Syllabus
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. The course may not be taught every academic year, it will be taught at least once every two years.
Annotation
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.