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Geometric Fundamentals for Robot Design

From WikIRI

With an emphasis on mechanisms and kinematically constrained systems

Master's degree in Automatic Control and Robotics

UPC-BarcelonaTech

Update: This course will no longer be offered. However, you can still enjoy its contents through this website. It contains the full slides and lecture notes, which are suitable for self-study. Please contact the course professors for feedback, questions, or suggestions.


Haptic telemanipulation with the Catalan Ictineu 3 submarine (exam 2014)
The Shuttle Atlantis and the Canadarm for space manipulation (exam 2015)
The Stickybot III robot from Stanford while climbing a wall (exam 2012)


Contents

Course data

The students' opinion

Here's the opinion of past students on this course, collected by the UPC through anonymous surveys. Note that the course title has suffered a few changes over the years. Missing years correspond to those in which no survey was collected.

Course assessment:

Teachers' assessment:

Objective and skills to be gained

An Arduino-based 3-RRR robot that avoids singularities, by Alejandro Rajoy (former student of this course), Patrick Grosch, and Lluís Ros (KRD group). Its singularity-free path planner and mechatronic design are described in Alejandro's Master thesis.
See these planar 3R arms in action, as part of the highly innovative robotic system TriVex SL/SLi, by Douglas Machine.
A robotized submarine developed by Ictineu submarins, Catalonia. It is among the World's top ten submersibles as for its immersion depth.
Festo's smartbird and its wing mechanism. See how it flies. Learn more in this TED talk.
A 3-PRR parallel manipulator for 3-DOF positioning designed at University of Cluj Napoka, Romania.
A 3-RRR manipulator for pick-and-place operations, designed by Jens Kotlarski at University of Hannover. See how it moves.
A Stewart platform by F. Thomas and P. Grosch (Kinematics and Robot Design group, IRI, Barcelona).
A cable-driven hexacrane by the KRD group. A singularity-free path planner for this robot has recently been devised. Learn more.

Geometry is essential to many human activities and it is deeply embodied in how humans think. In Robotics, it brings deep insight into the principles of robot motion and control, and develops creativity and intuition, abilities much needed for the proper design and study of robotic mechanisms. A main goal of this course is to get acquainted with such abilities.

Traditionally, the theories of statics and instantaneous kinematics have been learned separately in mechanical engineering courses. However, they proceed alongside one another, with 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 learning the two subjects in a unified manner. This simplifies the kinetostatic analysis of a robot, and allows us to derive rich information for robot design and programming. A global picture of the robot behaviour is gained, both in regular or singular configurations.

The course techniques are applied to conventional serial or parallel robots, but also to innovative systems like cable-driven manipulators, flying or climbing robots, or multi-robot formations.

At the end of this course, the successful student will know:

  • How to formulate the constraint equations of multibody systems of arbitrary architecture, and how to solve them using advanced methods of position analysis.
  • How to analyze the kinematic and static behavior of a robot using projective-geometric and screw-theoretic tools, both in regular and singular configurations.
  • How the static behavior is tightly coupled to the kinematic one due to the principle of reciprocity.
  • What are the physical consequences of traversing a singular configuration, and how this leads to control or dexterity issues.
  • How to implement a hybrid control of force and position using the rigorous background of the course.
  • How to apply the course knowledge to real-world systems like those in the inset pictures of this page.

Learning methodology

The subject will be worked out in theory and problem sessions mainly, and by means of a few practice miniprojects. Depending on the evolution of the course, a number of seminar sessions might be programmed as well. In such sessions, the active participation of the assistants is a fundamental aspect, and the teacher's task is, essentially, to direct the session, presenting and setting the topics in context, and coordinating the discussion among participants.

Grading

Grading is based on the score obtained in mandatory miniprojects and in a final exam. Small roundings of the score will be made to reflect the student's participation in the course: contributions to the debate of the topics, questions raised, and their resolution.

Clarity of presentation is a must, and may have an impact on the student score. If a solution report or exam is not clear or polished enough, the score can be decreased up to 30% of the maximum one achievable.

The final mark, M, will be:

M = 0.25 P + 0.75 E

where:

  • P = mark obtained in practice mini-projects (between 0 and 10)
  • E = mark of the final exam (between 0 and 10)

A student will pass the course if M ≥ 5.

Commonly, the final exam consists of two parts:

  • Part I: One or two problems, similar to those solved in exercise sessions.
  • Part II: A quiz of short questions with multiple-choice answers.

Here there are some examples of such problems and questions:

In the final exam, the student can only bring one calculator (with the capacity to perform matrix operations), 3 DINA A4 sheets of paper summarizing the course content, ball pen, pencil and rubber. Any device having wi-fi capability is not allowed.

Schedule, readings and exercises

See the course schedule at a glance.

The course is structured into five modules. Module 1 provides background tools to compute robot configurations needed through the course. Modules 2 to 4 are devoted to analyze such configurations from the statics and kinematics viewpoint, stressing the connections between the two theories. Module 5 applies this knowledge to develop hybrid control strategies for robot tasks involving contact with the environment.

There is an Appendix Module for those wishing to see an introduction to spatial screw theory (the extension to spatial mechanisms of the theory given in Modules 2 and 3).

You'll here find the whole course material. It includes commented slides or detailed lecture notes, all suitable for self-study:

Course presentation: 15 min., on Feb. 14 Slides.

Module 1: Mobility and position analysis

Theory: 3.75 hours, on Feb. 14 and 21.
Slides alone. Slides with notes.
Geogebra and CUIK session: 2 hours, on March 7.
On March 7 we shall have a practical session from 9:30 to 12:00, in the computer room PC3 of the FME. We shall explain the basics of two software suites: Geogebra and Cuik. They are needed to solve two of the course miniprojects.
Prior to this session, please solve problem 4 of the theory slides. Please also try to install Geogebra and CUIK in your laptop computer. The latter is not required for the session (we will work with the computer PCs), but it will allow you to solve the miniprojects later on. For the installation, refer to the instructions below.
Slides worked out in the session.
Files used during the session.
Exercises: 1 hour, on Feb. 28.
Exercise list: We'll do problems 1, 2, and 3.

Module 2: Statics

Theory: 4 hours, on Feb. 21 and 28.
Lecture notes.
Exercises: 2.5 hours, on March 7, 14, and 21:
Exercise list
March 7: Problem 3.
March 14: Short questions 1-4.
March 21: Problem 4.

Module 3: Instantaneous kinematics

Theory: 4.5 hours, on March 14, 21, and 28.
Slides, and their companion notes.
Geogebra animation of a velocity field, and its ggb file.
A real 3R robot used in packaging.
Note on infinitesimal displacements.
Exercises: 2.5 hours, on March 21 and 28, April 18, and May 2.
Exercise list.
March 21: Problem 1.
March 28: Problem 2 + short questions 1, 2, 4.
April 18: Problem 3 + short question 3.

Module 4: Duality:

Theory: 8.5 hours, on March 28, and April 18 and 25.
Principle of Virtual Power and reciprocity: 1.5 hours.
Slides, and companion notes.
Twists of freedom and wrenches of constraint of simple robots: 0.5 hours.
Lecture notes
Static analysis and duality diagram of a serial manipulator: 2 hours.
Lecture notes
Videos showing singularity effects on a Kuka robot
Geogebra animation of the 3R arm passing close to a singularity and its *.ggb file
Kinematic analysis and duality diagram of a parallel manipulator: 1.5 hours
Lecture notes.
Videos showing singularity effects on a 3-RPR robot.
Dramatic loss of rigidity in a spatial parallel robot.
Forward singularity of a Stewart platform (1 of 2).
Forward singularity of a Stewart platform (2 of 2).
Reciprocal product methods and their extensions for fully-parallel robots: 3 hours.
Lecture notes.
Slides and videos showing fully-parallel robots.
Exercises: 4 hours, on April 25, and May 9, 16, and 23.
Exercise list.
April 25: Problem 1 + short question 5.
May 9: Problem 4 + short question 7.
May 16: Problem 2 + short question 3.
May 23: Problem 5 + short question 8.

Module 5: Introduction to hybrid control of force and position

Theory: 4 hours, on May 9 and 16.
Lecture notes.
Exercises: 2 hours, on May 23.
Exercise list.
May 23: Problem 1. Short questions 1, 2, and 4.

Appendix: General wrenches and twists

We share these lecture notes with those wishing to see an introduction to spatial screw theory, i.e., the extension of the theory given in Modules 2 and 3 to spatial mechanisms. The student can also work out these exercises on his own, whose solutions can be found in these slides.

Miniprojects

To pass the course, the student has to work out these miniprojects:

Miniproject 1: Position analysis of wing mechanisms and quadrotor formations
Issued on March 7. Due on April 4.
Miniproject 2: Manipulation in the space shuttle
Issued on March 28. Due on May 31 (Part B requires the hybrid control module).
Miniproject 3: Singularity analysis of a parallel robot
Issued on May 2. Due on May 31.

You'll need to install Geogebra and CUIK to solve miniprojects 1 and 3.

The students can work individually or in groups of at most 3 people. Every group has to deliver just one report explaining their solution to the miniproject, and the source files asked for in the miniproject. The report (in pdf form) and the files (either cuik or ggb files) should be sent by email to Lluís Ros no later than the due date indicated.

Handwritten manuscripts are allowed, but clarity of presentation is a must. If a report is not polished enough in its writing, the final score may be reduced in up to 30% of the maximum score achievable. Please justify all your developments.

Miniproject reports will be reviewed by the teachers during the course, and returned back to students with annotated feedback, and a score.

Geogebra and CUIK: Installation and usage

Installing CUIK:

Installing Geogebra:

Help on the CUIK suite:

  • The class slides should be sufficient, but this paper gives a short introduction to the software (see Section "Branch-and-prune methods").
  • Further help in the CUIK suite web page.

Help on Geogebra:

Bibliography

The central part of the course follows the beautiful line of argument traced by Joseph Duffy in his book:

Recommended material for further study:

  • What is a parallel robot? Definition, origins, design issues, manufacturers, and more, beautifully described and illustrated.
  • 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.
  • 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

Retrieved from "http://wiki.iri.upc.edu/index.php/Geometric_Fundamentals_for_Robot_Design"

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