mlsanityData to 7 Oct 2026

Learning Stable Vector Fields on Lie Groups

arXiv 2110.11774 ↗First posted 22 Oct 2021cs.RO cs.LGcited by 12

Not on the map. Why?

Abstract (arXiv)

Learning robot motions from demonstration requires models able to specify vector fields for the full robot pose when the task is defined in operational space. Recent advances in reactive motion generation have shown that learning adaptive, reactive, smooth, and stable vector fields is possible. However, these approaches define vector fields on a flat Euclidean manifold, while representing vector fields for orientations requires modeling the dynamics in non-Euclidean manifolds, such as Lie Groups. In this paper, we present a novel vector field model that can guarantee most of the properties of previous approaches i.e., stability, smoothness, and reactivity beyond the Euclidean space. In the experimental evaluation, we show the performance of our proposed vector field model to learn stable vector fields for full robot poses as SE(2) and SE(3) in both simulated and real robotics tasks.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 19 of its 44 references that are in the map. First posted on arXiv 22 Oct 2021.

Builds on

19 of 44 references.

References · 19

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7 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 6; 2025: 1; 2026: 1.

12 papers.

  1. 2024Riemannian Flow Matching Policy for Robot Motion Learningcited by 61
  2. 2024Deep Generative Models in Robotics: A Survey on Learning from Multimodal Demonstrationscited by 35
  3. 2024Fast and Robust Visuomotor Riemannian Flow Matching Policycited by 18
  4. 2022Learning Riemannian Stable Dynamical Systems via Diffeomorphismscited by 17
  5. 2024Neural Contractive Dynamical Systemscited by 14
  6. 2023Task Generalization with Stability Guarantees via Elastic Dynamical System Motion Policiescited by 10
  7. 2023Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learningcited by 6
  8. 2025Riemann2: Learning Riemannian Submanifolds from Riemannian Datacited by 5
  9. 2023PUMA: Deep Metric Imitation Learning for Stable Motion Primitivescited by 3
  10. 2024Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overviewcited by 3
  11. 2024Extended Neural Contractive Dynamical Systems: On Multiple Tasks and Riemannian Safety Regionscited by 1
  12. 2026Let the Dynamics Flow: Stable Flow Matching Dynamical Systemscited by 0