# Geometric Reinforcement Learning For Robotic Manipulation

arXiv: https://arxiv.org/abs/2210.08126 · HTML: https://mlsanity.com/paper/2210.08126/

## Key facts

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

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

- [ILBiT: Imitation Learning for Robot Using Position and Torque Information based on Bilateral Control with Transformer](https://mlsanity.com/paper/2401.16653/) (2024)
- [Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learning](https://mlsanity.com/paper/2310.07902/) (2023)
- [A Primer on SO(3) Action Representations in Deep Reinforcement Learning](https://mlsanity.com/paper/2510.11103/) (2025)
- [Reinforcement Learning with Lie Group Orientations for Robotics](https://mlsanity.com/paper/2409.11935/) (2024)
- [World-Task Factorization for Robot Learning](https://mlsanity.com/paper/2606.02027/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) is a popular technique that allows an agent to learn by trial and error while interacting with a dynamic environment. The traditional Reinforcement Learning (RL) approach has been successful in learning and predicting Euclidean robotic manipulation skills such as positions, velocities, and forces. However, in robotics, it is common to encounter non-Euclidean data such as orientation or stiffness, and failing to account for their geometric nature can negatively impact learning accuracy and performance. In this paper, to address this challenge, we propose a novel framework for RL that leverages Riemannian geometry, which we call Geometric Reinforcement Learning (G-RL), to enable agents to learn robotic manipulation skills with non-Euclidean data. Specifically, G-RL utilizes the tangent space in two ways: a tangent space for parameterization and a local tangent space for mapping to a nonEuclidean manifold. The policy is learned in the parameterization tangent space, which remains constant throughout the training. The policy is then transferred to the local tangent space via parallel transport and projected onto the non-Euclidean manifold. The local tangent space changes over time to remain within the neighborhood of the current manifold point, reducing the approximation error. Therefore, by introducing a geometrically grounded pre- and post-processing step into the traditional RL pipeline, our G-RL framework enables several model-free algorithms designed for Euclidean space to learn from non-Euclidean data without modifications. Experimental results, obtained both in simulation and on a real robot, support our hypothesis that G-RL is more accurate and converges to a better solution than approximating non-Euclidean data.