 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2021/2022

Code Completion Credits Range Language
B3M33PKR Z,ZK 6 2P+2C Czech
The course cannot be taken simultaneously with:
The course is a substitute for:
Lecturer:
Tomáš Pajdla (guarantor)
Tutor:
Tomáš Pajdla (guarantor), Viktor Korotynskiy, Kateryna Zorina
Supervisor:
Department of Cybernetics
Synopsis:

We will explain and demonstrate techniques for modelling, analyzing and identifying robot kinematics. We will explain more advanced principles of the representation of motion in space and the robot descriptions suitable for identification of kinematic parameters from measured data. We will explain how to solve the inverse kinematic task of 6DOF serial manipulators and how it can be used to identify its kinematic parameters. Theory will be demonstrated on simulated tasks and verified on a real industrial robot.

Requirements:

A course of basic robotics, e.g. B3B33ROB1.

Syllabus of lectures:

1. Introduction, algebraic equations and eigenvalues

2. Motion: Motion as a transformation of coordinates

3. Kinematics: Denavit-Hartenberg convention for a manipulator

4. Motion axis and angle, the rotation matrix and its eigenvalues.

5. Rotation parametrization: angle-axis, quaternions, Cayley parametrization, rational rotation.

6. Algebraic geometry I: monomial ordering, polynom „division“

7. Groebner basis.

8. Algebraic-numerical solving of polynomial equation systems.

9. Algebraic solution of Inverse kinematic task of a general 6R serial manipulator I

10. Algebraic solution of Inverse kinematic task of a general 6R serial manipulator II

11. Manipulator kinematic calibration.

12. Manipulator kinematic singularities.

13. Review.

14. Reserve.

Syllabus of tutorials:

1. Introduction to laboratory, Maple, a-test.

2. Correcting a-test, Maple.

3. Spatial rotations, representations, axis of motion.

4. Modified Denavit-Hartenberg notation.

5. Kinematics of redundant manipulator.

6. Solving algebraic equations.

7. Singular poses of a manipulator and their determination.

8. Task 1: Solving inverse kinematics task for a general 6DOF serial manipulator.

9. Task 1: Solving inverse kinematics task for a general 6DOF serial manipulator.

10. Task 1: Solving inverse kinematics task for a general 6DOF serial manipulator.

11. Task 2: Identification of kinematical parameters of a general 6DOF serial manipulator.

12. Task 2: Identification of kinematical parameters of a general 6DOF serial manipulator.

13. Task 2: Identification of kinematical parameters of a general 6DOF serial manipulator.

14. Presentation of solutions.

Study Objective:

The goal is do present more advanced methods of analysis and modeling of robot kinematics.

Study materials:

Reza N. Jazar: Theory of Applied Robotics: Kinematics, Dynamics, and Control. Springer, second edition, 2010.

A text book covering the geometry and kinematics of manipulators. Available in th e library of the CTU in Prague.

M. Meloun, T. Pajdla. Inverse Kinematics for a General 6R Manipulator. CTU-CMP?2013-29. 2013.

Algebraic-numeric solution to Inverse kinematic task of a 6R manipulator.

ftp://cmp.felk.cvut.cz/pub/cmp/articles/meloun/Meloun-TR-2013-29.pdf

T. Pajdla. Elements of Geometry for Robotics. 2014.

Geometry and representation of motion.

Available in PDF: cmp.felk.cvut.cz/cmp/courses/PRO/2014/Lecture/PRO-2014-Lecture.pdf

Note:
Further information:
https://cw.fel.cvut.cz/wiki/courses/pro
Time-table for winter semester 2021/2022:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomJP:B-670Pajdla T.11:00–12:30(lecture parallel1)Jugoslávských partyzánů 3roomJP:B-670Zorina K.Korotynskiy V.12:45–14:15(lecture parallel1parallel nr.101)Jugoslávských partyzánů 3
Time-table for summer semester 2021/2022:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2022-08-14
For updated information see http://bilakniha.cvut.cz/en/predmet6652306.html