Geometric Representations

The Roles of Modern Screw Theory, Lie algebra, and Geometric Algebra in Robotics

Overview

The scope and goal of the proposed workshop is to focus on geometric algebra, differential geometry, and related methods and applications of geometric tools to robotics. Although the theoretical origins of these tools can be traced back to Descartes’s introduction of coordinated systems, Ball’s designs of screws motion, and Clifford’s and Study’s studies (pun intended), contemporary applications have changed drastically. Indeed, screw theory along with its multifarious manifestations such as Plücker coordinates and unit dual quaternions, coupled with Riemannian geometry and Lie algebra, have re-emerged and become fundamental in the shaping and formalization of the latest problems in robot mechanics, multi-body dynamics, mechanical design, robot control, optimization and robot learning. 

The overall theme of the workshop is aligned with multiple fields of robotics research and aims to build a roadmap towards a sound and unified theoretical basis for addressing elaborated robotics problems, scaling and leveraging data-driven methods from Euclidean domains to proper geometric groups, and improving overall human-robot co-existence through geometric methods and tools. Furthermore, recent studies which will be presented by selected keynote speakers have shown that the exploitation of geometric properties within Lie groups and Riemannian manifolds has led to better exploration of the human-environment. The results to be presented in this event as well as the theoretical machinery plays an important role in making robots that can operate around humans (ICRA 2023 theme).

In this context, the main objective of this full-day workshop is to stimulate and revisit the latest developments and applications concerning algebraic and differential geometry concepts, and to understand how models, algorithms and data-driven methods initially developed for Euclidean spaces can be further extended to special geometric groups. We also expect this workshop to be instrumental in inspiring the junior researchers in the community to understand and include these fundamental geometrical concepts, paving the foundation for new applications, and reinforcing the cross-pollination and exchange of ideas between stakeholders, researchers and practitioners within our increasingly thriving community.  

Invited Speakers

Given our list of selected speakers, we believe that our workshop is uniquely positioned to bring together researchers from different applied fields of robotics research with geometers and researchers of core robotics' methods.

Organizers

Contact

Dr. Luis Figueredo
luis.figueredo@tum.de 

Note: For further information, please contact the organizers or the corresponding organizers