Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Control
This is an incremental review that synthesizes existing methods for robotics applications, without introducing new results.
The paper provides an overview of how Gaussian distributions on Riemannian manifolds can be applied to robot learning and adaptive control, including techniques like clustering and regression, with examples in prosthetic hand control and underwater robot teleoperation.
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.