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

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 discussed, and several forms of manifolds already employed in robotics are explained. A varied range of techniques employing Gaussian distributions on Riemannian manifolds is then introduced, and two example applications are presented, involving the control of a prosthetic hand from surface electromyography (sEMG) data and the teleoperation of a bimanual underwater robot.