Ellipsoïde

Résumé

En mathématiques, et plus précisément en géométrie euclidienne, un ellipsoïde est une surface du second degré de l'espace euclidien à trois dimensions. Il fait donc partie des quadriques, avec pour caractéristique principale de ne pas posséder de point à l'infini. L'ellipsoïde admet un centre et au moins trois plans de symétrie. L'intersection d'un ellipsoïde avec un plan est une ellipse, un point ou l'ensemble vide. L'équation d'un ellipsoïde centré à l'origine d'un repère orthonormé et aligné avec les axes du repère est de la forme :{x^2 \over a^2}+{y^2 \over b^2}+{z^2 \over c^2}=1 où a, b et c, appelés demi-axes de l'ellipsoïde, sont des paramètres strictement positifs. Les ellipsoïdes dans l'histoire des sciences Depuis la fin du , les propriétés des ellipsoïdes ont fait l'objet d'intenses études par les mathématiciens et les physiciens en raison de leurs applications en physique céleste, en mécanique des fluides et

Source officielle

https://fr.wikipedia.org/wiki/Ellipso%C3%AFde

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Analysis and Transfer of Human Movement Manipulability in Industry-like Activities

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

Humans exhibit outstanding learning, planning and adaptation capabilities while performing different types of industrial tasks. Given some knowledge about the task requirements, humans are able to plan their limbs motion in anticipation of the execution of specific skills. For example, when an operator needs to drill a hole on a surface, the posture of her limbs varies to guarantee a stable configuration that is compatible with the drilling task specifications, e.g. exerting a force orthogonal to the surface. Therefore, we are interested in analyzing the human arms motion patterns in industrial activities. To do so, we build our analysis on the so-called manipulability ellipsoid, which captures a posture-dependent ability to perform motion and exert forces along different task directions. Through thorough analysis of the human movement manipulability, we found that the ellipsoid shape is task dependent and often provides more information about the human motion than classical manipulability indices. Moreover, we show how manipulability patterns can be transferred to robots by learning a probabilistic model and employing a manipulability tracking controller that acts on the task planning and execution according to predefined control hierarchies.

IEEE2020

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Humans exhibit outstanding learning and adaptation capabilities while performing various types of manipulation tasks. When learning new skills, humans are able to extract important information by observing examples of a task and efficiently refine a priori knowledge to master new tasks. However, learning does not happen in isolation, and the planning and control abilities of humans also play a crucial role to properly execute manipulation tasks of varying complexity. In the last years, a lot of attention has been devoted to the problem of providing robots with close-to-human-level abilities. In this context, this thesis proposes to enhance robot learning and control capabilities by introducing domain knowledge into the corresponding models. Our approaches, built on Riemannian manifolds, exploit the geometry of non-Euclidean spaces, which are ubiquitous in robotics to represent rigid-body orientations, inertia matrices, manipulability ellipsoids, or controller gain matrices. We initially consider the problem of transferring skills to a robot and propose a probabilistic framework to learn symmetric positive definite (SPD) matrices from demonstrations. Given a learned reference trajectory in the form of SPD matrices, the goal of the robot is to reproduce the task by tracking this sequence using appropriate controllers. This challenge is tackled in the second part of this thesis. We focus on a specific application and propose a complete geometry-aware framework to learn, control and transfer posture-dependent task requirements from humans to robots via manipulability profiles. The third part of this thesis focuses on refining the skills learned by the robot and on adapting them to new situations by introducing a geometry-aware Bayesian optimization framework. Overall, this thesis proves that geometry-awareness is crucial for successfully learning, controlling and refining non-Euclidean parameters in addition to providing a proper mathematical treatment of the different problems. Finally, the last part of this work shows that domain knowledge can be introduced not only through geometry-awareness, but also through structure-awareness, which may be considered either as prior models or as intrinsically present in the data. With its final part, this thesis emphasizes that domain knowledge, that can be introduced into robot learning algorithms through various means, may be significant for providing robots with close-to-humans abilities.

EPFL2020

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Geometry-aware Manipulability Learning, Tracking and Transfer

Sylvain Calinon, Noémie Laure Gwendoline Jaquier

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.

Sage2020

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EPFL2020