ENEE 769R - Advanced Topics in Control

ENEE 769R - Advanced Topics in Control

Principles and Algorithms for Collectives: from Biology to Robotics

Fall 2012

Last Update October 15, 2012

Course Information

Special Announcements (most recent first)

11. Added link to Wei-Norman paper on Product of Exponentials Representations.

10. Link to Lecture 3 reference material added - J. M. Selig's book, readable on-line and also downloadable PDF chapters; link to Roger Howe's expository paper.

9. Link to wiki page for Denavit Hartenberg paramterization added (following lecture notes 2).

8. Added a link to Kinematic Models for Design a digital library at Cornell University on Mechanisms, a very rich resource containing numerous examples, and multimedia presentations of mechanisms in action.

7. Added a link to Kinematic Synthesis of Linkages (by Hartenberg and Denavit) under the heading of "interesting resources on the web" below. This is a classic text that gives a wide variety of examples and rigorous methods for analysis of mechanisms. In contrast with the programmability inherent to robots, mechanisms are characterised by single function design (e.g. motion transfer, motion conversion - say from reciprocating to rotary, force amplifcation etc.). The book also introduces formal methods of synthesis as known in the 1960's.

6. Added a link to Murray-Li-Sastry book - related to Lecture 2.

5. Make-up class, Tuesday September 11, 6:00 - 7:30 p.m., A.V. Williams Building room 2168.

4. Notes uploaded on robotics basics (kinematics of rigid bodies, serial link manipulators, Jacobians, dynamics).

3. Added link to paper of Rust (AMM 1934) on solution to Volterra integral equation of second kind.

2. NO CLASS on September 5 (Wednesday) - I am off-campus at a conference. (see email for suggested make-up times)

1. Lecture notes (1a) and (1b) on frames, and link to Bishop paper posted.

Weekly Lecture Notes by P. S. Krishnaprasad

Lecture 1a (Frenet Serret Frame) Lecture 1b (Natural Frame or Relatively Parallel Adapted Frame)Bishop's paper (on Relatively Parallel Adapted Frame) Rust paper on Volterra integral equation of second kind (for proof of existence and uniqueness of solutions to integral equations for natural curvatures)

Lecture 2a (Kinematics, rigid motions) Lecture 2b (Kinematics of linkages, typical manipulator) Lecture 2c (Forward kinematics and Jacobians) Lecture 2d (Dynamics) A Mathematical Introduction to Robotic Manipulation (a book by R. Murray, Z. Li and S. Sastry) Denavit Hartenberg paramterization for manipulators see animation for explanation

Lecture 3 reference material (link to J. M. Selig's book Geometric Fundamentals of Robotics, Second Edition, 2005, for material on Lie algebras and Lie groups - read chapters 2, 3, 4) Roger Howe's 1983 paper (Very basic Lie theory); corrections to Howe's paper (1984)

Lecture 4 reference material - Paper of Wei and Norman (1964) on representing solutions to linear differential equations by products of exponentials (or constructing canonical coordinates of the second kind in a neighborhood of identity on a Lie group)

Lecture 5 reference material G-Snakes paper on undulatory locomotion on a Lie group Two module SE(2)-snake paper


Homework Assignments

Exercises are embedded in the Lecture Notes. Occasionally, some exercises may be displayed here.


Homework solutions are sent by email


Some interesting resources on the web

Book on Kinematic Synthesis of Linkages (1964) by R. S. Hartenberg and J. Denavit

Kinematic Models for Design a digital library at Cornell University on Mechanisms

Link to biography of Sophus Lie originator of the theory of Lie algebras and Lie groups

Link to book by Daniel Liberzon on Calculus of Variations and Optimal Control

Real Analysis Book by Cinlar and Vanderbei - material useful in Systems courses

Impact of Control Technology vignettes, and, full report (warning 35 MB)