ARTICLE Jaquier_IJRR_2020/IDIAP Geometry-aware Manipulability Learning, Tracking and Transfer Jaquier, N. Rozo, L. Caldwell, D. G. Calinon, Sylvain differential kinematics manipulability ellipsoids programming by demonstration Riemannian manifolds robot learning EXTERNAL http://publications.idiap.ch/attachments/papers/2021/Jaquier_IJRR_2020.pdf PUBLIC International Journal of Robotic Research 40 2-3 624-650 2021 Body posture influences human and robots performance in manipulation tasks, as appropriate poses facilitate motion or force exertion along different axes. In robotics, manipulability ellipsoids arise as a powerful descriptor to analyze, control and design the robot dexterity as a function of the articulatory joint configuration. This descriptor can be designed according to different task requirements, such as tracking a desired position or apply a specific force. In this context, this paper presents a novel manipulability transfer framework, a method that allows robots to learn and reproduce manipulability ellipsoids from expert demonstrations. The proposed learning scheme is built on a tensor-based formulation of a Gaussian mixture model that takes into account that manipulability ellipsoids lie on the manifold of symmetric positive definite matrices. Learning is coupled with a geometry-aware tracking controller allowing robots to follow a desired profile of manipulability ellipsoids. Extensive evaluations in simulation with redundant manipulators, a robotic hand and humanoids agents, as well as an experiment with two real dual-arm systems validate the feasibility of the approach.