,,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.
|01||02.10.||TP: Introduction, algebraic equations and eigenvalues|
|02||09.10.||VS: Denavit-Hartenberg Convention|
|03||16.10.||TP: Motion as a transformation of coordinates, rotation matrix R|
|04||23.10.||TP: R's eigenvalues, eigenvectors, rotation axis and angle|
|05||30.10.||TP: Rodriguez parameterization, Angle-axis, Euler vector|
|06||06.11.||TP: Quaternions, Cayley parameterization, Rational rotations|
|07||13.11.||TP: Axis of motion|
|08||20.11.||TP: Monomial ordering & polynomial division|
|09||27.11.||CA: Buchberger & “F4-like” algorithms|
|10||04.12.||TP: Ideals & Multiplication matrix|
|11||11.12.||TP: Inverse kinematics computation|
|12||18.12.||TP: Kinematics calibration|
|13||08.01.||TP: Analysis of singularities|
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.