Geometry and Topology in Robotics: Learning, Optimization, Planning, and Control

Robots operate in environments that are often unstructured, dynamic and uncertain; yet, they still feature a form of latent mathematical structure. For instance, several physical quantities such as rigid-body orientations or inertia tensors feature specific geometric characteristics. Moreover, real-world tasks such as navigation in crowds, or object manipulation feature topological attributes.

For robots entering complex environments with limited computational and sensing resources, exploiting this latent geometric or topological structure is a crucial paradigm for enabling robust and safe performance. This elevates the study of geometric and topological methods, representations and tools to a research thread of major significance for robotics. In fact, several important advances in robotics over the past few decades drew from Riemannian geometry, Lie algebras, or algebraic and differential topology. Such abstractions offer a variety of benefits that can expand the potential of existing tools from machine learning, optimization, and control. Specifically, they can not only offer greater model interpretability and behavior guarantees, but enable high-level symbolic reasoning, and computational or sample efficiency gains.

Despite their benefits and promises, geometric and topological tools are often overlooked by roboticists due to their steep learning curve, the extensive mathematical background required, or simply the lack of crosstalk across the disciplines. In this workshop, we seek to raise awareness about the value of geometric and topological methods for robotics applications, and aim for an interactive exchange that will expose roboticists to relevant tools for their research, and accelerate progress in the field.

Specifically, this workshop aims to bring together:

1. Roboticists already working with topological/geometric techniques, seeking to pose new questions and present solutions to existing problems from that perspective, and/or offer associated tools.

2. Researchers broadly working with analytical and computational methods in robotics, interested in obtaining a different view about problems in the field and looking for available solutions.

3. A broader audience from different disciplines, applying topological and geometric techniques to computational problems in different fields.

Our end goal is to lay the foundations for organizing a community of researchers at the interface of topological and geometric methods, and modern robotics research.