# Learning Deep Robotic Skills on Riemannian manifolds

arXiv: https://arxiv.org/abs/2210.15244 · HTML: https://mlsanity.com/paper/2210.15244/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2022.

## Built on by (most cited first, 5 of 5)

- [Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learning](https://mlsanity.com/paper/2310.07902/) (2023)
- [Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overview](https://mlsanity.com/paper/2403.19916/) (2024)
- [Non-parametric regression for robot learning on manifolds](https://mlsanity.com/paper/2310.19561/) (2023)
- [Imitation Learning-based Direct Visual Servoing using the Large Projection Formulation](https://mlsanity.com/paper/2406.09120/) (2024)
- [Stable Robot Motions on Manifolds: Learning Lyapunov-Constrained Neural Manifold ODEs](https://mlsanity.com/paper/2510.05707/) (2025)

## Abstract (arXiv)

In this paper, we propose RiemannianFlow, a deep generative model that allows robots to learn complex and stable skills evolving on Riemannian manifolds. Examples of Riemannian data in robotics include stiffness (symmetric and positive definite matrix (SPD)) and orientation (unit quaternion (UQ)) trajectories. For Riemannian data, unlike Euclidean ones, different dimensions are interconnected by geometric constraints which have to be properly considered during the learning process. Using distance preserving mappings, our approach transfers the data between their original manifold and the tangent space, realizing the removing and re-fulfilling of the geometric constraints. This allows to extend existing frameworks to learn stable skills from Riemannian data while guaranteeing the stability of the learning results. The ability of RiemannianFlow to learn various data patterns and the stability of the learned models are experimentally shown on a dataset of manifold motions. Further, we analyze from different perspectives the robustness of the model with different hyperparameter combinations. It turns out that the model's stability is not affected by different hyperparameters, a proper combination of the hyperparameters leads to a significant improvement (up to 27.6%) of the model accuracy. Last, we show the effectiveness of RiemannianFlow in a real peg-in-hole (PiH) task where we need to generate stable and consistent position and orientation trajectories for the robot starting from different initial poses.