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AA/EE/ME 570 Winter 2008 |
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Instructor Prof.
Kristi A. Morgansen |
Office Hours Office: Guggenheim 318B |
Lectures:
T/Th 1:30-3:20, MGH 242
Homework
section (optional): TBD
This course provides an introduction to the fundamentals of calculus on manifolds and group theory focusing on applications in robotics and control theory. We will begin with an overview of the use of differential geometry in control theory relative to other techniques and build a rigorous foundation from which current literature can be understood. Topics to be covered include: manifolds, tangent spaces and bundles, Lie algebras, groups and semi-groups, and coordinate versus coordinate-free representations. Applications that will be addressed are modeling of mechanical systems, potential fields, nonholonomic systems, and self-assembling systems.
Suggested prerequisites: EE510
Expectations
My role: The role of an instructor is
to help the students acquire new knowledge and skills more quickly than they
could on their own, to guide the approach to learning with effective tools, to
provide completeness of subject matter, and to place material in context
relative to the larger field.
Student role: The role of a student is, of
course, to learn. Students in this
course are expected to read the notes associated with a topic before the
material is presented in class, to prepare questions on the reading (need for
clarification, connections to previous material, placement of the material in a
larger context, etc), to not wait until 24 hours before assignments are due to
begin them, to utilize the office hours of the professor and TA, and to
interact professionally with all members of the course.
General: Students interested in pursuing graduate degrees in control theory and
robotics come from a variety of backgrounds.
From the point of view of course material, this course provides the
fundamental groundwork on which all other control theory topics are built. Because of the differences in experience,
this course also serves the purpose of alignment of student capabilities with a
common set of tools. Students who take
this course generally find that the material is challenging, that homework
requires significant effort, but that in the end, the time and effort are well
worth the payoff. The structure of the
course is an emphasis on homework. This
emphasis is chosen because, while a number of activities in the world beyond
the classroom do function as exams, more often than not activities (such as
research) function like homework.
Office hours: All students are requested to
attend office hours once during the first week of class. This request allows me a chance to get to
know you personally, and familiarizes you with the path to at least one of my
offices.
Resources
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Robotics, Control and Mechatronics web site: http://www.engr.washington.edu/rcm
Homework and Exam Policy
Collaboration on homework assignments is allowed. You may consult outside reference materials, other students, or the instructor. All solutions that are handed in should reflect your understanding of the subject matter at the time of writing. Existing solution sets from previous years or other sources are not to be used. No collaboration is allowed on the midterm or the final exam.
Homework format: Homework assignments will have some number of problems assigned from the text, and some number of challenge problems or problems related to your project. When composing your homework for submission, please adhere to the following guidelines: (1) all problems should be submitted in the same order as in the assignment, (2) give each problem the same label as in the assignment, (3) begin each problem by restating the problem then indicate how you will approach the solution, (4) show all relevant work indicating how you reach your solution, and (5) indicate or discuss why your answer is correct or appropriate (e.g. check your answer). For more information see the Five Steps to Problem Solving. Additional points: (1) clearly mark your answer, (2) keep relevant information associated (e.g. eigenvectors belong to specific eigenvalues), (3) again, show all relevant work, (4) take pride in your work—neatness counts in whatever profession you have in the future, so practice now!
Homework section:
Homework is due at the beginning of lecture on Thursdays (
Homework section format: Assignment list. The homework section will be split into two parts. In the first part, three people will present during each section (following alphabetical order of the entire class). In the second part, I will answer questions. You are welcome to exchange slots, but please let me know if you choose to do so or if you do not wish to participate. Each presentation will earn up to 10% of full assignment score of extra credit on a given assignment (assignments will generally have a total of 50pts). The problems being presented will be the project-related problems or the challenge problems. Each presenter will have 10 minutes total. Plan accordingly. Be aware of the following guidelines for presenting: plan for the time limit, start at the top of one board section, work down the section, then start in the next board section, state your reasoning clearly, and talk through the solution. Credit is given for presentation and a valid attempt at solution, not necessarily an entirely correct solution.
Grading
The final grade will be based on homework, a midterm, a final exam, and a project. Grading is not done on a curve, but on a scale. Specifically, if the top grade at the end of the course is not a 4.0, a constant is added to all grades so that the top grade is a 4.0. Grade scaling is determined before extra credit is applied to any grades. If everyone performs well, the possibility exists for everyone to receive a 4.0.
· Homework: 50%. Due date Thursdays 1:30pm. Late homework will not be accepted without prior permission from the instructor.
· Midterm: 20%. The midterm will be a take home exam on Thursday Feb. 7.
· Final exam: 20%. The final exam will be a take-home exam.
· Project: 10%. Students will complete a project using the tools from the course on a physical system. Project guidelines
Course Text and References
The required reading source for the course is
F. Bullo and A. D. Lewis, Geometric Control of Mechanical Systems, Springer, 2005.
Additional references that may be useful:
· J. E. Marsden, T. Ratiu, and R. Abraham, Manifolds, Tensor Analysis, and Applications, 2ed.,
Springer-Verlag, 2003.
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W. Boothby, An Introduction to Differentiable
Manifolds and Riemannian Geometry, 2nd ed. Academic Press, 1986.
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Anthony Bloch, Nonholonomic Mechanics and Control, Springer Verlag.
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V. Guilleman and A. Pollak, Differential Topology,
Prentice-Hall, 1974.
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J. Milnor, Topology from the Differentiable
Viewpoint, University Press of Virginia, 1965.
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B. Schutz, Geometrical Methods of Mathematical
Physics, Cambridge University Press, 1980.
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M. Spivak, A Comprehensive Introduction to
Differentiable Geometry, v. 1. Publish or Perish, 1970.
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F. W. Warner, Foundations of Differentiable Manifolds
and Lie Groups, Springer-Verlag, 1983.
Schedule
This schedule is an initial guideline and is subject to adjustment as the course progresses.
Prof. Morgansen will be traveling the
following dates:
Jan. 10-12 (UCSD)
Feb. 24-25 (Georgia Tech)
Date |
Topics |
Reading |
Ref Material |
Assignments |
Jan 8 |
Introduction |
BL 1, bl-ch1.pdf |
Homework #1: Assignment
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Jan 10 |
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Jan 15 |
Sets and sequences; Vector spaces |
BL 2.1-2.2 |
Homework #2: Assignment (Solutions) |
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Jan 17 |
Inner products and bilinear maps; Tensors |
BL 2.3-2.5 |
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Jan 22 |
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Homework #3:
Assignment
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Jan 24 |
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Jan 29 |
Homework #4:
Assignment
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Jan 31 |
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Feb 5 |
Homework #5: Assignment (Solutions) |
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Feb 7 |
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Feb 12 |
BL 3.3 | |||
Feb 14 |
BL 3.3, |
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Feb 19 |
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Homework #6:
Assignment
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Feb 21 |
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Feb 26 |
Homework #7:
Assignment
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Feb 28 |
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Mar 4 |
Lie groups and
Lie algebras
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Homework #8:
Assignment
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Mar 6 |
Lie groups and
Lie algebras
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BL 5.1 |
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Mar 11 |
BL 5.2 |
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Mar 13 |
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FINAL EXAMINATION |
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Web page maintained by K. Morgansen (morgansn@u.washington.edu)
Last
updated:
21-mar-08