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arXiv 2203.03374cs.ROcs.SYeess.SY

几何感知动态运动原语的统一表述

A Unified Formulation of Geometry-aware Dynamic Movement Primitives

Mondragon Unibertsitatea(蒙德拉贡大学);University of Trento(特伦托大学);Aalto University(阿尔托大学)

Fares J. Abu-Dakka, Matteo Saveriano, Ville Kyrki

AI总结:

本文提出一种基于黎曼几何的数学框架,使动态运动原语(DMPs)能够正确嵌入几何约束,从而处理单位四元数和对称正定矩阵等非欧几里得数据,并在仿真和真实机器人实验中验证了其收敛性和目标变更特性。

摘要:

从演示中学习(LfD)被认为是一种将人类技能迁移到机器人的有效方式。传统上,LfD已被用于从人类演示中迁移笛卡尔和关节位置以及力。传统方法对某些机器人任务效果良好,但对于许多感兴趣的任务,有必要学习具有特定几何特征的技能,如方向、阻抗和/或可操作性。只有考虑到技能流形的底层几何结构,并在学习和执行过程中满足由该结构产生的约束,才能有效编码此类技能。然而,典型的学习技能模型,如动态运动原语(DMPs),仅限于欧几里得数据,无法正确嵌入具有几何约束的量。在本文中,我们提出了一个新颖且在数学上严谨的框架,该框架使用黎曼几何的概念来允许DMPs正确嵌入几何约束。由此产生的DMP表述可以处理从任何黎曼流形采样的数据,包括但不限于单位四元数以及对称正定矩阵。所提出的方法已在模拟数据和真实机器人实验中进行了广泛评估。所进行的评估表明,DMPs的有益特性,例如收敛到给定目标以及在操作过程中改变目标的可能性,同样适用于所提出的表述。

英文摘要:

Learning from demonstration (LfD) is considered as an efficient way to transfer skills from humans to robots. Traditionally, LfD has been used to transfer Cartesian and joint positions and forces from human demonstrations. The traditional approach works well for some robotic tasks, but for many tasks of interest, it is necessary to learn skills such as orientation, impedance, and/or manipulability that have specific geometric characteristics. An effective encoding of such skills can be only achieved if the underlying geometric structure of the skill manifold is considered and the constrains arising from this structure are fulfilled during both learning and execution. However, typical learned skill models such as dynamic movement primitives (DMPs) are limited to Euclidean data and fail in correctly embedding quantities with geometric constraints. In this paper, we propose a novel and mathematically principled framework that uses concepts from Riemannian geometry to allow DMPs to properly embed geometric constrains. The resulting DMP formulation can deal with data sampled from any Riemannian manifold including, but not limited to, unit quaternions and symmetric and positive definite matrices. The proposed approach has been extensively evaluated both on simulated data and real robot experiments. The performed evaluation demonstrates that beneficial properties of DMPs, such as convergence to a given goal and the possibility to change the goal during operation, apply also to the proposed formulation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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