Geometric Algebra for Robotics

University of Southern Denmark

Title: Geometric Algebra for Robotics
The Maersk Mc Kinney Moller Institute, SDU Robotics
Teaching language: English
Teachers: Christoffer Sloth chsl@mmmi.sdu.dk / Inigo Iturrate inju@mmmi.sdu.dk
ECTS: 2.5 ECTS
Period: October 2024
Offered in: Odense 

Prerequisites

It is recommended that students participating in the course have:

1. Significant experience in robotics
2. Knowledge in representation of orientation (Quaternions, Euler angles etc.)
    

Content

This course gives an introduction to the application of geometric algebra in robotics, by showing the potential for using geometric algebra for modelling, learning, and control in robotics.

Geometric algebra extends elementary algebra to operate on geometric concepts such as vectors and has in recent years found applications in various engineering fields. As many robotics tasks involve geometric environmental constraints, e.g., a normality constraint to a surface, alignment to an axis, tangent motion to a circle, etc., geometric algebra is well-suited to the modelling of such tasks and can greatly simplify their mathematic formulation [1].

The course will cover the main theoretical underpinnings of geometric algebra, with a focus on conformal geometric algebra, the subset which finds most common use in engineering applications. The focus of the course will be on developing an intuitive understanding of how geometric algebra can be applied to robotics problems. As such, the approach will be practical, with emphasis on implementation and on making use of existing software libraries [2] for modelling and control of robotic manipulators.

[1] T. Löw and S. Calinon, "Geometric Algebra for Optimal Control with Applications in Manipulation Tasks," in IEEE Transactions on Robotics, vol. 39, no. 5, pp. 3586-3600, Oct. 2023, doi: 10.1109/TRO.2023.3277282.

[2] T. Löw, P. Abbet, and S. Calinon, "gafro: Geometric Algebra for Robotics." arXiv preprint arXiv:2310.19090, 2023.
 

Learning outcomes

The aim of the course is, to give the student knowledge about:

• geometric algebra

Be able to work with the following skills:

• Formulate optimization problems on manifolds
• Describe robot motion of a given manifold

And have the competences to:

• Implement robot controls for constrained motion of robot manipulators
   

Time of classes

The course will start in October 2024 and will have five sessions.

The course will last of 5 days, i.e., 40 hours.

2.5 ECTS = 67.5 h (40 h teaching, 15 h preparation, 12.5 h hand-in)

More information and registration

Via email to Christoffer Sloth (chsl@mmmi.sdu.dk) or Inigo Iturrate (inju@mmmi.sdu.dk).
Deadline: 1 week before the classes start.
 

Form of instruction

The teaching is a mixture of lectures and exercises, where the students can apply the theory in practice.
 

Examination conditions

Following is a prerequisite to attend the final project exam:

• Participation in 80 % of the classes.
   

Evaluation

Internal examination with no co-examiner based on a submitted report with solutions to problems addressed during the classes. The assessment will be pass/fail.
 

Price

No charge

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