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 discussed, and several forms of manifolds already employed in robotics are explained. A varied range of techniques employing Gaussian distributions on Riemannian manifolds is then introduced, and two example applications are presented, involving the control of a prosthetic hand from surface electromyography (sEMG) data and the teleoperation of a bimanual underwater robot.

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，它们可以从黎曼几何和概率表示的联合使用中受益。讨论了黎曼流形，测地学和并行传输在机器人技术中的作用，并解释了已经在机器人技术中采用的几种形式的歧管。然后介绍了在黎曼流形上采用高斯分布的各种技术，并给出了两个示例应用程序，包括通过表面肌电图（sEMG）数据控制假手和双手水下机器人的遥控操作。