Riemannian geometry as a unifying theory for robot motion learning and control

TL;DR

This paper advocates for using Riemannian geometry as a comprehensive framework to analyze, generate, and improve robot motion and control, especially for complex, high-degree-of-freedom systems, by leveraging its mathematical tools.

Contribution

It introduces Riemannian geometry as a unifying theoretical approach for robot motion learning and control, highlighting its potential for designing energy-efficient and coordinated movements.

Findings

Riemannian geometry offers effective tools for analyzing robot motions.

Potential to design physically meaningful motion synergies.

Framework for coupling motion with perceptual inputs.

Abstract

Riemannian geometry is a mathematical field which has been the cornerstone of revolutionary scientific discoveries such as the theory of general relativity. Despite early uses in robot design and recent applications for exploiting data with specific geometries, it mostly remains overlooked in robotics. With this blue sky paper, we argue that Riemannian geometry provides the most suitable tools to analyze and generate well-coordinated, energy-efficient motions of robots with many degrees of freedom. Via preliminary solutions and novel research directions, we discuss how Riemannian geometry may be leveraged to design and combine physically-meaningful synergies for robotics, and how this theory also opens the door to coupling motion synergies with perceptual inputs.