Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Control

TL;DR

This paper reviews how Riemannian geometry and Gaussian probabilistic models can enhance robot learning and adaptive control, highlighting applications, techniques, and future research directions.

Contribution

It provides a comprehensive overview of Gaussian methods on Riemannian manifolds and their applications in robotics, including new potential manifolds and techniques.

Findings

Gaussian techniques enable improved clustering and regression in robot learning.

Applications demonstrated include prosthetic control and underwater robot teleoperation.

Future research directions are identified for expanding manifold-based methods.

Abstract

This article presents an overview of robot learning and adaptive control applications that can benefit from a joint use of Riemannian geometry and probabilistic representations. The roles of Riemannian manifolds, geodesics and parallel transport in robotics are first discussed. Several forms of manifolds already employed in robotics are then presented, by also listing manifolds that have been underexploited but that have potentials in future robot learning applications. A varied range of techniques employing Gaussian distributions on Riemannian manifolds is then introduced, including clustering, regression, information fusion, planning and control problems. Two examples of applications are presented, involving the control of a prosthetic hand from surface electromyography (sEMG) data, and the teleoperation of a bimanual underwater robot. Further perspectives are finally discussed, with suggestions of promising research directions.