This 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 first discussed. Several forms of manifolds already employed in robotics are then presented, by also listing manifolds that have been underexploited but that have potentials in future robot learning applications. A varied range of techniques employing Gaussian distributions on Riemannian manifolds is then introduced, including clustering, regression, information fusion, planning and control problems. Two examples of applications are presented, involving the control of a prosthetic hand from surface electromyography (sEMG) data, and the teleoperation of a bimanual underwater robot. Further perspectives are finally discussed, with suggestions of promising research directions.

中文翻译：

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黎曼流形上的高斯：机器人学习和自适应控制的应用

本文概述了机器人学习和自适应控制应用程序，这些应用程序可以从黎曼几何和概率表示的联合使用中受益。首先讨论黎曼流形、测地线和平行传输在机器人技术中的作用。然后通过列出尚未充分利用但在未来机器人学习应用中具有潜力的流形，介绍了机器人技术中已经采用的几种形式的流形。然后介绍了在黎曼流形上采用高斯分布的各种技术，包括聚类、回归、信息融合、规划和控制问题。介绍了两个应用示例，涉及从表面肌电图 (sEMG) 数据控制假手，以及双手水下机器人的遥控操作。