The Geometry of Motion: Physics-Informed Structures for Learning and Control

Outline and Objectives

Robotic systems do not move through flat Euclidean spaces. Their motion naturally evolves on non-Euclidean manifolds, whose underlying geometric structure dictates the physics of their behavior. Rigid-body motion, robot configurations, and constrained dynamics are shaped by invariance, symmetries, and constraints—principles that lie beneath classical formulations such as Lagrangian and Hamiltonian mechanics.

At the same time, modern robotics increasingly relies on data-driven methods for motion generation, planning, and control. While these approaches have become highly expressive, they often operate on representations that ignore or distort the natural geometry of the underlying state spaces. This creates a growing gap between learning-based behavioral policies and the structured physical worlds in which robots must act.

This workshop revisits robot motion from a geometric and physics-informed perspective. We aim to explore how tools such as Lie group theory, Riemannian geometry, and geometric mechanics can be used to construct representations and algorithms that respect the structure of robotic systems. By explicitly encoding geometry and physics, we seek to promote data-efficient learning, improved generalization, greater robustness, interpretability, and safety.

Specifically, this workshop aims to bring together:

1. Researchers and practitioners in robot learning and control interested in incorporating physical and geometric structure into their methods.

2. Researchers in geometric robotics, applied mathematics, and physics-informed machine learning seeking connections between theoretical tools and practical robotic algorithms.

3. A broader community interested in motion representation, generation, planning, and decision-making for next-generation robotic systems.

Our goal is to foster cross-fertilization between these communities and outline a research agenda in which geometry and physics are not treated as afterthoughts, but as central organizing principles for robotic motion learning and control.