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Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control

arXiv 2106.12782 ↗First posted 24 Jun 2021cs.RO cs.LG cs.SYcited by 37

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Abstract (arXiv)

Accurate models of robot dynamics are critical for safe and stable control and generalization to novel operational conditions. Hand-designed models, however, may be insufficiently accurate, even after careful parameter tuning. This motivates the use of machine learning techniques to approximate the robot dynamics over a training set of state-control trajectories. The dynamics of many robots, including ground, aerial, and underwater vehicles, are described in terms of their SE(3) pose and generalized velocity, and satisfy conservation of energy principles. This paper proposes a Hamiltonian formulation over the SE(3) manifold of the structure of a neural ordinary differential equation (ODE) network to approximate the dynamics of a rigid body. In contrast to a black-box ODE network, our formulation guarantees total energy conservation by construction. We develop energy shaping and damping injection control for the learned, potentially under-actuated SE(3) Hamiltonian dynamics to enable a unified approach for stabilization and trajectory tracking with various platforms, including pendulum, rigid-body, and quadrotor systems.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). Builds on 18 of its 48 references that are in the map. First posted on arXiv 24 Jun 2021.

Builds on

18 of 48 references.

References · 18

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 748
  3. 2019Hamiltonian Neural Networkscited by 702
  4. 2020Lagrangian Neural Networkscited by 388
  5. 2018Graph networks as learnable physics engines for inference and controlcited by 242
  6. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 205
  7. 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
  8. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 183
  9. 2019Symplectic Recurrent Neural Networkscited by 148
  10. 2019Hamiltonian Generative Networkscited by 136
  11. 2020Incorporating Symmetry into Deep Dynamics Models for Improved Generalizationcited by 123
  12. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 102
6 more
  1. 2018Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systemscited by 88
  2. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 77
  3. 2019Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systemscited by 32
  4. 2020Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanicscited by 32
  5. 2019A General Framework for Structured Learning of Mechanical Systemscited by 13
  6. 2021AutoTune: Controller Tuning for High-Speed Flightcited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 3; 2022: 9; 2023: 13; 2024: 3; 2025: 5; 2026: 4.

37 papers.

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  1. 2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 40
  2. 2022Learning Articulated Rigid Body Dynamics with Lagrangian Graph Neural Networkcited by 22
  3. 2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 17
  4. 2022Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networkscited by 17
  5. 2022Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Trackingcited by 16
  6. 2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraintscited by 15
  7. 2022Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Controlcited by 13
  8. 2021Distributed neural network control with dependability guarantees: a compositional port-Hamiltonian approachcited by 12
  9. 2023Pseudo-Hamiltonian neural networks for learning partial differential equationscited by 10
  10. 2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10
  11. 2026SkyJEPA: Learning Long-Horizon World Models for Zero-Shot Sim-to-Real Control of Quadrotorscited by 9
  12. 2022Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systemscited by 7
25 more
  1. 2023Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distributioncited by 7
  2. 2024A Riemannian Framework for Learning Reduced-order Lagrangian Dynamicscited by 7
  3. 2021Adaptive Control of SE(3) Hamiltonian Dynamics with Learned Disturbance Featurescited by 6
  4. 2022Guaranteed Conformance of Neurosymbolic Models to Natural Constraintscited by 6
  5. 2022Learning Interpretable Dynamics from Images of a Freely Rotating 3D Rigid Bodycited by 4
  6. 2023Discovering interpretable Lagrangian of dynamical systems from datacited by 3
  7. 2023Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamicscited by 3
  8. 2025Forecasting Continuous Non-Conservative Dynamical Systems in SO(3)cited by 3
  9. 2023A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from datacited by 2
  10. 2024Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approachcited by 2
  11. 2025Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approachcited by 2
  12. 2022Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltoniancited by 1
  13. 2023Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Controlcited by 1
  14. 2023Pseudo-Hamiltonian system identificationcited by 1
  15. 2023Learning Latent Dynamics via Invariant Decomposition and (Spatio-)Temporal Transformerscited by 1
  16. 2025Plug-and-Play Physics-informed Learning using Uncertainty Quantified Port-Hamiltonian Modelscited by 1
  17. 2026Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equationscited by 1
  18. 2023Node Embedding from Hamiltonian Information Propagation in Graph Neural Networkscited by 0
  19. 2023Leveraging Predictive Models for Adaptive Sampling of Spatiotemporal Fluid Processescited by 0
  20. 2023Ortho-ODE: Enhancing Robustness and of Neural ODEs against Adversarial Attackscited by 0
  21. 2024Optimal Potential Shaping on SE(3) via Neural ODEs on Lie Groupscited by 0
  22. 2025Geometric Fault-Tolerant Neural Network Tracking Control of Unknown Systems on Matrix Lie Groupscited by 0
  23. 2025A Robust Task-Level Control Architecture for Learned Dynamical Systemscited by 0
  24. 2026HYPERPOSE: Hyperbolic Kinematic Phase-Space Attention for 3D Human Pose Estimationcited by 0
  25. 2026Learning Manifold and Ito Dynamics with Branched Neural Rough Differential Equationscited by 0