## Geometric Algebra for Robotics

### The PhD School at the Faculty of Engineering at 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: November 2024

Offered in: Odense

**Prerequisites**

It is recommended that students participating in the course have:

- Significant experience in robotics
- 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 November 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