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Course, academic year 2023/2024
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Geometric Problems in Robotics - NMMB442
Title: Geometrické problémy v robotice
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: winter
E-Credits: 6
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. Ing. Tomáš Pajdla, Ph.D.
Class: M Mgr. MMIB
M Mgr. MMIB > Povinně volitelné
Classification: Mathematics > Geometry
Annotation -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (14.05.2019)
We will explain some fundamental notions appearing in advanced robotics. We shall, e.g., learn how to solve the inverse kinematics task of a general serial manipulator with 6 degrees of freedom. There is a general solution to this problem but it can't easily be obtained by elementary methods. We shall present some more advanced algebraic tools for solving algebraic equations. We will also pay special attention to representing and parameterizing rotations and motions in 3D space. We will solve simulated problems as well as problems with real data in labs and assignments.
Course completion requirements - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (11.06.2019)

Předmět je zakončen ústní zkouškou.

Literature -
Last update: T_KA (30.04.2015)

H. Asada, J.-J. E. Slotine. Robot Analysis and Control. Wiley-Interscience, 1986

Requirements to the exam - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (11.06.2019)

Zkouška má ústní formu. Její požadavky odpovídají obsahu přednesené látky.

Syllabus -
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (14.05.2019)

1. Introduction, algebraic equations and eigenvalues

2. Motion: Motion as a transformation of coordinates

3. Kinematics: Denavit-Hartenberg convention for a manipulator

4. Solving algebraic equations

5. Motion axis and the rotation matrix

6. Inverse kinematic task of a general 6R serial manipulator I 7. Inverse kinematic task of a general 6R serial manipulator II

8. Rotation reprezentation and parameterization

9. Angle-axis parameterization

10. Quaternions

11. Manipulator calibration

12. Summary and review.

The course may not be taught every academic year, it will be taught at least once every two years.

 
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