Annotation Schedule Students Submission system Forum 2016(2015)(2014)(2013)(2012)

The Adobe Flash Plugin is needed to display this content.

A3M33PRO − Advanced Robotics

,,Drahá slečno Gloryová, Roboti nejsou lidé. Jsou mechanicky dokonalejší než my, mají úžasnou rozumovou inteligenci, ale nemají duši. Ó, slečno Gloryová, výrobek inženýra je technicky vytříbenější než výrobek přírody.” - Karel Čapek, R.U.R.

[“Miss Glory, robots are not people. They are mechanically much better than we are, they have an amazing ability to understand things, but they don't have a soul. Young Rossum created something much more sophisticated than Nature ever did - technically at least!”]


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.

Lecture: Monday 11:00-12:30, KN:E-127

Lecturers: Tomáš Pajdla, Čeněk Albl, Vladimír Smutný

WeekDate Content
01 03.10. TP: Introduction, algebraic equations and eigenvalues
02 10.10. VS: Denavit-Hartenberg Convention
03 17.10. TP: Motion: Motion as a transformation of coordinates, rotation matrix
04 24.10. TP: Rotation representation I: Rotation matrix, eigenvalues, eigenvectors, rotation axis
05 31.10. TP: Rotation representation II: Rotation matrix, eigenvalues, eigenvectors, rotation axis
06 07.11. TP: Rotation representation III: Angle-Axis, Euler Vector
07 14.11. TP: Axis of motion
08 21.11. TP: Solving algebraic equations I: Monomial ordering & division
09 28.11. VS: Rotation representation IV: Quaternions
10 05.12. TP: Solving algebraic equations II: Buchberger & “F4-like” algorithms
11 12.12. TP: Solving algebraic equations III: Ideals & Multiplication matrix
12 02.01. CA: Inverse kinematics by GB computation - I, IK Formulation
14 09.01. TP: Inverse kinematics by GB computation - II

Exercises: Monday 12:45-14:15 KN:E-220

Teachers: Čeněk Albl. Michal Polic

See Exercises for details.

Assesment (zápočet)

Grading (2015)

  1. All home works must be submitted and accepted (0 in the column ~HW)
  2. At least 50% of points in total from the home works (at least 0,5 in the column HW).
  3. At least 50% of points in total from the tests (at least 0,5 in the column T).
  4. Regular submission of home works ends on 09 Jan 2017. Later submissions are possible only by agreement with teaching assistants.
  5. All the above conditions have to be fulfilled and the results have to be recorded in the Submission system before coming to the exam.


The exam consists of a written and an oral part. It is required to achieve at least 50% of points from the written exam to be admitted to the oral exam.

Exam content:

  1. Linear algebra: linear space, basis, coordinates, linear dependence/independence, matrices, rank, determinant, eigenvalues and eigenvectors, solving systems of linear equations, Frobenius theorem and linear independence, linear function, affine function, linear mapping and its matrix, computing roots of a polynomial via eigenvalues of its companion matrix, dual space, dual basis, change of the dual basis corresponding to a change of a basis, vector product and derived linear mappings.
  2. Course material: PRO-2016-Lecture.pdf.


  1. Lecture: It is very difficult to pass the course without attending lectures.
  2. Exercises: It is impossible to pass the course without attending labs.
  3. Home works: Home works are assigned at a lab where they can be discussed with teaching assistants. Students work out homweorks independently (rulesin Czech). The deadline for submitting a homework is on the next Monday 6:00 in the morning. Late submissions are penalized (10% for each commenced day of delay but not more than 50% of points).
  4. Assesment: see above.
  5. Tests: Students work out test independently.
  6. The final grade: depends on the exam (40%), tests (30%), and home works (30%). The ratios may be slightly adjusted according to the relative difficulty of the home works and tests.


  1. Math Doctor Bob. Math Instruction Online. In Plain Language.
  2. Lung-Wen Tsai. Robot Analysis And Design: The Mechanics of Serial And Parallel Manipulators, John Wiley and Sons, 1999.
  3. P. Olšák. Úvod do algebry, zejména lineární. ČVUT 2007.
  4. P. Pták. Introduction to Linear Algebra. Vydavatelství ČVUT, Praha, 2007.
  5. E. Krajník. Maticový počet. Vydavatelství ČVUT, Praha, 2000.
  6. D. Cox, J. Little, D. O'Shea. Ideals, Varieties, and Algorithms. 2nd edition, Springer, 1998.
  7. Maple - A0B01MVM Matematika v Maple Maple download


  1. A0B01LAG Linear Algebra (must have)
  2. A3B33ROB Robotics (nice to have)


Tomáš PajdlaČeněk AlblMichal Polic
KN, room G 104AKN, room G 104KN, room G 104
tel. (22435) 7348tel. (22435) 5725
courses/a3m33pro/start.txt · Last modified: 2017/01/01 03:55 by pajdla