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Course, academic year 2018/2019
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Geometric Problems in Robotics - NMMB442
Title in English: Geometrické problémy v robotice
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2018
Semester: summer
E-Credits: 6
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Guarantor: doc. Ing. Tomáš Pajdla, Ph.D.
Class: 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.
Literature -
Last update: T_KA (30.04.2015)

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

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.

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