Gaussians on Riemannian Manifolds By Sylvain Calinon T his 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. Riemannian Geometry in Robotics Data encountered in robotics are characterized by simple but varied geometries that are sometimes underexploited in robot learning and adaptive control algorithms. Such data include joint angles in revolving articulations [1], rigid body motions [2], [3], unit quaternions to represent orientations ©ISTOCKPHOTO.COM/VCHAL Applications for Robot Learning and Adaptive Control Digital Object Identifier 10.1109/MRA.2020.2980548 Date of current version: 6 April 2020 1070-9932/20©2020IEEE JUNE 2020 * IEEE ROBOTICS & AUTOMATION MAGAZINE * 33http://www.ISTOCKPHOTO.COM/VCHAL