# Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Control

arXiv: https://arxiv.org/abs/1909.05946 · HTML: https://mlsanity.com/paper/1909.05946/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2019.

## Built on by (most cited first, 17 of 17)

- [The Exact Sample Complexity Gain from Invariances for Kernel Regression](https://mlsanity.com/paper/2303.14269/) (2023)
- [Graph Neural Networks on SPD Manifolds for Motor Imagery Classification: A Perspective from the Time-Frequency Analysis](https://mlsanity.com/paper/2211.02641/) (2022)
- [The Gaussian kernel on the circle and spaces that admit isometric embeddings of the circle](https://mlsanity.com/paper/2302.10623/) (2023)
- [Elastic Motion Policy: An Adaptive Dynamical System for Robust and Efficient One-Shot Imitation Learning](https://mlsanity.com/paper/2503.08029/) (2025)
- [GraffMatch: Global Matching of 3D Lines and Planes for Wide Baseline LiDAR Registration](https://mlsanity.com/paper/2212.12745/) (2022)
- [Gaussian kernels on non-simply-connected closed Riemannian manifolds are never positive definite](https://mlsanity.com/paper/2303.06558/) (2023)
- [Geometric Learning with Positively Decomposable Kernels](https://mlsanity.com/paper/2310.13821/) (2023)
- [High-Dimensional Bayesian Optimization via Random Projection of Manifold Subspaces](https://mlsanity.com/paper/2412.16554/) (2024)
- [Reasoning and Learning a Perceptual Metric for Self-Training of Reflective Objects in Bin-Picking with a Low-cost Camera](https://mlsanity.com/paper/2503.20207/) (2025)
- [A Structured Prediction Approach for Robot Imitation Learning](https://mlsanity.com/paper/2309.14829/) (2023)
- [A survey of manifold learning and its applications for multimedia](https://mlsanity.com/paper/2310.12986/) (2023)
- [Microstructure-based Variational Neural Networks for Robust Uncertainty Quantification in Materials Digital Twins](https://mlsanity.com/paper/2512.18104/) (2025)
- [Imitation of Manipulation Skills Using Multiple Geometries](https://mlsanity.com/paper/2203.01171/) (2022)
- [Non-parametric regression for robot learning on manifolds](https://mlsanity.com/paper/2310.19561/) (2023)
- [Intrinsic Gaussian Process Regression Modeling for Manifold-valued Response Variable](https://mlsanity.com/paper/2411.18989/) (2024)
- [Riemannian Time Warping: Multiple Sequence Alignment in Curved Spaces](https://mlsanity.com/paper/2506.01635/) (2025)
- [World-Task Factorization for Robot Learning](https://mlsanity.com/paper/2606.02027/) (2026)

## Abstract (arXiv)

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.