Advanced robot kinematics
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| BE3M33PKR | Z,ZK | 6 | 2P+2C | English |
- Relations:
- It is not possible to register for the course BE3M33PKR if the student is concurrently registered for or has already completed the course B3M33PKR (mutually exclusive courses).
- During a review of study plans, the course B3M33PKR can be substituted for the course BE3M33PKR.
- During a review of study plans, the course B3M33PRO can be substituted for the course BE3M33PKR.
- It is not possible to register for the course BE3M33PKR if the student is concurrently registered for or has already completed the course B3M33PRO (mutually exclusive courses).
- During a review of study plans, the course BE3M33PRO can be substituted for the course BE3M33PKR.
- It is not possible to register for the course BE3M33PKR if the student is concurrently registered for or has already completed the course BE3M33PRO (mutually exclusive courses).
- It is not possible to register for the course BE3M33PKR if the student is concurrently registered for or has previously completed the course B3M33PKR (mutually exclusive courses).
- It is not possible to register for the course BE3M33PKR if the student is concurrently registered for or has previously completed the course B3M33PRO (mutually exclusive courses).
- It is not possible to register for the course BE3M33PKR if the student is concurrently registered for or has previously completed the course BE3M33PRO (mutually exclusive courses).
- Course guarantor:
- Tomáš Pajdla
- Lecturer:
- Tomáš Pajdla
- Tutor:
- Tomáš Pajdla
- Supervisor:
- Department of Cybernetics
- Synopsis:
-
The course will explain and demonstrate theoretical and computational methods for describing and analyzing the kinematics of industrial robots, the principles of representing spatial motionrotation matrices, quaternions, Euler vectors, and Cayley parametrizationand robot description using the DenavitHartenberg convention for the kinematic analysis of manipulators. The main topics will be: a) solving the inverse kinematics problem for a general 6-DOF serial manipulator, and b) analyzing its singularities. The fundamental theoretical and computational tools will be linear and polynomial algebra, as well as methods of computational algebraic geometry. The theoretical techniques will be verified through implementation tasks using simulations. The course is theoretical and suitable for students interested in mathematics and interested in pursuing an academic career.
- Requirements:
-
B0B01LAG Linear algebra, B3B33ROB1 Robotics
- Syllabus of lectures:
-
1. Algebraic equations and eigenvalues of a matrix, Test A
2. Motion as a coordinate transformation, rotation matrices, axis, and angle of rotation
3. Parametrization of rotation: axisangle, quaternions, Cayley parametrization, rational rotations
4. DenavitHartenberg convention for a serial manipulator
5. Test 1
6. Rings, varieties, ideals
7. Monomial ordering, polynomial division
8. Gröbner bases
9. Buchbergers algorithm
10. Test 2
11. Algebraic solution of the inverse kinematics problem for a general 6R serial manipulator I
12. Algebraic solution of the inverse kinematics problem for a general 6R serial manipulator II
13. Kinematic singularities of a manipulator I
14. Test 3
- Syllabus of tutorials:
- Study Objective:
-
The aim of the course is to introduce methods for analyzing and modeling robot kinematics based on algebraic geometry.
- Study materials:
-
Reza N. Jazar: Theory of Applied Robotics: Kinematics, Dynamics, and Control. Springer, second edition, 2010. A textbook covering the geometry and kinematics of manipulators. Available in the CTU library.
M. Meloun, T. Pajdla. Inverse Kinematics for a General 6R Manipulator. CTU-CMP 2013-29. 2013. An algebraic-numerical solution of the inverse kinematics problem for a 6R manipulator.
ftp://cmp.felk.cvut.cz/pub/cmp/articles/meloun/Meloun-TR-2013-29.pdf
T. Pajdla. Elements of Geometry for Robotics. 2025. Geometry and representation of motion.
Available as a PDF: https://cw.fel.cvut.cz/b251/_media/courses/pkr/pkr-lecture-2025-09-20.pdf
- Note:
- Further information:
- https://cw.fel.cvut.cz/wiki/courses/pkr
- Time-table for winter semester 2025/2026:
-
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
Mon Tue Wed Thu Fri - Time-table for summer semester 2025/2026:
- Time-table is not available yet
- The course is a part of the following study plans:
-
- Cybernetics and Robotics (compulsory elective course)