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Seminar "Differential Geometry and Robotics" (Summer Semester 2023)

For the assignment of the talks, we will meet on Wednesday, February 15th, at 11:30 a.m. in seminar room -1.015 (UG) of the math building (20.30).
The seminar poster can be found here.

Seminar: Wednesday 11:30-13:00 SR -1.009

The seminar shall provide an introduction into the mathematical modelling of robot motions. Specifically, differential geometric and algebraic methods of Lie group and Lie algebra theory are used to describe the kinematics of robot arms. At the heart of our investigation lies the group of rigid body motions in three-space \operatorname{SE}(3). This is the group of orientation preserving motions that keep the Euclidean distance fixed. Besides its group structure, the motion group
                  \operatorname{SE}(3)=\operatorname{SO}(3)\ltimes \mathbb{R}^3
also has the structure of a differentiable manifold. Both structures are compatible which makes \operatorname{SE}(3) a Lie group. The aim of the seminar is to analyse the group \operatorname{SE}(3)
and to discuss its applications in theoretical robotics. During the seminar we will develop necessary foundations from the areas of Lie groups, representation theory, quadrics and Clifford algebras. In this sense, the discussed contents are also of interest for a larger mathematical audience outside of robotics.

The courses 'Analysis I,II,III', 'Linear Algebra I, II', 'Elemantare Geometrie'.
The seminar is suitable for advanced Bachelor students and Master students. Basic notions of differential geometry are needed, but the seminar can also be attended in parallel to the differential geometry lecture.

Our main source will be J.M. Selig: Geometric Fundamentals of Robotics