PKR − Advanced Robot Kinematics

,,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., explain 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 in assignments.

Course material: PKR-Lecture-2021.pdf.

Lecturers: Tomáš Pajdla

Teachers: Viktor Korotynskiy, Kateryna Zorina

See Labs for details.

1. All homework must be submitted via BRUTE and accepted.
2. At least 50% of points in total for the homework.
3. At least 50% of points in total from the tests.
4. Regular submission of homeworks ends on January 14, 2024. Later submissions are possible only by an agreement with the assistants.

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. The grade depends on the exam (40%), tests (30%), and homework (30%). You may skip the oral exam if you are satisfied with the result after the written exam.

Exam content:

1. Linear algebra [7,8,9,10]: 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, SVD, dual space, and dual basis.
2. - Course material: PKR-Lecture-2021.pdf.

Written In-Person exam organization:

1. The written exam is sat in a classroom.
2. You may NOT use any prepared material.

Oral exam organization:

1. You may skip the oral exam if you are satisfied with the result after the written exam.
2. The face-to-face oral exam will be done online via MS Teams and will take about 30 mins.

1. Lecture: It is very difficult to pass the course without attending lectures.
2. Labs: It is impossible to pass the course without attending labs.
3. Homework: Homework is assigned at a lab where it can be discussed with teaching assistants. Students work out homework individually (rulesin Czech). The deadline for submitting homework via BRUTE is on Monday at 6:00 in the morning two weeks after the assignment. Late submissions are penalized (10% for each commenced day of delay but not more than 50% of points).
4. Assessment: see above.
5. Tests: Students work out test independently.

1. PKR-Lecture-2021.pdf

1. Basic algebra (Groups, Rings, Ideals, Fields, Vector spaces) in 33 simple videos @ Socratica
2. Northwestern University Coursera Course Modern Robotics
3. Stanford cs223a Introduction to Robotics
4. Math Doctor Bob. Math Instruction Online. In Plain Language.
5. Lung-Wen Tsai. Robot Analysis And Design: The Mechanics of Serial And Parallel Manipulators, John Wiley and Sons, 1999.
6. G Sanderson Essence of Linear Algebra from 3Blue1Brown
7. J Strom, K Astrom, T Akenine-Moller Interactive Linear Algebra Course
8. P Pták. Introduction to Linear Algebra. Vydavatelství ČVUT, Praha, 2007.
9. E Krajník. Maticový počet. Vydavatelství ČVUT, Praha, 2000.
10. D Cox, J Little, D O'Shea. Ideals, Varieties, and Algorithms. 2nd edition, Springer, 1998.
11. B Sturmfels. Polynomials, Ideals, and Grobner Bases
12. M Michalek, B Sturmfels. Invitation to Nonlinear Algebra
13. B Sturmfels. Inroduction to Groebner bases youtube

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