSpace (or via email if you are unable
to use BSpace) Feel free to use a computer to help you with this pro
Lecture 3
Rigid Motion, Homogeneous
coordinates
Ruzena Bajcsy
EE125,2013.
General rigid motion
Rigid motion acting on a point
Rigid Motion acting on two points
Special Euclidean group SE(3)
Introduction of Homogeneous
coordinates
Simplify notation
Homogen
Homework 3: Inverse Kinematics, Velocities, Jacobians
Due Friday, 10/31, 11:59 pm
October 13, 2014
Problems:
1. Velocities
Calculate the velocity of the end eector with respect to the tool frame for the following two manipuT
T
lators (calculate VST ). Als
Lecture 2
Rotational Motion
Ruzena Bajcsy
Outline
Excursion to group theory
Properties of Rotation Transformation
Exponential Coordinates for rotation,
Chapter 2, section 2.
Representations of rotations
Examples of groups
Rotations form a group
Rotation m
EE/BIOE 125 Problem Set 8 Assigned 11/21/05; Due 12/8/05 1. Answer the questions from the Adept robot lab. You do not need to implement a full pick-and-place program, but please outline the steps. 2. Show that the control law = M ()(d e) + C(, )(d e) + N