mlsanityData to 7 Oct 2026

Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems

arXiv 2005.13143 ↗First posted 27 May 2020cs.RO cs.LG cs.SYcited by 32

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Abstract (arXiv)

Robotic tasks often require motions with complex geometric structures. We present an approach to learn such motions from a limited number of human demonstrations by exploiting the regularity properties of human motions e.g. stability, smoothness, and boundedness. The complex motions are encoded as rollouts of a stable dynamical system, which, under a change of coordinates defined by a diffeomorphism, is equivalent to a simple, hand-specified dynamical system. As an immediate result of using diffeomorphisms, the stability property of the hand-specified dynamical system directly carry over to the learned dynamical system. Inspired by recent works in density estimation, we propose to represent the diffeomorphism as a composition of simple parameterized diffeomorphisms. Additional structure is imposed to provide guarantees on the smoothness of the generated motions. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.

Key facts. Cited by 32 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 May 2020.

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Citing papers per year: 2021: 5; 2022: 3; 2023: 3; 2024: 12; 2025: 8; 2026: 1.

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  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. 2021Learning Stable Vector Fields on Lie Groupscited by 12
  7. 2021Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memorycited by 11
  8. 2024Learning Neural Contracting Dynamics: Extended Linearization and Global Guaranteescited by 11
  9. 2021Robot Skill Adaptation via Soft Actor-Critic Gaussian Mixture Modelscited by 9
  10. 2021RMP2: A Structured Composable Policy Class for Robot Learningcited by 8
  11. 2022Reactive Motion Generation on Learned Riemannian Manifoldscited by 6
  12. 2023Unraveling the Single Tangent Space Fallacy: An Analysis and Clarification for Applying Riemannian Geometry in Robot Learningcited by 6
20 more
  1. 2025Projected Coupled Diffusion for Test-Time Constrained Joint Generationcited by 6
  2. 2024Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recoverycited by 5
  3. 2025Elastic Motion Policy: An Adaptive Dynamical System for Robust and Efficient One-Shot Imitation Learningcited by 4
  4. 2023PUMA: Deep Metric Imitation Learning for Stable Motion Primitivescited by 3
  5. 2024Globally Stable Neural Imitation Policiescited by 3
  6. 2024Fusion Dynamical Systems with Machine Learning in Imitation Learning: A Comprehensive Overviewcited by 3
  7. 2021KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Losscited by 2
  8. 2024Learning Dynamical Systems Encoding Non-Linearity within Space Curvaturecited by 2
  9. 2025Geometric Contact Flows: Contactomorphisms for Dynamics and Controlcited by 2
  10. 2022Linearization and Identification of Multiple-Attractor Dynamical Systems through Laplacian Eigenmapscited by 1
  11. 2023Learning Orbitally Stable Systems for Diagrammatically Teachingcited by 1
  12. 2024Single-Shot Learning of Stable Dynamical Systems for Long-Horizon Manipulation Taskscited by 1
  13. 2024Extended Neural Contractive Dynamical Systems: On Multiple Tasks and Riemannian Safety Regionscited by 1
  14. 2025Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representationscited by 1
  15. 2025KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planningcited by 1
  16. 2024Learning to Represent Surroundings, Anticipate Motion and Take Informed Actions in Unstructured Environmentscited by 0
  17. 2025TamedPUMA: safe and stable imitation learning with geometric fabricscited by 0
  18. 2025Learning Geometrically-Informed Lyapunov Functions with Deep Diffeomorphic RBF Networkscited by 0
  19. 2025A Robust Task-Level Control Architecture for Learned Dynamical Systemscited by 0
  20. 2026Let the Dynamics Flow: Stable Flow Matching Dynamical Systemscited by 0