# Port-Hamiltonian Neural ODE Networks on Lie Groups For Robot Dynamics Learning and Control

arXiv: https://arxiv.org/abs/2401.09520 · HTML: https://mlsanity.com/paper/2401.09520/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2024.

## Built on by (most cited first, 12 of 12)

- [Landing with the Score: Riemannian Optimization through Denoising](https://mlsanity.com/paper/2509.23357/) (2025)
- [Morphological-Symmetry-Equivariant Heterogeneous Graph Neural Network for Robotic Dynamics Learning](https://mlsanity.com/paper/2412.01297/) (2024)
- [Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networks](https://mlsanity.com/paper/2412.11215/) (2024)
- [Context-Aware Deep Lagrangian Networks for Model Predictive Control](https://mlsanity.com/paper/2506.15249/) (2025)
- [Learning Physical Systems: Symplectification via Gauge Fixing in Dirac Structures](https://mlsanity.com/paper/2506.18812/) (2025)
- [Frequency-Separable Hamiltonian Neural Network for Multi-Timescale Dynamics](https://mlsanity.com/paper/2603.06354/) (2026)
- [NN-OpInf: an operator inference approach using structure-preserving composable neural networks](https://mlsanity.com/paper/2603.08488/) (2026)
- [Optimal Potential Shaping on SE(3) via Neural ODEs on Lie Groups](https://mlsanity.com/paper/2401.15107/) (2024)
- [On the Generalization of Data-Assisted Control in port-Hamiltonian Systems (DAC-pH)](https://mlsanity.com/paper/2506.07079/) (2025)
- [SSP: Safety-guaranteed Surgical Policy via Joint Optimization of Behavioral and Spatial Constraints](https://mlsanity.com/paper/2603.07032/) (2026)
- [Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems](https://mlsanity.com/paper/2604.13297/) (2026)
- [Co-Learning Port-Hamiltonian Systems and Optimal Energy-Shaping Control](https://mlsanity.com/paper/2604.26172/) (2026)

## 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 are described in terms of their generalized coordinates on a matrix Lie group, e.g. on SE(3) for ground, aerial, and underwater vehicles, and generalized velocity, and satisfy conservation of energy principles. This paper proposes a port-Hamiltonian formulation over a Lie group of the structure of a neural ordinary differential equation (ODE) network to approximate the robot dynamics. In contrast to a black-box ODE network, our formulation embeds energy conservation principle and Lie group's constraints in the dynamics model and explicitly accounts for energy-dissipation effect such as friction and drag forces in the dynamics model. We develop energy shaping and damping injection control for the learned, potentially under-actuated Hamiltonian dynamics to enable a unified approach for stabilization and trajectory tracking with various robot platforms.