GCR 2010-2011

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This is the state of the wiki page by the end of course 2010-2011.

Course data

• Course code: 34011-GCR.
• Prerequisites: Entry level courses in linear algebra, mechanics, and a working knowledge of some computer language. Here's a summary of the main concepts needed from such courses.
• Official course name: The official course name is "Geometria Computacional en Robòtica (GCR)". Though eminently geometric, the course contents has evolved in precedent years, and the title of this page better describes the current course structure. Actions are being made to adapt the official course name to the title of this page.
• Academic year: 2010-2011 (Previous years: 2009-2010, 2008-2009).
• Master programme: Master in Automatic Control and Robotics.
• Semester: Second.
• ECTS Credits: 5.
• Teaching language: Catalan mainly. Spanish and English sometimes. Our university provides a comprehensive range of Catalan courses for beginners to advanced learners, which are supported with self-learning resources and language exchange services. More resources can be found on the Intercat web site.
• Professors in charge: Lluís Ros, Pablo Jiménez, Montse Manubens, and Oriol Bohigas.
• Unit: Institut de Robòtica i Informàtica Industrial.
• Room: We meet on monday from 10:00 to 12:00, and thursday from 10:00 to 11:00, at aula 103 of the FME.
• Consultation hours: Friday from 12:30 to 13:00 (Pablo Jimenez), and from 15:00 to 15:30 (Lluís Ros).

Please see these hints on using the wiki space.

Presentation and objective

This course is devoted to the statics and instantaneous kinematics of robot mechanisms, a basic set of tools for the analysis and control of manipulation devices, including serial/parallel manipulators, and multifingered hands.

Traditionally, the theories of statics and instantaneous kinematics have been learned separately in mechanical engineering courses. However, they proceed alongside one another, the important principle of reciprocity linking them together. Using this principle, and the homogeneous representation of forces and velocities as screw vectors, this course aims at studying the two subjects in a unified manner. In this way, the kinetostatic analysis of robots becomes computationally much simpler, the conclusions derived much richer, and the techniques turn out to be applicable to arbitrary mechanisms. Overall, a global picture of the behaviour of manipulation devices in and out a singular configuration is gained.

Although the presented techniques were well established by the end of the 19th century, with the work of Robert Ball, Felix Klein, James C. Maxwell, Luigi Cremona, Jean Bernouilli, Hermann Grassmann, Arthur Cayley, Julius Plücker, and others, the subject, yet important, has remained largely unnoticed by the Robotics Community, where the rigorous study of statics and instantaneous kinematics is apparently receding. An additional goal of this course is to help reversing this trend.

Learning methodology

The subject will be worked out in theory and problem sessions mainly. Depending on the evolution of the course, a number of seminar sessions might be programmed too. In such sessions, the active participation of the assistants is a fundamental aspect, and the professor's task is, essentially, to direct the session, presenting and setting the topics in a context, and coordinating the debate and the discussion among the students.

Grading

Grading is mainly based on a final examination. The final mark will also take into account the student's participation in class or in this wiki space (contributions to the debate of the topics, questions raised, and their resolution).

The final exam will have two parts:

• Part I: Two problems, similar to those solved in exercise sessions.

• Part II: Ten questions with multiple-choice answers.

Here there are some examples of such problems and questions:

• Exam 2011: Problems, questions.

• Exam 2010: Problems, questions.

• Exam 2009: Questions.

If the group of students is not large, the final exam might be oral. In that case, the exam will consist of a first block of conceptual questions, and a second block of questions regarding the exercises solved in class.

Schedule, readings and exercises

The course has two parts. Although we divide the course into "Part A: Planar Robots" and "Part B: Spatial Robots", the theory given in Part A easily generalizes to the spatial case. Part B is devoted to see such generalization, and thus requires much less time than Part A. We found that this path is amenable to students, specially to those with less background on Mechanics.

The following schedule and related pages is subject to change. Please watch this page and all its sub-pages if you want to be notified by e-mail about any changes introduced.

Part A: Planar robots

Part A mainly follows the book by Joseph Duffy, "Statics and Kinematics with Applications to Robotics", Cambridge University Press, 1996. However, some of the modules contain additional material not covered in such book. We will try to make all of the course contents available on-line, either in the form of slides (that the student should complement with class notes), or detailed lecture notes.

Module 0: Introduction

Course presentation: 1 hour, on February 14 (PDF slides, PPT slides)

Module 1: Mobility and displacement analysis

Theory: 2 hours, on February 14 and 17 (PDF slides, PPT slides, note, FAQ)

Exercises: 1 hour, on February 24.

Module 2: Statics

Theory: 4 hours, on February 21 and 28 (Lecture notes in PDF, FAQ)

Exercises: 3 hours, On March 3, 10, and 17.

Module 3: Instantaneous kinematics

Theory: 4 hours, on March 14 and 21 (PDF Slides, FAQ)

Exercises: 3 hours, on March 24, 31, and April 7.

Module 4: Series-parallel dualities on planar robots

Theory: 8 hours (FAQ)

Principle of Virtual Power: 2 hours, on March 28 (PDF Slides).

Reciprocity: 1 hour, on April 4 (Lecture notes in PDF).

Static analysis of the 3R manipulator: 1 hour, on April 4 (Lecture notes in PDF).

The duality diagram of a serial manipulator: 2 hours, on April 11 (Lecture notes in PDF).

Kinematic analysis and duality diagram of a parallel manipulator: 2 hours, on May 2 (Lecture notes in PDF).

Exercises: 4 hours, on April 28 (2 hours), May 5 (1 hour), and May 12 (1 hour).

Module 5: Introduction to hybrid control of force and position

Theory: 4 hours, on May 9 and May 16 (Lecture notes in PDF)

Exercises: 1.5 hours, on May 19 and May 26.

Part B: Spatial robots

Part B slightly follows the book by J. K. Davidson and K. Hunt, "Robots and Screw Theory", Oxford University Press 2004.

Module 6: General twists and wrenches and kinetostatic analysis of spatial manipulators

Theory: 4 hours, on May 23 and 30

Index and introduction (Lecture notes in PDF)

Part A: General wrenches and Poinsot's theorem (Lecture notes in PDF)

Part B: General twists and Chasles' theorem (Lecture notes in PDF)

Part C: Kinetostatics of general serial and parallel manipulators (Lecture notes in PDF))

Appendix: Couples as force systems (Lecture notes in PDF)

Module 7: Kinetostatics of multifingered hands

To be scheduled.

Terminology

Here's a free translation to Catalan, of the principal English words used for the main concepts of the course.

Bibliography

Course main books:

• Joseph Duffy. "Statics and Kinematics with Applications to Robotics". Cambridge University Press, 1996. Book partially available from Google Books. Here's a review of this book by J.-P. Merlet, appeared in The International Journal of Robotics Research, Vol. 16, No. 3, page 410, June 1997. Please see also this errata file compiled by the course members, and this table of notation used in the book.

• Joseph K. Davidson and Kenneth H. Hunt. "Robots and Screw Theory: Applications of Kinematics and Statics to Robotics". Oxford University Press, 2004. Book partially available in Google books. Here's a review of this book by G. Pennock, appeared in the ASME Journal of Mechanical Design, Vol. 126, pp. 763-764, July 2004.

Recommended material for further study:

• Gilbert Strang. "The fundamental theorem of Linear Algebra". The American Mathematical Monthly, Vol. 100, No. 9 (Nov. 1993), pp. 848-855.

• Gilbert Strang. Introduction to Linear Algebra, 4th edition. Wellesley-Cambridge Press, 2009.

• The excellent video lectures associated with the previous book.

• Felix Klein. "Elementary Mathematics from an Advanced Standpoint". Dover 2004.

• Kenneth H. Hunt. "Kinematic Geometry of Mechanisms". Oxford Science Publications 1978.

• Robert Stawell Ball. "A Treatise on the Theory of Screws". Cambridge University Press. Reprinted in 1998, from the first 1900 edition.

Links

• Wiki pages of previous years: Course 2009-2010, Course 2008-2009.
• Academic calendar of master courses at UPC.
• Timetable of all master courses.
• Teacher's space (Access restricted to teachers only).