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 \emph{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.

中文翻译：

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几何感知可操作性学习、跟踪和转移

身体姿势会影响人类和机器人在操作任务中的表现，因为适当的姿势会促进沿不同轴的运动或力的施加。在机器人技术中，可操纵性椭球作为一种强大的描述符出现，用于分析、控制和设计作为关节配置的函数的机器人灵巧性。该描述符可以根据不同的任务要求进行设计，例如跟踪所需的位置或施加特定的力。在此背景下，本文提出了一种新颖的 \emph {manipulability transfer} 框架，这是一种允许机器人从专家演示中学习和再现可操纵性椭球的方法。所提出的学习方案建立在高斯混合模型的基于张量的公式之上，该模型考虑到可操纵性椭球位于对称正定矩阵的流形上。学习与几何感知跟踪控制器相结合，使机器人能够遵循所需的可操纵性椭球轮廓。使用冗余机械手、机械手和类人机器人进行的大量仿真评估以及两个真实双臂系统的实验验证了该方法的可行性。