# Subject description - BE3M33PKR

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BE3M33PKR Advanced robot kinematics
Roles:PV Extent of teaching:2P+2C
Department:13133 Language of teaching:EN
Guarantors:Pajdla T. Completion:Z,ZK
Lecturers:Korotynskiy V., Pajdla T., Smutný V. Credits:6
Tutors:Korotynskiy V., Pajdla T., Zorina K. Semester:Z

Web page:

https://cw.fel.cvut.cz/wiki/courses/pkr

Anotation:

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.

Study targets:

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

Course outlines:

 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.

Exercises outline:

 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.

Literature:

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

Requirements:

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

Keywords:

robotics, kinematics, trajectory, identification, modelling

Subject is included into these academic programs:

 Program Branch Role Recommended semester MEKYR_2021 Common courses PV 1

 Page updated 3.12.2022 17:51:28, semester: L/2022-3, Z/2024-5, L/2021-2, Z/2022-3, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)