# Reactive Motion Generation on Learned Riemannian Manifolds

**Authors:** Hadi Beik-Mohammadi, Søren Hauberg, Georgios Arvanitidis, Gerhard Neumann, Leonel Rozo  
**arXiv:** [2203.07761](https://arxiv.org/abs/2203.07761)  
**Date:** 2022-03-15  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2203.07761v1/

## Key points

- Significant advancements in motion learning for robots
- Methods capture relevant patterns and adapt to dynamic obstacles or changing targets
- Robot motion learning from a Riemannian manifold perspective
- Geodesics represent natural motion skills learned through human demonstrations
- Use of a novel variational autoencoder (VAE) to generate geodesics for full-pose end-effector states and joint space configurations
- Technique for on-the-fly obstacle avoidance by reshaping the learned manifold using an obstacle-aware ambient metric
- Testing on a 7-degree-of-freedom robotic manipulator demonstrated capability to learn and generate complex motion skills based on human operator demonstrations
- Successful generation of multiple-solution tasks using geodesics
- Potential of leveraging Riemannian manifolds for reactive motion generation in robotics

## Summary

Significant advancements have been made in motion learning, allowing robots to acquire new skills and adapt to various conditions in structured and unstructured environments. These methods capture relevant patterns and adjust them for dynamic obstacles or changing targets. This paper explores robot motion learning from a Riemannian manifold perspective, proposing that these manifolds can be learned through human demonstrations where geodesics represent natural motion skills. A novel variational autoencoder (VAE) is used to generate these geodesics, specifically tailored to recover full-pose end-effector states and joint space configurations. Additionally, the authors introduce a technique for on-the-fly obstacle avoidance by reshaping the learned manifold using an obstacle-aware ambient metric. The effectiveness of this approach was extensively tested on a 7-degree-of-freedom robotic manipulator, demonstrating its capability to learn and generate complex motion skills based on intricate patterns demonstrated by a human operator. Multiple-solution tasks were also successfully generated using these geodesics. This study highlights the potential of leveraging Riemannian manifolds for reactive motion generation in robotics, showcasing promising avenues for future research and development in this domain.