Equivariant Systems:

Whether it is improved resiliency in localization, robustness in control, or more efficient and faster learning of physical systems, the continuous enhancement of robotic systems has a long history of finding and exploring new mathematical structures tailored to the needs of these systems and their tasks. Symmetry, exploiting the tools of Lie group theory and differential geometry, has proven to be a powerful framework to analyse and improve real-world algorithms leading to significant performance gains across a range of fields such as state estimation, machine vision, AI, and control. The goal of this workshop is to provide a platform for leading researchers to advocate for this new perspective by highlighting and explaining the benefits of using symmetry as the foundation for algorithm analysis and design compared to classical methods. Viewing the world through the lens of symmetry, and exploiting invariance and equivariance properties, allows for a simpler and more holistic reexamination of classical problems.

The workshop will be structured in three parts:

1. In the first part, after an introductory tutorial on symmetry, two senior keynote speakers will deliver educational talks including state-of-the art applications on the use of equivariant systems theory in (a) state estimation and (b) control. This part will conclude with an intimate panel discussion between three senior experts in the field (disjoint from the keynote speakers). This change of protagonists on the stage will naturally foster discussions between the keynote speakers and the panelists, triggering also the audience's participation in a lively discussion.
2. The second part will feature young researchers presenting their recent findings in a poster session, sharing their journeys into this complex mathematical field.
3. The third part will consist of an educational third keynote talk on the benefit of equivariance in (c) artificial intelligence (of similar character to the first two keynote talks). A second, summarizing panel discussion with three senior experts and active audience participants will be moderated to merge the findings, questions, and challenges from all three subcommunities, thus highlighting novel avenues for the overall robotics community.

Both panel discussions will be guided by three overarching questions:

1. How can we provide an easy entry point from which to engage young scientists and other interested individuals in this mathematically demanding field (and what are the audience's experiences)?
2. What defines a good symmetry for a given problem set, and in which fields do we expect new symmetries to have the greatest impact?
3. What are the open challenges in applying equivariant theory in robotics?