Difference between revisions of "Engineering Analysis 3"

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** Example 2
** Example 2
** Example 3
** Example 3


'''

==Course Text and Software==

This course uses the textbook ''Modern Robotics: Mechanics, Planning, and Control'', Kevin M. Lynch and Frank C. Park, Cambridge University Press 2017. If you find an error or typo in the book, please '''[http://hades.mech.northwestern.edu/index.php/Modern_Robotics_Errata report it here].'''

[[Coursera_Resources#Things_you_should_complete_before_taking_any_course|Get the book, install and test the Modern Robotics code library, and install and test the CoppeliaSim robot simulator.]] You will program in Python, Mathematica, or MATLAB in this course.

'''[[Modern Robotics Linear Algebra Review|Here is a linear algebra refresher appendix to accompany the book.]]'''

==Approximate Syllabus and Schedule==

Here is a summary of the structure of the course. '''All items are due 30 minutes before the associated class time (1:30 PM Central). The deadlines are controlled by Coursera, so do not be late!''' You may work ahead if you wish, but then you won't get as much out of the classes.
* Before some classes, you should complete a quiz on earlier material.
* Before most classes, you will watch the associated videos on Coursera and answer the "lecture comprehension" (LC) questions. (Designed to be relatively quick, to solidify your understanding.)
* You are encouraged to read the corresponding portions of the textbook after watching the videos. I suggest you watch first, then read, then possibly re-watch, but you can determine what works best for your learning style.
* During the class period '''after''' you watch those videos, I will typically summarize what we learned, work a problem, take any questions you have about the material, and possibly assign you a problem to work on.
* There are two kinds of assessments on Coursera (Coursera refers to both of them as "quizzes"): "lecture comprehension" questions (LCs), which are short and immediately follow lectures, and summative quizzes, which are usually longer assessments/assignments occurring at the middle or end of a chapter.
* Within Coursera there are also "discussion prompts," open-ended group questions that you should reply to (responses can be simple) and forums where you can post questions and reply to other students' questions.
* Assignments outside Coursera will be submitted through Canvas.

Below is the approximate syllabus and schedule. Next to each date is the Coursera material that should have been covered '''at least 30 minutes before''' that class. "LC" refers to brief lecture comprehension questions that should be completed before that class, and "quiz" is a longer summative quiz on earlier material.

'''Chapter 2, Configuration Space'''
* Wed Sept 21: welcome to the course and syllabus review; intro to Coursera. '''The schedule for completing Coursera items is set by this wiki!'''
* Fri Sept 23: office hours; check for working CoppeliaSim implementation and summarize installation process for each OS; make sure Coursera invitation is accepted; material through Chapter 2.2 (3 videos and 2 LCs on dof of a robot) '''[[Media:MRslides-ch02a.pdf|CLASS SLIDES]]'''
* Mon Sept 26: course staff and office hours; meet the class; and material through Chapter 2.3 (quiz, Chapter 2 through 2.2; 2 videos and 2 LCs on C-space topology and representation) '''[[Media:MRslides-ch02b.pdf|CLASS SLIDES]]'''
* Wed Sept 28: finish Chapter 2 (2 videos and 2 LCs on configuration and velocity constraints, task space and workspace) '''[[Media:MRslides-ch02c.pdf|CLASS SLIDES]]'''
'''Chapter 3, Rigid-Body Motions'''
* Fri Sept 30: through Chapter 3.2.1 (quiz, Chapter 2.3 through 2.5; 3 videos and 3 LCs on rotation matrices SO(3)) '''[[Media:MRslides-ch03a.pdf|CLASS SLIDES]]'''
* Mon Oct 3: finish Chapter 3.2 (3 videos and 3 LCs on angular velocities, so(3), exponential coordinates) '''[[Media:MRslides-ch03b.pdf|CLASS SLIDES]]'''
* Wed Oct 5: asst 1 will be due Oct 14. New material: through Chapter 3.3.2 (quiz, Chapter 3 through 3.2; 3 videos and 3 LCs on transform matrices SE(3) and twists) '''[[Media:MRslides-ch03c.pdf|CLASS SLIDES]]'''
* Fri Oct 7: finish Chapter 3 (2 videos and 2 LCs on se(3), exponential coordinates, and wrenches) '''[[Media:MRslides-ch03d.pdf|CLASS SLIDES]]'''
'''Chapter 4, Forward Kinematics (skip section 4.2 on URDF)'''
* Mon Oct 10: finish Chapter 4 (quiz, Chapters 3.3 and 3.4; 3 videos and 3 LCs on product of exponentials formula, space and e-e frame) '''[[Media:MRslides-ch04a.pdf|CLASS SLIDES]]'''
'''Chapter 5, Velocity Kinematics and Statics'''
* Wed Oct 12: through Chapter 5.1 (quiz, Chapter 4; 3 videos and 3 LCs on space Jacobian, body Jacobian) '''[[Media:MRslides-ch05a.pdf|CLASS SLIDES]]'''
* Fri Oct 14: '''ASST 1, DUE 1:30 PM'''. New material: through Chapter 5.2 1 video and 1 LC on statics of open chains) '''[[Media:MRslides-ch05b.pdf|CLASS SLIDES]]'''
* Mon Oct 17: through Chapter 5.4 (2 videos and 2 LCs on singularity analysis, manipulability) '''[[Media:MRslides-ch05c.pdf|CLASS SLIDES]]'''
'''Chapter 6, Inverse Kinematics (focus on section 6.2)'''
* Wed Oct 19: Chapter 6 (quiz, Chapter 5; 3 videos and 3 LCs on numerical inverse kinematics) '''[[Media:MRslides-ch06a.pdf|CLASS SLIDES]]'''
'''Chapter 8, Dynamics of Open Chains (skip sections 8.4, 8.7, 8.8, and 8.9)'''
* Fri Oct 21: through Chapter 8.1.2 (quiz, Chapter 6; 2 videos and 2 LCs on Lagrangian dynamics) '''[[Media:MRslides-ch08a.pdf|CLASS SLIDES]]''' Guest lecturer: Andrew Thompson.
* Mon Oct 24: New material: Chapter 8.1.3 (1 video and 1 LC on understanding the mass matrix) '''[[Media:MRslides-ch08b.pdf|CLASS SLIDES]]''' Guest lecturer: Lin Liu.
* Wed Oct 26: '''MIDTERM''', chapters 2-5 (no electronic devices allowed [calculator, laptop, tablet, etc.]; study sheets and book allowed) '''[[Media:ME449-midterm-solutions-2022.pdf|2022 midterm and solutions]]''' (average score 22.9/32)
* Fri Oct 28: Chapter 8.2 (2 videos and 2 LCs on dynamics of a single rigid body) '''[[Media:MRslides-ch08c.pdf|CLASS SLIDES]]''' Guest lecturer: Dan Lynch.
* Mon Oct 31: '''ASST 2, DUE 1:30 PM'''. Chapter 8.3 and 8.5 (2 videos and 2 LCs on Newton-Euler inverse dynamics, forward dynamics) '''[[Media:MRslides-ch08d.pdf|CLASS SLIDES]]'''
'''Chapter 9, Trajectory Generation'''
* Wed Nov 2: through Chapter 9.3 (quiz, Chapter 8 through 8.3; 3 videos and 3 LCs on point-to-point trajectories, polynomial via point trajectories) '''[[Media:MRslides-ch09a.pdf|CLASS SLIDES]]'''
* Fri Nov 4: Chapter 9.4 (quiz, Chapter 9 through 9.3; 3 videos and 3 LCs on time-optimal time scaling) '''[[Media:MRslides-ch09b.pdf|CLASS SLIDES]]'''
* Mon Nov 7: Chapter 9.4 recap.
* Wed Nov 9: '''ASST 3, DUE 1:30 PM'''; final project discussion
'''Chapter 11, Robot Control (focus on sections 11.1 through 11.4)'''
* Fri Nov 11: up to (not including) Chapter 11.2.2.1 (quiz, Chapter 9.4; 3 videos and 3 LCs on linear error dynamics) '''[[Media:MRslides-ch11a.pdf|CLASS SLIDES]]'''
* Mon Nov 14: finish Chapter 11.2.2 (2 videos and 2 LCs on first- and second-order error dynamics) '''[[Media:MRslides-ch11b.pdf|CLASS SLIDES]]'''
* Wed Nov 16: through Chapter 11.3 (3 videos and 3 LCs on motion control with velocity inputs) '''[[Media:MRslides-ch11c.pdf|CLASS SLIDES]]'''
* Fri Nov 18: Chapter 11.4 (quiz, Chapter 11 through 11.3; 3 videos and 3 LCs on motion control with torque or force inputs) '''[[Media:MRslides-ch11d.pdf|CLASS SLIDES]]'''
'''Chapter 13, Wheeled Mobile Robots (skip section 13.3)'''
* Mon Nov 21: '''FINAL PROJECT MILESTONE 2, DUE 1:30 PM'''; new material through Chapter 13.2 (quiz, Chapter 11.4; 3 videos and 3 LCs on omnidirectional wheeled mobile robots) '''[[Media:MRslides-ch13a.pdf|CLASS SLIDES]]'''
* Wed Nov 23: CLASS CANCELED
* Mon Nov 28: Chapter 13.4 (quiz, Chapter 13 through 13.2; 1 video and 1 LC on odometry) '''[[Media:MRslides-ch13b.pdf|CLASS SLIDES]]'''
* Wed Nov 30: Chapter 13.5 (1 video and 1 LC on mobile manipulation) '''[[Media:MRslides-ch13c.pdf|CLASS SLIDES]]'''
* Fri Dec 2: wrap-up
* Thurs Dec 8, noon: final project due

==Practice Exercises==
[[Modern_Robotics#Useful_Supplemental_Documents|Sample exercises and their solutions, useful for practicing your understanding of the material.]]

== Practice Tests ==

* [[Media:ME449-quiz1-2018.pdf|Quiz 1, 2018]]
* Quiz 2, 2018: Exercises 4.2, 5.3, 6.1, 8.6, and 8.7 from [[Modern_Robotics#Useful_Supplemental_Documents|the practice exercises document]].
* [[Media:ME449-quiz1-solutions-2019.pdf|Quiz 1, 2019]]

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==Student-Created Exercises==
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<!-- [https://docs.google.com/spreadsheets/d/1cIX4_U8lkWAL6LqQBgDrE5WX1TAmJaD6-ykG7GNACkI/edit?usp=sharing '''Click here for student exercise assignments.''']

'''Bring two printed copies to class Monday Nov 18, for feedback. Turn in the final version online on Wednesday Nov 20 at 1:30 PM, as two files: FamilyName_GivenName.pdf, with the pdf of the exercise and its solution, and FamilyName_GivenName.zip, with all the source files for your exercise taken from Overleaf. Also bring a printout to class on Wed Nov 20. If it is more than one page, staple it.'''
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<!--
All students will be responsible for creating a practice exercise, consisting of the exercise and the solution. A good exercise should test an important concept in the context of a real robotics application (e.g., motion planning for a quadrotor, robot localization, computer vision, grasping, etc.), require the learner to understand and apply equations in the book or use the book's software, and require a bit of thought (i.e., not just "plug and chug" questions). For many exercises, a good figure or two is helpful. You could use a figure of a real robot and add your own annotations to it (e.g., frames or objects in its environment), or you could hand-draw something, or you could use CoppeliaSim or other software to help create the figure. You should not confine your question to an application discussed in the textbook. Make your exercise interesting and motivating! Exercises that require synthesizing two or more concepts or equations are more interesting and useful. Think about what kind of exercise would have helped you to really understand the material. Your questions should be very clearly worded, so anyone can understand it without you having to be there to interpret it for them.

You should look at the practice exercise document and end-of-chapter exercises for inspiration, but obviously your exercises should not be copies.

You will create your exercise using [https://en.wikipedia.org/wiki/LaTeX LaTeX] (pronounced "lay teck" or "lah teck"), the standard for scientific document preparation. [https://www.overleaf.com/ Overleaf] is a free online implementation of LaTeX. To get started on your exercise,

# Download [[Media:ME449-exercise.zip|'''this .zip file''']] and uncompress it. There are five files: main.tex, prelims.tex, twist-wrench.pdf, table-lamp.PNG, and LampSolution.PNG.
# Create an account on [https://www.overleaf.com/ Overleaf].
# Create a new (blank) project on Overleaf called "exercise."
# Upload the five files to this project. (You may get a warning that your default main.tex file is being overwritten; don't worry about it.)
# Click on main.tex to see your main LaTeX document.
# Press the "Recompile" button to see the pdf document that is compiled from the five files. You can download the pdf file, or all the "source" files, by clicking on "Menu" and choosing which to download. '''[[Media:ME449-exercise-output.pdf|This is the .pdf file you should have created.]]'''

main.tex is the main file of the project, and the only one that you will edit, so you should understand what is going on in that file. prelims.tex tells LaTeX what packages to use and defines some macros, e.g., \twist creates <math>\mathcal{V}</math> and \wrench creates <math>\mathcal{F}</math>. The other three files are image files that get included in the document. You will create different image files depending on your exercise. For example, you can make a nice hand drawing and then scan it.

To learn more about typesetting in LaTeX, google is your friend! Try googling "latex math" or "latex math symbols," for example.

You will turn in the source for your exercise as a zip file, as well as the final pdf file.
-->
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The final student assignments to topics is given below:

[[File:StudentExercises2019.jpg|x400px]]
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==Assignments==

'''As mentioned above, in the Honor Code:''' You are encouraged to discuss the material with the instructor, course assistants, and your classmates, but you are not allowed to share your answers or code with others. Anyone asking for answers or code, or providing answers or code, or becoming aware of others doing so without reporting to the instructor, is considered in violation of the honor code.

Assignments are graded based on correctness, how well you organize your homework (it should be easy to understand your thinking and easy to find your responses), and how well you follow the submission instructions below. You will lose points if you don't follow these instructions. If more detailed submission instructions are given with a particular assignment, make sure to follow those, too.

'''You will not receive credit if you just give an answer. Your solution must demonstrate how you got the answer. It must be easy to follow.'''

If you ever think a problem is stated incorrectly, not enough information is given, or it is impossible to solve, don't panic! Simply make a reasonable assumption that will allow you to solve the problem (but clearly state what this assumption is), or indicate why it is not possible to solve the problem.

'''Instructions for uploading assignments to Canvas:'''

* '''Upload on time! Late submissions are not accepted.'''
* For every assignment, you should upload exactly one pdf file, named FamilyName_GivenName_asst#.pdf. This pdf file should have answers to all the questions, including screen shots, text logs of code running, etc. Always include output of your code running on the exercises, so the grader can see what you got when you ran your code. You may scan handwritten solutions (provided they are neat!), but in any case, all answers should be in a single pdf file. DO NOT UPLOAD SCANS AS JPGS! THEY MUST ALL BE COMPILED INTO A SINGLE PDF FILE.
* If required by the assignment, in addition you may be asked to provide a zip file including all source code in their original forms, such as .m, .py, or .nb. This zip file should be named FamilyName_GivenName_asst#.zip. Always create a script that the grader can easily invoke to run your code for a particular exercise. Don't expect the grader to search through your code to find sample code to cut-and-paste. Make it as easy as possible for the grader (you can include a "README.txt" file in your zip file, for example, to tell the grader how everything works). Your code should be commented well enough that it is easy for someone else to pick it up and understand more or less how it works.

'''[http://hades.mech.northwestern.edu/index.php/ME_449_Assignment_1 Assignment 1]''', due 1:30 PM CT Friday October 14 on Canvas.

'''[[Media:ME449-asst2-2022.pdf|Assignment 2]]''', due 1:30 PM CT Monday October 31 on Canvas.

'''[[Media:ME449-asst3-2022.pdf|Assignment 3]]''', due 1:30 PM CT Wednesday November 9 on Canvas.

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'''[[Media:ME449-asst3-2022.pdf|Assignment 3]]''', due 1:30 PM CT Wednesday November 10 on Canvas.
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'''[[Media:ME449-asst3-2020.pdf|Assignment 3]]''', due 1 PM CST Thursday November 5 on Canvas. (With the automatic one-day extension, it is now due at 1 PM CST Friday November 6 on Canvas. No assignment will be accepted after that time.)
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* '''Assignment 1, due 30 minutes before class on Canvas, Wed Oct 9.''' Exercises 2.1, 2.4, 2.5, 2.9(c) (mechanism (c) from Fig 2.18), 2.20, 2.31, 3.1, and 3.5.
* '''Assignment 2, due 30 minutes before class on Canvas, Wed Oct 16.''' Exercises 3.16, 3.26, 3.31, 4.2, 4.5, and 4.6.
* '''Assignment 3, due 30 minutes before class on Canvas, Wed Oct 23.''' Exercises 5.3(a,c,d,e) and 5.26.
* '''Assignment 4, due 30 minutes before class on Canvas, Wed Oct 30.''' [[Media:ME449-asst4-2019.pdf|The programming assignment described here]].
* '''Assignment 5, due 30 minutes before class on Canvas, Wed Nov 6.''' [[Media:ME449-asst5-2019.pdf|This assignment]] makes use of (approximate) [[Modern_Robotics#Supplemental_Information|dynamic parameters for the UR5 robot, given in MATLAB, Mathematica, and Python form]].

* '''Assignment 3, due 30 minutes before class on Canvas, Wed Oct 24.''' Exercises 4.2, 4.5, 4.14, 5.7, and 5.11(a).
* '''Assignment 4, due 30 minutes before class on Canvas, Wed Oct 31.''' Exercises 5.2, 5.25, 6.7, 6.8, and [[Media:IKexercise.pdf|this programming project]]. You should submit a zip file containing your answers to the four exercises plus the directory structure described in the programming project.
* '''Assignment 5, due 30 minutes before class on Canvas, Wed Nov 7.''' Book exercises 8.2 and 8.3, and [[Media:ME449-practice-81.pdf|practice exercise 8.1]].
* '''Assignment 6, due 30 minutes before class on Canvas, Wed Nov 14.''' Book exercise 8.14 (turn in your code), book exercise 8.15 (make a video of the motion using V-REP), and practice exercise 9.1(a), trajectory planning for the WAM robot. For each trajectory in 9.1(a), plot the (x,y,z) components of the trajectory and the three exponential coordinates of rotation of the trajectory (each taken from the transformation matrices) as a function of time. Make sure your plots are labeled so we can tell which curve is which.
* [http://hades.mech.northwestern.edu/index.php/Mobile_Manipulation_Capstone '''CAPSTONE PROJECT''']. We will do milestone 2 first, then 1, 3, 4 to complete it.
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==Final Project: Mobile Manipulation==
<!--
'''Office hours for capstone:''' We will have office hours at the normal times (Tues 9 AM, Wed 7:30 PM) on Dec 1 and 2 during finals week, and one bonus office hour at 9 AM CDT Friday Dec 4. The Dec 4 office hour will be in our class Zoom room.
-->

The final project is described [http://hades.mech.northwestern.edu/index.php/Mobile_Manipulation_Capstone_2022 '''on this page''']. It is due in Canvas on Thursday December 8 at noon.

* '''Due Monday November 21 at 1:30 PM on Canvas''': Milestone 2. ''(You will do milestone 2 first! Milestone 1 will come next.)'' You will turn in a single zip file named FamilyName_GivenName_milestone2.zip with your solution to milestone 2. The zip file should include a README.pdf file with a brief summary of your solution and how to use it, and if your code is not working properly, it should correctly point out the problems. The zip file should also include a directory with the commented code you wrote, including a cut-and-pastable comment at the beginning showing how to execute the code to generate the csv file included in the submission; a CoppeliaSim video showing your reference trajectory of the end-effector (similar to [https://www.youtube.com/watch?v=8d_cYwV58lI&feature=youtu.be this video]); and the csv file that your code generated to create the video.
* ''' Due Thursday December 8 at 12:00 PM (noon) on Canvas''': The entire final writeup, as described [http://hades.mech.northwestern.edu/index.php/Mobile_Manipulation_Capstone_2022 '''at this page'''], in a single zip file named FamilyName_GivenName_capstone.zip. '''You may earn up to 10% extra credit on the capstone project by implementing self-collision avoidance.''' See the description of the final project writeup.

<!--
Reminders:
# Read and follow closely the instructions on what to submit! If you are missing requested files, or if you use a different directory structure, you will lose points. Make sure your top-level README file is clear on what you've done and what you've submitted.
# If your code does not work well, please describe the remaining issues in your README file. Don't gloss over them or only provide examples where the code works well if the code does not work well for other example problems. Otherwise, if the graders find problems with your software, you will not receive credit for having identified them yourself.
# You can get up to 10 pts of extra credit for correctly implementing joint-limit avoidance (so the robot links and chassis do not self-intersect) and singularity avoidance (e.g., using joint limits that keep the arm in a portion of its workspace where it does not encounter any singularities). If you implement these, you should submit examples of your code solving the same problem two ways---not using joint-limit avoidance and using it---so the usefulness of the joint-limit avoidance is apparent. '''Also, your README file should clearly describe your approach to solving joint-limit and singularity avoidance.'''
# Make sure to keep your problem inputs separate from the code. The exact same code should solve all your problem instances; you shouldn't have different copies of your code for different problem inputs. You could have an input file for each of your examples (e.g., bestScript, overshootScript, newTaskScript) which defines the inputs (e.g., block configurations, controller gains, initial robot configuration) and invokes your code. Then a grader just needs to invoke those scripts to verify your results. (If you implemented joint-limit avoidance, this could just be one of your inputs, e.g., a variable called "avoidJointLimits" which is 0 if you don't care about avoiding joint limits and 1 if you do.)
# Make sure your videos are good quality. They shouldn't be too fast (at least 5 seconds long) or low resolution. The motion should be smooth.
# If your code is written in Python, indicate which version of Python should be used.
# '''Only submit the code that you wrote.''' DO NOT submit MR library functions. The TAs will test your code using the MR library functions imported into MATLAB or Python as appropriate.
-->
<!--
==Quizzes==
* [[Media:ME449-quiz1-solutions-2019.pdf|Quiz 1 Solutions]] (average score 22.4/27)
* [[Media:ME449-quiz2-solutions-2019.pdf|Quiz 2 Solutions]] (average score 31.2/35)

==Detailed Syllabus==
[https://docs.google.com/spreadsheets/d/1UrBFai-1Z98Ry48bW50OMqxvvqZ3Jo8pHgZmljOgPpo/edit?usp=sharing '''The course calendar'''], including video lecture and reading assignments due before each class.

[https://docs.google.com/spreadsheets/d/1jWd_POLlQYxQLv1Igv-eVmORdtEcLi0mU_rVLkNguYI/edit?usp=sharing '''Click here for a graphical view of the class schedule, including student lectures.''']

Homeworks are due at the beginning of class every Wednesday, unless otherwise noted. You will watch the videos and do the reading in advance of class using the material, as noted in the syllabus below. A typical weekly schedule will consist of:
: M: Video/reading comprehension quick quiz and help with homework.
: W: Video/reading comprehension quick quiz, homework solutions, plus '''EITHER''' student lecture '''OR''' quiz preparation.
: F: Video/reading comprehension quick quiz plus '''EITHER''' student lecture '''OR''' quiz.

'''Class 1''' (W 9/20)
: Welcome to the course and course website. Structure of the course (HW due Wed, student-generated lectures and learning materials, in-class assignments, feedback on student lectures, occasional Friday quizzes). Book, software, (lack of) D-H parameters, syllabus, V-REP simulator, office hours.

At home:
: Videos: first 3 videos of Chapter 2, through Chapter 2.2
: Reading: Chapters 2.1 and 2.2
: Software: download github software with book, install V-REP and verify that you can use Scenes 1 and 2 (the UR5)
: '''HW1, due 1:30 PM 9/27''': Exercises 2.3, 2.9, 2.20, 2.29. Also, create your own example system with closed loops, something not in the book, and solve for the degrees of freedom using Grubler's formula. Make it something that exists or occurs in common experience, not necessarily a robot. Imagine using it to teach someone about Grubler's formula.

'''Class 2''' (F 9/22)
: Quick quiz
: Sample student lecture

At home:
: Videos: 2 videos on Chapter 2.3
: Reading: Chapter 2.3

'''Class 3''' (M 9/25)
: Quick quiz
: Bring your laptop, demo V-REP UR5 scenes
: Help with HW

At home:
: Videos: 2 videos, Chapter 2.4 and 2.5
: Reading: Chapters 2.4 and 2.5
: Turn in HW1

'''Class 4''' (W 9/27)
: Quick quiz
: Solutions to HW1; student examples of Grubler's formula

At home:
: Videos: first 3 videos of Chapter 3, through Chapter 3.2.1
: Reading: through Chapter 3.2.1
: '''HW2, due 1:30 PM 10/4''':
:: 1) Exercise 3.1, except the y_a axis points in the direction (1,0,0).
:: 2) Exercise 3.2, except p = (1,2,3).
:: 3) Exercise 3.5.
:: 4) Exercise 3.9.
:: 5) In Figure 1.1(a) of the book is an image of a UR5 robot, with a frame at its base and a frame at its end-effector. Eyeballing the end-effector frame, approximately write the rotation matrix that represents the end-effector frame orientation relative to the base frame. Your rotation matrix should satisfy the properties of a rotation matrix (R^T R = I, det(R) = 1). The x-axes are in red, the y-axes are in green, and the z-axes are in blue.
:: 6) Write a program that takes a set of exponential coordinates for rotation from the user as input. It then prints out the following: (a) the corresponding unit rotation axis and the angle of rotation about that axis; (b) the so(3) 3x3 matrix representation of the exponential coordinates; (c) the 3x3 SO(3) rotation matrix corresponding to the exponential coordinates; (d) the inverse of the rotation matrix from (c); (e) the 3x3 so(3) matrix log of the matrix from (d); and (f) the corresponding exponential coordinates for the so(3) matrix (e). Use the code from the book and write your program in Mathematica, MATLAB, or Python. Turn in your code and the output of an example run using (0.5, 1, 0) as the input to part (a).
:: 7) Write a function that returns "true" if a given 3x3 matrix is with a distance epsilon of being a rotation matrix and "false" otherwise. It is up to you to define the "distance" between a random 3x3 real matrix and members of SO(3). Test the function on two matrices, neither of which is exactly in SO(3), but one of which is close (so the result is "true") and one of which is not. Turn in your code and provide the test run output, which also outputs the distance to SO(3) that you defined.
:: 8) Following up on the previous exercise: describe (don't implement, unless you want to) a function that takes a "close by" 3x3 matrix and returns the closest rotation matrix. How would you use the fact that R^T R - I must be equal to zero to modify the initial 3x3 matrix to make it a "close by" rotation matrix? Would the function be iterative? You are free to do some research online, but as always, '''cite your sources'''!

'''Class 5''' (F 9/29)
: Quick quiz
: Lecture

At home:
: Videos: videos 4-6 of Chapter 3, through Chapter 3.2.3
: Reading: through Chapter 3.2.3

'''Class 6''' (M 10/2)
: Quick quiz
: Help with HW

At home:
: Videos: videos 7-9 of Chapter 3, Chapters 3.3.1 and 3.3.2
: Reading: same sections
'''Class 7''' (W 10/4)
: Quick quiz
: Exam prep

At home:
: Videos: videos 10-11, Chapter 3.3.3 and 3.4
: Reading: same sections
: '''HW3, due 1:30 PM 10/11''': Exercises 3.16, 3.17, 3.27, 3.31, and 3.48 (as always, for programming assignments, turn in your code and sample output demonstrating it).

'''Class 8''' (F 10/6)
: EXAM 1

At home:
: Videos: video 1 of Chapter 4, through Chapter 4.1.2
: Reading: same sections

'''Class 9''' (M 10/9)
: Quick quiz
: Help with HW

At home:
: Videos: videos 2-3 of Chapter 4, Chapter 4.1.3
: Reading: same sections
'''Class 10''' (W 10/11)
: Quick quiz
: Student lecture 1 (Pawar, Subramanian, Goyal, Cai)

At home:
: Videos: video 1 of Chapter 5, up to (not including) Chapter 5.1
: Reading: same sections
: '''HW4, due 1:30 PM 10/18''': Exercises 4.2, 4.8, 4.14, and 5.7(a). Question 5: In Chapter 3.5 (Summary), there is a list of analogies between rotations and rigid-body motions. Read it carefully and report anything that is either unclear or incorrect.

'''Class 11''' (F 10/13)
: Quick quiz
: Student lecture 2 (Wang, Wu, Xia, Zheng)

At home:
: Videos: video 2 of Chapter 5, Chapter 5.1.1
: Reading: same sections

'''Class 12''' (M 10/16)
: Quick quiz
: Help with HW

At home:
: Videos: videos 3 and 4 of Chapter 5, Chapter 5.1.2 through 5.2
: Reading: same sections
'''Class 13''' (W 10/18)
: Quick quiz
: Student lecture 3 (Wiznitzers, Hutson, Spies)

At home:
: Videos: videos 5 and 6 of Chapter 5, Chapter 5.3 and 5.4
: Reading: same sections
: '''HW5, due 1:30 PM 10/25''': Exercises 5.2, 5.3, 5.23, 5.25, 6.7, and 6.8.

'''Class 14''' (F 10/20)
: Quick quiz
: Student lecture 4 (Don, Chien, Husain, Sulaiman)

At home:
: Videos: videos 1 and 2 of Chapter 6,
: Reading: intro of Chapter 6 and Chapter 6.2

'''Class 15''' (M 10/23)
: Quick quiz
: Help with HW

At home:
: Videos: video 3 of Chapter 6
: Reading: Chapter 6.2
'''Class 16''' (W 10/25)
: Quick quiz
: Exam prep

At home:
: Videos: video 1 of Chapter 8, through 8.1.1
: Reading: same sections
: [[Media:ME449-HW6-2017.pdf|HW6, due 1:30 PM 11/1]]

'''Class 17 ''' (F 10/27)
: EXAM 2

At home:
: Videos: video 2 of Chapter 8, through 8.1.2
: Reading: same sections

'''Class 18''' (M 10/30)
: Quick quiz
: Help with HW

At home:
: Videos: video 3 of Chapter 8, through 8.1.3
: Reading: same sections
'''Class 19''' (W 11/1)
: Quick quiz
: Student lecture 5 (Zhang, Zhu, Meng, Luo)

At home:
: Videos: videos 4-5 of Chapter 8, through 8.2
: Reading: same sections
: '''HW7, due 1:30 PM 11/8''': Exercises 8.2, 8.3, 8.11 (you should build on the MR code), and 8.15(a).

'''Class 20''' (F 11/3)
: Quick quiz
: Student lecture 6 (Lyu, Yi, Wang, Swissler)

At home:
: Videos: video 6 of Chapter 8, up to (not including) 8.4
: Reading: same sections

'''Class 21''' (M 11/6)
: Quick quiz
: Help with HW

At home:
: Videos: video 7 of Chapter 8, Chapter 8.5 (skip 8.4)
: Reading: same sections
'''Class 22''' (W 11/8)
: Quick quiz
: Student lecture 7 (Warren, Kilaru, Wang, Mandana)

At home:
: Videos: videos 1-2 of Chapter 9, through Chapter 9.2
: Reading: same sections
: '''HW8, due 1:30 PM 11/15''': Exercises 8.15(b) (use your previous results from 8.15(a), and turn in any code you write as well as a V-REP movie of your simulation), 8.14 (turn in your testable code and evidence your code returns similar results), 9.14, and 9.26.

'''Class 23''' (F 11/10)
: Quick quiz
: Student lecture 8 (Wang, Dai, Ma, Peng)

At home:
: Videos: video 4 of Chapter 9, Chapter 9.4 - 9.4.1 (skip 9.3)
: Reading: same sections

'''Class 24''' (M 11/13)
: Quick quiz
: Help with HW

At home:
: Videos: videos 5-6 of Chapter 9, up to (not including) Chapter 9.5
: Reading: same sections
'''Class 25''' (W 11/15)
: Quick quiz
: Exam prep

At home:
: Videos: videos 1-3 of Chapter 11, up to (not including) Chapter 11.2.2.1
: Reading: same sections
: '''Final project. This project is part of the assignment grade, cannot be dropped, and has the weight of 2 normal assignments.''' The assignment is split into two parts: a relatively simple Part I, due after 1 week, followed by the programming-heavy Part II, due during finals week. You will receive a single grade for the entire assignment, after Part II has been submitted.
:: '''Part I, due 1:30 PM 11/22''': Exercise 13.33 (a) and (b). Turn in your solutions (handwritten or typed) and any code you wrote.
:: '''Part II, due 11:59 PM 12/6''': Exercise 13.33 (c), (d), and (e). Turn in 1) any solutions (handwritten or typed), 2) your code, 3) any plots you created with your code, 4) your short V-REP videos (made using the youbot csv animation scene), and 5) the .csv files corresponding to the videos.

'''Class 26''' (F 11/17)
: EXAM 3

At home:
: Videos: videos 4-5 of Chapter 11, Chapter 11.2.2.1 and 11.2.2.2
: Reading: same sections

'''Class 27''' (M 11/20)
: Quick quiz
: Help with HW

At home:
: Videos: videos 6-8 of Chapter 11, Chapter 11.3
: Reading: same sections
: '''Turn in Part I of your final project on Canvas.'''
'''Class 28''' (W 11/22)
: Quick quiz
: Student lecture 9 (Abiney, Aubrun, Anthony, Alston)

At home:
: Videos: videos 1-3 of Chapter 13, through Chapter 13.2
: Reading: same sections

'''Class 29''' (M 11/27)
: Quick quiz
: Help with HW

At home:
: Reading: odometry and mobile manipulation, Chapter 13.4 and 13.5
'''Class 30''' (W 11/29)
: Quick quiz
: Student lecture 10 (Miller, Berrueta, Davis, Tobia)

At home:
: Final assignment work

'''Class 31''' (F 12/1)
: Student lecture 11 (Fernandez, Lutzen, SaLoutos, Iwankiw)

At home:
: '''Your final project is due on Canvas by 11:59 PM on Wednesday Dec 6.'''

-->

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==Archive==

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Revision as of 13:37, 15 March 2023

EA3 System Dynamics

Spring Quarter 2023

Instructors, TAs, and Sections

  • Section 21, 10-10:50 MWF, Tech M345: Prof. Kevin Lynch, kmlynch@northwestern.edu. Tuesday: Tech M345.
  • Section 20, 11-11:50 MWF, Pancoe Auditorium: Prof. Jeremy Keys, jeremy.keys@northwestern.edu. Tuesday: Frances Searle 1421.
  • Section 23, 1-1:50 MWF, Pancoe Auditorium: Prof. Cheng Sun, c-sun@northwestern.edu. Tuesday: Annenberg G15.
  • Section 22, 2-2:50 MWF, Pancoe Auditorium: Prof. Sandip Ghosal, s-ghosal@northwestern.edu. Tuesday: Tech L211.

TAs:

  • Ayesha Ahmed, ayesha.ahmed1@northwestern.edu
  • Caralyn Collins, CaralynCollins2024@u.northwestern.edu
  • Shizhou Jiang, shizhou.jiang@northwestern.edu
  • Shuting Lai, ShutingLai2023@u.northwestern.edu
  • Haklae Lee, haklae.lee@northwestern.edu
  • Rui Li, ruili2024@u.northwestern.edu
  • Asma Meem, asma.meem@northwestern.edu
  • Nibir Pathak, NibirPathak2021@u.northwestern.edu
  • Dono Toussaint, DonoToussaint2027@u.northwestern.edu

Course Summary

EA3 focuses on the modeling of dynamic systems, the reduction of models to differential equations of motion, and some exploration of the system behavior relating to the solution of those equations.

The goal is to learn system modeling across disparate physical domains (mechanical, electrical systems). We will typically proceed using the following steps:

  • to understand the elements of each domain (e.g. spring, capacitor; or force, voltage)
  • to express precisely the way in which the elements interact (e.g. free-body diagrams, circuit diagrams)
  • to reduce the idealized systems to equations
  • to understand the behavior of the system by solving equations

There will be a strong emphasis on understanding how physical processes are described by mathematical equations.

Course Policies

Supportive Class Environment

All members of this class (instructors, TAs, students) are expected to contribute to a respectful, inclusive, and supportive environment for every other member of the class.

We are partners in your education; help us help you get the most out of this class. Please engage during class meetings.

Honor Code

You are encouraged to discuss the material with the instructor, course assistants, and your classmates, but you are not allowed to copy answers or code or share your answers or code with others. Anyone copying answers or code, or providing answers or code, or becoming aware of others doing so without reporting to the instructor, is in violation of the honor code.

Academic Support and Learning Advancement (ASLA)

Northwestern's Academic Support and Learning Advancement office offers peer-guided study groups, drop-in peer tutoring, individual and group peer academic coaching, and consultations to help students navigate their academic paths and refine their study strategies.

Grading

Three quizzes count for 90% of your class grade. Homeworks account for the remaining 10%. Each quiz is in class (50 minutes). Students must attend the quiz in their own section, and the quizzes in each section will be different. Grades are assigned in each section independently of the other sections.

Homework

Assignments must be submitted electronically through Canvas. Late assignments are not accepted. No exceptions, so please don't ask. Your lowest homework grade will be dropped from the calculation of your homework score.

Syllabus and Web Textbook

General Introduction

  • Big picture, the EA3 three-step process, and what you will learn

Mechanical Systems

  • Mechanical systems
  • Springs
  • Formulating equations of motion for spring-damper systems
  • Solving equations of motion
  • Masses
  • Newtonian mechanics
  • System dynamics and momentum conservation
  • System dynamics and mechanical energy equation
  • Transformers
  • Numerical solution of coupled differential equations
  • Analytic solution of coupled differential equations

Electrical Systems

  • Introduction
  • Resistors
  • Capacitors
  • Formulating equatios for circuits
  • Simple RC circuits
  • Complex RC circuits
  • Inductors
  • Circuits with inductors

Reference

  • Important concepts and formulas
  • Famous scientists
  • Mode analysis
    • Example 1
    • Example 2
    • Example 3
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